Prof. Dr. Daniel Loss


Department of Physics
University of Basel
Klingelbergstrasse 82
CH-4056 Basel, Switzerland
office:office 4.12

email:view address

tel: ++41 (0)61 267 37 49 (office)
++41 (0)61 267 37 50 (secretary)
fax:++41 (0)61 267 13 49

CV and Research Interests

Daniel Loss received a Ph.D. in Theoretical Physics at the University of Zurich in 1985 under the supervision of Prof. A. Thellung. He stayed there as postdoctoral researcher for four more years before moving to the US in 1989. From 1989 to 1991 he worked as postdoctoral researcher in the group of Prof. A. J. Leggett, Urbana, and from 1991 to 1993 at IBM Research Center, NY (USA). In 1993 he moved to Vancouver (Canada) to become Assistant and then Associate Professor of Physics at Simon Fraser University. In 1996 he returned to Switzerland to become full Professor of Theoretical Physics at the University of Basel. Loss is director of the Basel Center for Quantum Computing and Quantum Coherence (QC2), and co-director (2006) of the Swiss National Center of Competence and Research (NCCR) in Nanoscale Science at the University of Basel. He received several prestigious fellowships, is a Fellow of the American Physical Society, has been awarded the Humboldt Research Prize in 2005, and the Marcel Benoist Prize in 2010 — the most prestigious science prize in Switzerland (see, and Uni news). He is married and has two sons.

Loss's research interests include many aspects of the theory of condensed matter systems with a particular focus on spin-dependent and phase-coherent phenomena (mesoscopics) in semiconducting nanostructures and molecular magnets. A major portion of Loss's current research involves the theory of spin dynamics, spin coherence, spintronics in two-dimensional electron gases, and spin-related phenomena in semiconducting quantum dots--artificial atoms and molecules. Part of this work is related to quantum information processing (QIP)--quantum computing and quantum communication in solid state systems with focus on spin qubits, where Loss and collaborators made seminal contributions. Their theoretical predictions and proposals have stimulated many further investigations, and in particular many experimental programs on spin qubits worldwide. Current research includes spin relaxation and decoherence in quantum dots due to spin-orbit and hyperfine interaction; non-Markovian spin dynamics in bosonic and nuclear spin environments; generation and characterization of non-local entanglement with quantum dots, superconductors, Luttinger liquids or Coulomb scattering in interacting 2DEGs; spin currents in magnetic insulators and in semiconductors; spin Hall effect in disordered systems; spin orbit effects in transport and noise; asymmetric quantum shot noise in quantum dots; entanglement transfer from electron spins to photons; QIP with spin qubits in quantum dots and molecular magnets; macroscopic quantum phenomena (spin tunneling and coherence) in molecular and nanoscale magnetism.

Extended CV

Download an extended CV here.

Open Positions

We are constantly looking for outstanding, highly motivated, and enthusiastic graduate students and/or postdoctoral fellows.

PhD Candidates need to hold a Master's (or equivalent) degree in theoretical condensed matter physics. Postdoc Candidates should have a PhD in theoretical condensed matter physics.

To apply please submit the following documents per email to Prof. Daniel Loss:
  1. a curriculum vitae
  2. a list of publications
  3. your academic records (Bachelor's, Master's or PhD diploma)
  4. names of three potential referees
  5. a short statement of your research interests and how they relate to the work of our group


Show all abstracts.

1.  RKKY Interaction On Surfaces of Topological Insulators With Superconducting Proximity Effect
Alexander A. Zyuzin and Daniel Loss.

We consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities on the surface of a three-dimensional topological insulator with proximity induced superconductivity. A superconductor placed on the top of the topological insulator induces a gap in the surface electron states and gives rise to a long-ranged in-plane antiferromagnetic RKKY interaction. This interaction is frustrated due to strong spin-orbit coupling, decays as 1/r for r<ξ, where r is the distance between two magnetic impurities and ξ the superconducting coherence length, and dominates over the ferromagnetic and Dzyaloshinskii-Moriya type interactions for r>ξ. We find the condition for the Yu-Shiba-Rusinov intragap states that are bound to the magnetic impurities.

2.  Helical nuclear spin order in a strip of stripes in the Quantum Hall regime
Tobias Meng, Peter Stano (RIKEN), Jelena Klinovaja (Harvard), and Daniel Loss.

We investigate nuclear spin effects in a two-dimensional electron gas in the quantum Hall regime modeled by a weakly coupled array of interacting quantum wires. We show that the presence of hyperfine interaction between electron and nuclear spins in such wires can induce a phase transition, ordering electrons and nuclear spins into a helix in each wire. Electron-electron interaction effects, pronounced within the one-dimensional stripes, boost the transition temperature up to tens to hundreds of millikelvins in GaAs. We predict specific experimental signatures of the existence of nuclear spin order, for instance for the resistivity of the system at transitions between different quantum Hall plateaus.

3.  Nuclear Spin Relaxation in Rashba Nanowires
Alexander A. Zyuzin, Tobias Meng, Viktoriia Kornich, and Daniel Loss.

We study the nuclear spin relaxation in a ballistic nanowire with hyperfine and Rashba spin-orbit interactions (SOI) and in the presence of magnetic field and electron interactions. The relaxation rate shows pronounced peaks as function of magnetic field and chemical potential due to van Hove singularities in the Rashba bands. As a result, the regimes of weak and strong SOIs can be distinguished by the number of peaks in the rate. The relaxation rate increases with increasing magnetic field if both Rashba subbands are occupied, whereas it decreases if only the lowest one is occupied.

4.  Josephson and Persistent Spin Currents in Bose-Einstein Condensates of Magnons
Kouki Nakata, Kevin A. van Hoogdalem, Pascal Simon (Paris), and Daniel Loss.

Using the Aharonov-Casher (A-C) phase, we present a microscopic theory of the Josephson and persistent spin currents in quasi-equilibrium Bose-Einstein condensates (BECs) of magnons in ferromagnetic insulators. Starting from a microscopic spin model that we map onto a Gross-Pitaevskii Hamiltonian, we derive a two-state model for the Josephson junction between the weakly coupled magnon-BECs. We then show how to obtain the alternating-current (ac) Josephson effect with magnons as well as macroscopic quantum self-trapping in a magnon-BEC. We next propose how to control the direct-current (dc) Josephson effect electrically using the A-C phase, which is the geometric phase acquired by magnons moving in an electric field. Finally, we introduce a magnon-BEC ring and show that persistent magnon-BEC currents flow due to the A-C phase. Focusing on the feature that the persistent magnon-BEC current is a steady flow of magnetic dipoles that produces an electric field, we propose a method to directly measure it experimentally.

5.  Single-spin manipulation in a double quantum dot with micromagnet
Stefano Chesi (Beijing), Ying-Dan Wang (Beijing), Jun Yoneda (Tokyo), Tomohiro Otsuka (Tokyo), Seigo Tarucha (Tokyo), and Daniel Loss.

The manipulation of single spins in double quantum dots by making use of the exchange interaction and a highly inhomogeneous magnetic field was discussed in [W. A. Coish and D. Loss, Phys. Rev. B 75, 161302 (2007)]. However, such large inhomogeneity is difficult to achieve through the slanting field of a micromagnet in current designs of lateral double dots. Therefore, we examine an analogous spin manipulation scheme directly applicable to realistic GaAs double dot setups. We estimate that typical gate times, realized at the singlet-triplet anticrossing induced by the inhomogeneous micromagnet field, can be a few nanoseconds. We discuss the optimization of initialization, read-out, and single-spin gates through suitable choices of detuning pulses and an improved geometry. We also examine the effect of nuclear dephasing and charge noise. The latter induces fluctuations of both detuning and tunneling amplitude. Our results suggest that this scheme is a promising approach for the realization of fast single-spin operations.

6.  Quantum charge pumping through fractional Fermions in charge density modulated quantum wires and Rashba nanowires
Arijit Saha, Diego Rainis, Rakesh P. Tiwari, and Daniel Loss.
Phys. Rev. B 90, 035422 (2014); arXiv:1405.5719.

We study the phenomenon of adiabatic quantum charge pumping in systems supporting fractionally charged fermionic bound states, in two different setups. The first quantum pump setup consists of a charge-density-modulated quantum wire, and the second one is based on a semiconducting nanowire with Rashba spin-orbit interaction, in the presence of a spatially oscillating magnetic field. In both these quantum pumps transport is investigated in a N-X-N geometry, with the system of interest (X) connected to two normal-metal leads (N), and the two pumping parameters are the strengths of the effective wire-lead barriers. Pumped charge is calculated within the scattering matrix formalism. We show that quantum pumping in both setups provides a unique signature of the presence of the fractional-fermion bound states, in terms of asymptotically quantized pumped charge. Furthermore, we investigate shot noise arising due to quantum pumping, verifying that quantized pumped charge corresponds to minimal shot noise.

7.  Acoustic phonons and strain in core/shell nanowires
Christoph Kloeffel, Mircea Trif (Paris), and Daniel Loss.

We study theoretically the low-energy phonons and the static strain in cylindrical core/shell nanowires (NWs). Assuming pseudomorphic growth, isotropic media, and a force-free wire surface, we derive algebraic expressions for the dispersion relations, the displacement fields, and the stress and strain components from linear elasticity theory. Our results apply to NWs with arbitrary radii and arbitrary elastic constants for both core and shell. The expressions for the static strain are consistent with experiments, simulations, and previous analytical investigations; those for phonons are consistent with known results for homogeneous NWs. Among other things, we show that the dispersion relations of the torsional, longitudinal, and flexural modes change differently with the relative shell thickness, and we identify new terms in the corresponding strain tensors that are absent for uncapped NWs. We illustrate our results via the example of Ge/Si core/shell NWs and demonstrate that shell-induced strain has large effects on the hole spectrum of these systems.

8.  Characterization of spin-orbit interactions of GaAs heavy holes using a quantum point contact
Fabrizio Nichele, Stefano Chesi (RIKEN), Szymon Hennel, Angela Wittmann, Christian Gerl, Werner Wegscheider, Daniel Loss, Thomas Ihn, and Klaus Ensslin (ETHZ).
Phys. Rev. Lett. 113, 046801 (2014); arXiv:1405.2981.

We present transport experiments performed in high quality quantum point contacts embedded in a GaAs two-dimensional hole gas. The strong spin-orbit interaction results in peculiar transport phenomena, including the previously observed anisotropic Zeeman splitting and level-dependent effective g-factors. Here we find additional effects, namely the crossing and the anti-crossing of spin-split levels depending on subband index and magnetic field direction. Our experimental observations are reconciled in an heavy hole effective spin-orbit Hamiltonian where cubic- and quadratic-in-momentum terms appear. The spin-orbit components, being of great importance for quantum computing applications, are characterized in terms of magnitude and spin structure. In the light of our results, we explain the level dependent effective g-factor in an in-plane field. Through a tilted magnetic field analysis, we show that the QPC out-of-plane g-factor saturates around the predicted 7.2 bulk value.

9.  Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
Jelena Klinovaja (Harvard), Amir Yacoby (Harvard), and Daniel Loss.

We propose a scheme based on topological insulators to generate Kramers pairs of Majorana fermions or parafermions in the complete absence of magnetic fields. Our setup consists of two topological insulators whose edge states are brought close to an s-wave superconductor. The resulting proximity effect leads to an interplay between a non-local crossed Andreev pairing, which is dominant in the strong electron-electron interaction regime, and usual superconducting pairing, which is dominant at large separation between the two topological insulator edges. As a result, there are zero-energy bound states localized at interfaces between spatial regions dominated by the two different types of pairing. Due to the preserved time-reversal symmetry, the bound states come in Kramers pairs. If the topological insulators carry fractional edge states, the zero-energy bound states are parafermions, otherwise, they are Majorana fermions.

10.  Renormalization of anticrossings in interacting quantum wires with Rashba and Dresselhaus spin-orbit couplings
Tobias Meng, Jelena Klinovaja (Harvard), and Daniel Loss.
Phys. Rev. B 89, 205133 (2014); arXiv:1403.2759.

We discuss how electron-electron interactions renormalize the spin-orbit induced anticrossings between different subbands in ballistic quantum wires. Depending on the ratio of spin-orbit coupling and subband spacing, electron-electron interactions can either increase or decrease anticrossing gaps. When the anticrossings are closing due to a special combination of Rashba and Dresselhaus spin-orbit couplings, their gap approaches zero as an interaction dependent power law of the spin-orbit couplings, which is a consequence of Luttinger liquid physics. Monitoring the closing of the anticrossings allows to directly measure the related renormalization group scaling dimension in an experiment. If a magnetic field is applied parallel to the spin-orbit coupling direction, the anticrossings experience different renormalizations. Since this difference is entirely rooted in electron-electron interactions, unequally large anticrossings also serve as a direct signature of Luttinger liquid physics. Electron-electron interactions furthermore increase the sensitivity of conductance measurements to the presence of anticrossing.

11.  Nuclear Spin Diffusion Mediated by Heavy Hole Hyperfine Non-Collinear Interactions
Hugo Ribeiro, Franziska Maier, and Daniel Loss.

We show that the hyperfine mediated dynamics of heavy hole states confined in neutral self- assembled quantum dots leads to a nuclear spin diffusion mechanism. It is found that the oftentimes neglected effective heavy hole hyperfine non-collinear interaction is responsible for the low degree of nuclear spin polarization in neutral quantum dots. Moreover, our results demonstrate that after pumping the nuclear spin state is left in a complex mixed state, from which it is not straightforward to deduce the sign of the Ising-like interactions.

12.  Breakdown of surface-code error correction due to coupling to a bosonic bath
Adrian Hutter and Daniel Loss.
Phys. Rev. A 89, 042334 (2014); arXiv:1402.3108.

We consider a surface code suffering decoherence due to coupling to a bath of bosonic modes at finite temperature and study the time available before the unavoidable breakdown of error correction occurs as a function of coupling and bath parameters. We derive an exact expression for the error rate on each individual qubit of the code, taking spatial and temporal correlations between the errors into account. We investigate numerically how different kinds of spatial correlations between errors in the surface code affect its threshold error rate. This allows us to derive the maximal duration of each quantum error-correction period by studying when the single-qubit error rate reaches the corresponding threshold. At the time when error correction breaks down, the error rate in the code can be dominated by the direct coupling of each qubit to the bath, by mediated subluminal interactions, or by mediated superluminal interactions. For a two-dimensional Ohmic bath, the time available per quantum error-correction period vanishes in the thermodynamic limit of a large code size L due to induced superluminal interactions, although it does so only like 1/√lnL. For all other bath types considered, this time remains finite as L→∞.

13.  A quantum magnetic RC circuit
Kevin A. van Hoogdalem, Mathias Albert (Orsay), Pascal Simon (Orsay), and Daniel Loss.
Phys. Rev. Lett. 113, 037201 (2014); arXiv:1401.5712.

We propose a setup that is the spin analog of the charge-based quantum RC circuit. We define and compute the spin capacitance and the spin resistance of the circuit for both ferromagnetic (FM) and antiferromagnetic (AF) systems. We find that the antiferromagnetic setup has universal properties, but the ferromagnetic setup does not. We discuss how to use the proposed setup as a quantum source of spin excitations, and put forward a possible experimental realization using ultracold atoms in optical lattices.

14.  Time-Reversal Invariant Parafermions in Interacting Rashba Nanowires
Jelena Klinovaja (Harvard) and Daniel Loss.
Phys. Rev. B 90, 045118 (2014); arXiv:1312.1998.

We propose a scheme to generate pairs of time-reversal invariant parafermions. Our setup consists of two quantum wires with Rashba spin-orbit interactions coupled to an s-wave superconductor, in the presence of electron-electron interactions. The zero-energy bound states localized at the wire ends arise from the interplay between two types of proximity-induced superconductivity: the usual intrawire superconductivity and the interwire superconductivity due to crossed Andreev reflections. If the latter dominates, which is the case for strong electron-electron interactions, the system supports Kramers pair of parafermions. Moreover, the scheme can be extended to a two-dimensional sea of time-reversal invariant parafermions.

15.  Parafermions in Interacting Nanowire Bundle
Jelena Klinovaja (Harvard) and Daniel Loss.
Phys. Rev. Lett. 112, 246403 (2014); arXiv:1311.3259.

We propose a scheme to induce Z3 parafermion modes, exotic zero-energy bound states that possess non-Abelian statistics. We consider a minimal setup consisting of a bundle of four tunnel coupled nanowires hosting spinless electrons that interact strongly with each other. The hallmark of our setup is that it relies only on simple one-dimensional wires, uniform magnetic fields, and strong interactions, but does not require the presence of superconductivity or exotic quantum Hall phases.

16.  Phonon-Mediated Decay of Singlet-Triplet Qubits in Double Quantum Dots
Viktoriia Kornich, Christoph Kloeffel, and Daniel Loss.
Phys. Rev. B 89, 085410 (2014); arXiv:1311.2197.

We study theoretically the phonon-induced decoherence and relaxation of singlet-triplet qubits in lateral GaAs double quantum dots. For typical setups, the decoherence and relaxation rates due to one-phonon processes are proportional to the temperature T, whereas the rates due to two-phonon processes reveal a transition from T^2 to higher powers as T is decreased. In contrast to previous calculations of the phonon-limited lifetimes T_1 (relaxation) and T_2 (decoherence), we find T_2 \neq 2 T_1 in this system. Remarkably, both T_1 and T_2 exhibit a maximum when the external magnetic field is applied along a certain axis within the plane of the two-dimensional electron gas. We compare our results with recent experiments and analyze the dependence of T_1 and T_2 on system properties such as the detuning, the spin-orbit parameters, and the orientation of the double quantum dot and the applied magnetic field with respect to the main crystallographic axes.

17.  Anisotropic g factor in InAs self-assembled quantum dots
Robert Zielke, Franziska Maier, and Daniel Loss.
Phys. Rev. B 89, 115438 (2014); arXiv:1311.0908.

We investigate the wavefunctions, spectrum, and g factor anisotropy of low-energy electrons confined to self-assembled, pyramidal InAs quantum dots (QDs) subject to external magnetic and electric fields. We present the construction of trial wavefunctions for a pyramidal geometry with hard-wall confinement. We explicitly find the ground and first excited states and show the associated probability distributions and energies. Subsequently, we use these wavefunctions and 8-band k⋅p theory to derive a Hamiltonian describing the QD states close to the valence band edge. Using a perturbative approach, we find an effective conduction band Hamiltonian describing low-energy electronic states in the QD. From this, we further extract the magnetic field dependent eigenenergies and associated g factors. We examine the g factors regarding anisotropy and behavior under small electric fields. In particular, we find strong anisotropies, with the specific shape depending strongly on the considered subband. Our results are in good agreement with recent measurements [Takahashi et al., Phys. Rev. B 87, 161302 (2013)] and support the possibility to control a spin qubit by means of g tensor modulation.

18.  Decoding non-Abelian topological quantum memories
James R. Wootton, Jan Burri, Sofyan Iblisdir, and Daniel Loss.
Phys. Rev. X 4, 011051 (2014); Popular Summary; arXiv:1310.3846.

The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However, the question of how to obtain and process information about what errors have occurred in order to negate their effects has not yet been considered. This is in stark contrast with quantum computation proposals for Abelian anyons, for which decoding algorithms have been tailor-made for many topological error-correcting codes and error models. Here, we address this issue by considering the properties of non-Abelian error correction, in general. We also choose a specific anyon model and error model to probe the problem in more detail. The anyon model is the charge submodel of D(S3). This shares many properties with important models such as the Fibonacci anyons, making our method more generally applicable. The error model is a straightforward generalization of those used in the case of Abelian anyons for initial benchmarking of error correction methods. It is found that error correction is possible under a threshold value of 7% for the total probability of an error on each physical spin. This is remarkably comparable with the thresholds for Abelian models.

19.  Structure factor of interacting one-dimensional helical systems
Suhas Gangadharaiah, Thomas L. Schmidt, and Daniel Loss.
Phys. Rev. B 89, 035131 (2014); arXiv:1308.5982.

We calculate the dynamical structure factor S(q, {\omega}) of a weakly interacting helical edge state in the presence of a magnetic field B. The latter opens a gap of width 2B in the single-particle spectrum, which becomes strongly nonlinear near the Dirac point. For chemical potentials |{\mu}| > B, the system then behaves as a nonlinear helical Luttinger liquid, and a mobile-impurity analysis reveals interaction-dependent power-law singularities in S(q,{\omega}). For |{\mu}| < B, the low-energy excitations are gapped, and we determine S(q,{\omega}) by using an analogy to exciton physics.

20.  Transport signature of fractional Fermions in Rashba nanowires
Diego Rainis, Arijit Saha, Jelena Klinovaja (Harvard), Luka Trifunovic, and Daniel Loss.
Phys. Rev. Lett. 112, 196803 (2014); arXiv:1309.3738.

We theoretically study transport through a semiconducting Rashba nanowire (NW) in the presence of uniform and spatially modulated magnetic fields. The system is fully gapped, and the interplay between the spin orbit interaction and the magnetic fields leads to fractionally charged fermion (FF) bound states of the Jackiw-Rebbi type at each end of the nanowire. We investigate the transport and noise behavior of a N=NW=N system, where the wire is contacted by two normal leads (N), and we look for possible signatures that could help in the experimental detection of such states. We find that the differential conductance and the shot noise exhibit a subgap structure which fully reveals the presence of the FF state. Alternatively, another confirmation of the presence of the FFs is provided by a conductance measurement in an Aharonov-Bohm setup, where the FFs are responsible for oscillations with double period. Our predictions can be tested in InSb or InAs nanowires and are within reach of the present technology.

21.  Enhanced thermal stability of the toric code through coupling to a bosonic bath
Fabio L. Pedrocchi, Adrian Hutter, James R. Wootton, and Daniel Loss.
Phys. Rev. A 88, 062313 (2013); arXiv:1309.0621.

We propose and study a model of a quantum memory that features self-correcting properties and a lifetime growing arbitrarily with system size at non-zero temperature. This is achieved by locally coupling a 2D L x L toric code to a 3D bath of bosons hopping on a cubic lattice. When the stabilizer operators of the toric code are coupled to the displacement operator of the bosons, we solve the model exactly via a polaron transformation and show that the energy penalty to create anyons grows linearly with L. When the stabilizer operators of the toric code are coupled to the bosonic density operator, we use perturbation theory to show that the energy penalty for anyons scales with ln(L). For a given error model, these energy penalties lead to a lifetime of the stored quantum information growing respectively exponentially and polynomially with L. Furthermore, we show how to choose an appropriate coupling scheme in order to hinder the hopping of anyons (and not only their creation) with energy barriers that are of the same order as the anyon creation gaps. We argue that a toric code coupled to a 3D Heisenberg ferromagnet realizes our model in its low-energy sector. Finally, we discuss the delicate issue of the stability of topological order in the presence of perturbations. While we do not derive a rigorous proof of topological order, we present heuristic arguments suggesting that topological order remains intact when perturbative operators acting on the toric code spins are coupled to the bosonic environment.

22.  Low-energy properties of fractional helical Luttinger liquids
Tobias Meng, Lars Fritz (Koeln), Dirk Schuricht (Aachen), and Daniel Loss.
Phys. Rev. B 89, 045111 (2014); arXiv:1308.3169.

We investigate the low-energy properties of (quasi) helical and fractional helical Luttinger liquids. In particular, we calculate the Drude peak of the optical conductivity, the density of states, as well as charge transport properties of the interacting system with and without attached Fermi liquid leads at small and large (compared to the gap) frequencies. For fractional wires, we find that the low energy tunneling density of states vanishes. The conductance of a fractional helical Luttinger liquid is non-integer. It is independent of the Luttinger parameters in the wire, despite the intricate mixing of charge and spin degrees of freedom, and only depends on the relative locking of charge and spin degrees of freedom.

23.  Topological Superconductivity and Majorana Fermions in RKKY Systems
Jelena Klinovaja, Peter Stano (Riken), Ali Yazdani (Princeton), and Daniel Loss.
Phys. Rev. Lett. 111, 186805 (2013); arXiv:1307.1442.

We consider quasi one-dimensional RKKY systems in proximity to an s-wave superconductor. We show that a $2k_F$-peak in the spin susceptibility of the superconductor in the one-dimensional limit supports helical order of localized magnetic moments via RKKY interaction, where $k_F$ is the Fermi wavevector. The magnetic helix is equivalent to a uniform magnetic field and very strong spin-orbit interaction (SOI) with an effective SOI length $1/2k_F$. We find the conditions to establish such a magnetic state in atomic chains and semiconducting nanowires with magnetic atoms or nuclear spins. Generically, these systems are in a topological phase with Majorana fermions. The inherent self-tuning of the helix to $2k_F$ eliminates the need to tune the chemical potential.

24.  Circuit QED with Hole-Spin Qubits in Ge/Si Nanowire Quantum Dots
Christoph Kloeffel, Mircea Trif (UCLA), Peter Stano (RIKEN), and Daniel Loss.
Phys. Rev. B 88, 241405(R) (2013); arXiv:1306.3596.

We propose a setup for universal and electrically controlled quantum information processing with hole spins in Ge/Si core/shell nanowire quantum dots (NW QDs). Single-qubit gates can be driven through electric-dipole-induced spin resonance, with spin-flip times shorter than 100 ps. Long-distance qubit-qubit coupling can be mediated by the cavity electric field of a superconducting transmission line resonator, where we show that operation times below 20 ns seem feasible for the entangling square-root-of-iSWAP gate. The absence of Dresselhaus spin-orbit interaction (SOI) and the presence of an unusually strong Rashba-type SOI enable precise control over the transverse qubit coupling via an externally applied, perpendicular electric field. The latter serves as an on-off switch for quantum gates and also provides control over the g factor, so that single- and two-qubit gates can be operated independently. Remarkably, we find that idle states are insensitive to charge noise and phonons, and we discuss strategies for enhancing noise-limited gate fidelities.

25.  Vortex Loops and Majorana Fermions
Stefano Chesi (Riken), Arthur Jaffe (Harvard), Daniel Loss, and Fabio L. Pedrocchi.
J. Math. Phys. 54, 112203 (2013); arXiv:1305.6270.

We investigate the role that vortex loops play in characterizing eigenstates of certain systems of half-integer spins with nearest-neighbor interaction on a trivalent lattice. In particular we focus on ground states (and other low-lying states). We test our ideas on a "spin ladder" In certain cases we show how the vortex configuration of the ground state is determined by the relative signs of the coupling constants. Two methods yield exact results: i.) We utilize the equivalence of spin Hamiltonians with quartic interactions of Majorana fermions, and analyze that fermionic Hamiltonian. ii) We use reflection positivity for Majorana fermions to characterize vortices in ground states for reflection-symmetric couplings. Two additional methods suggest potential wider applicability of these results: iii.) Numerical evidence suggests similar behavior for certain systems without reflection symmetry. iv.) A perturbative analysis also suggests similar behavior without the assumption of reflection symmetry.

26.  Magnetically-Defined Qubits on 3D Topological Insulators
Gerson J. Ferreira and Daniel Loss.
Phys. Rev. Lett. 111, 106802 (2013); arXiv:1305.5003.

We explore time-reversal-symmetry-breaking potentials to confine the surface states of 3D topological insulators into quantum wires and quantum dots. A magnetic domain wall on a ferromagnet insulator cap layer provides interfacial states predicted to show the quantum anomalous Hall effect (QAHE). Here we show that confinement can also occur at magnetic domain heterostructures, with states extended in the inner domain, as well as interfacial QAHE states at the surrounding domain walls. The proposed geometry allows the isolation of the wire and dot from spurious circumventing surface states. For the quantum dots, we find that highly spin-polarized quantized QAHE states at the dot edge constitute a promising candidate for quantum computing qubits.

27.  Correlations between Majorana fermions through a superconductor
A.A. Zyuzin, Diego Rainis, Jelena Klinovaja, and Daniel Loss.
Phys. Rev. Lett. 111, 056802 (2013); arXiv:1305.4187.

We consider a model of ballistic quasi-one dimensional semiconducting wire with intrinsic spin-orbit interaction placed on the surface of a bulk s-wave superconductor (SC), in the presence of an external magnetic field. This setup has been shown to give rise to a topological superconducting state in the wire, characterized by a pair of Majorana-fermion (MF) bound states formed at the two ends of the wire. Here we demonstrate that, besides the well-known direct overlap-induced energy splitting, the two MF bound states may hybridize via elastic correlated tunneling processes through virtual quasiparticles states in the SC, giving rise to an additional energy splitting between MF states from the same as well as from different wires.

28.  Long-Range Interaction of Singlet-Triplet Qubits via Ferromagnets
Luka Trifunovic, Fabio L. Pedrocchi, and Daniel Loss.
Phys. Rev. X 3, 041023 (2013); arXiv:1305.2451.

We propose a mechanism of a long-range coherent interaction between two singlet-triplet qubits dipolarly coupled to a dogbone-shaped ferromagnet. An effective qubit-qubit interaction Hamiltonian is derived and the coupling strength is estimated. Furthermore we derive the effective coupling between two spin-1/2 qubits that are coupled via dipolar interaction to the ferromagnet and that lie at arbitrary positions and deduce the optimal positioning. We consider hybrid systems consisting of spin-1/2 and ST qubits and derive the effective Hamiltonian for this case. We then show that operation times vary between 1MHz and 100MHz and give explicit estimates for GaAs, Silicon, and NV-center based spin qubits. Finally, we explicitly construct the required sequences to implement a CNOT gate. The resulting quantum computing architecture retains all the single qubit gates and measurement aspects of earlier approaches, but allows qubit spacing at distances of order 1$\,\mu$m for two-qubit gates, achievable with current semiconductor technology.

29.  Integer and Fractional Quantum Hall Effect in a Strip of Stripes
Jelena Klinovaja and Daniel Loss.

We study anisotropic stripe models of interacting electrons in the presence of magnetic fields in the quantum Hall regime with integer and fractional filling factors. The model consists of an infinite strip of finite width that contains periodically arranged stripes (forming supercells) to which the electrons are confined and between which they can hop with associated magnetic phases. The interacting electron system within the one-dimensional stripes are described by Luttinger liquids and shown to give rise to charge and spin density waves that lead to periodic structures within the stripe with a reciprocal wavevector 8k_F. This wavevector gives rise to Umklapp scattering and resonant scattering that results in gaps and chiral edge states at all known integer and fractional filling factors \nu. The integer and odd denominator filling factors arise for a uniform distribution of stripes, whereas the even denominator filling factors arise for a non-uniform stripe distribution. We calculate the Hall conductance via the Streda formula and show that it is given by \sigma_H=\nu e^2/h for all filling factors. We show that the composite fermion picture follows directly from the condition of the resonant Umklapp scattering.

30.  Spintronics in MoS_2 monolayer quantum wires
Jelena Klinovaja and Daniel Loss.
Phys. Rev. B 88, 075404 (2013); arXiv:1304.4542.

We study analytically and numerically spin effects in MoS_2 monolayer armchair quantum wires and quantum dots. The interplay between intrinsic and Rashba spin orbit interactions induced by an electric field leads to helical modes, giving rise to spin filtering in time-reversal invariant systems. The Rashba spin orbit interaction can also be generated by spatially varying magnetic fields. In this case, the system can be in a helical regime with nearly perfect spin polarization. If such a quantum wire is brought into proximity to an s-wave superconductor, the system can be tuned into a topological phase, resulting in midgap Majorana fermions localized at the wire ends.

31.  Strongly anisotropic spin response as a signature of the helical regime in Rashba nanowires
Tobias Meng and Daniel Loss.
Phys. Rev. B 88, 035437 (2013); arXiv:1303.6994.

Rashba nanowires in a magnetic field exhibit a helical regime when the spin-orbit momentum is close to the Fermi momentum, k_F \approx k_{SO}. We show that this regime is characterized by a strongly anisotropic electron spin susceptibility, with an exponentially suppressed signal along one direction in spin space, and that there are no low frequency spin fluctuations along this direction. Since the spin response in the gapless regime k_F \not \approx k_{SO} has a power law behavior in all three directions, spin measurements provide a signature of the helical regime that complements spin-insensitive conductance measurements.

32.  Helical nuclear spin order in two-subband quantum wires
Tobias Meng and Daniel Loss.
Phys. Rev. B 87, 235427 (2013); arXiv:1303.1542.

In quantum wires, the hyperfine coupling between conduction electrons and nuclear spins can lead to a (partial) ordering of both of them at low temperatures. By an interaction-enhanced mechanism, the nuclear spin order, caused by RKKY exchange, acts back onto the electrons and gaps out part of their spectrum. In wires with two subbands characterized by distinct Fermi momenta kF1 and kF2, the nuclear spins form a superposition of two helices with pitches {\pi}/kF1 and {\pi}/kF2, thus exhibiting a beating pattern. This order results in a reduction of the electronic conductance in two steps upon lowering the temperature.

33.  Local Spin Susceptibilities of Low-Dimensional Electron Systems
Peter Stano, Jelena Klinovaja, Amir Yacoby (Harvard), and Daniel Loss.
Phys. Rev. B 88, 045441 (2013); arXiv:1303.1151.

We investigate, assess, and suggest possibilities for a measurement of the local spin susceptibility of a conducting low-dimensional electron system. The basic setup of the experiment we envisage is a source-probe one. Locally induced spin density (e.g. by a magnetized atomic force microscope tip) extends in the medium according to its spin susceptibility. The induced magnetization can be detected as a dipolar magnetic field, for instance, by an ultra-sensitive nitrogen-vacancy center based detector, from which the spatial structure of the spin susceptibility can be deduced. We find that one-dimensional systems, such as semiconducting nanowires or carbon nanotubes, are expected to yield a measurable signal. The signal in a two-dimensional electron gas is weaker, though materials with high enough $g$-factor (such as InGaAs) seem promising for successful measurements.

34.  Topological Edge States and Fractional Quantum Hall Effect from Umklapp Scattering
Jelena Klinovaja and Daniel Loss.
Phys. Rev. Lett. 111, 196401 (2013); arXiv:1302.6132.

We study anisotropic lattice strips in the presence of a magnetic field in the quantum Hall effect regime. At specific magnetic fields, causing resonant Umklapp scattering, the system is gapped in the bulk and supports chiral edge states in close analogy to topological insulators. These gaps result in plateaus for the Hall conductivity exactly at the known fillings n/m (both positive integers and m odd) for the integer and fractional quantum Hall effect. For double strips we find topological phase transitions with phases that support midgap edge states with flat dispersion. The topological effects predicted here could be tested directly in optical lattices.

35.  Tunable g factor and phonon-mediated hole spin relaxation in Ge/Si nanowire quantum dots
Franziska Maier, Christoph Kloeffel, and Daniel Loss.
Phys. Rev. B 87, 161305(R) (2013); arXiv:1302.5027.

We theoretically consider g factor and spin lifetimes of holes in a longitudinal Ge/Si core/shell nanowire quantum dot that is exposed to external magnetic and electric fields. For the ground states, we find a large anisotropy of the g factor which is highly tunable by applying electric fields. This tunability depends strongly on the direction of the electric field with respect to the magnetic field. We calculate the single-phonon hole spin relaxation times T1 for zero and small electric fields and propose an optimal setup in which very large T1 of the order of tens of milliseconds can be reached. Increasing the relative shell thickness or the longitudinal confinement length prolongs T1 further. In the absence of electric fields, the dephasing vanishes and the decoherence time T2 is determined by T2 = 2 T1.

36.  Long-Range Interaction of Spin-Qubits via Ferromagnets
Luka Trifunovic, Fabio L. Pedrocchi, and Daniel Loss.
Phys. Rev. X 3, 041023 (2013); arXiv:1302.4017.

We propose a mechanism of long-range coherent coupling between spins coupled to a ferromagnet by exchnage or dipolar coupling. An effective two-spin interaction Hamiltonian is derived and the coupling strength is estimated. We also discuss mechanisms of decoherence and consider possibilities for gate control of the interaction between neighboring spin-qubits. The resulting quantum computing architecture retains all the single qubit gates and measurement aspects of earlier approaches, but allows qubit spacing at distances of order 1$\,\mu$m for two-qubit gates, achievable with current semiconductor technology. The clock speed depends strongly on the dimensionality of the ferromagnet and is between MHz and GHz.

37.  Dynamic Generation of Topologically Protected Self-Correcting Quantum Memory
Daniel Becker, Tetsufumi Tanamoto (Toshiba), Adrian Hutter, Fabio L. Pedrocchi, and Daniel Loss.
Phys. Rev. A 87, 042340 (2013); arXiv:1302.3998.

We propose a scheme to dynamically realize a thermally stable quantum memory based on the toric code. The code is generated from qubit systems with typical two-body interactions (Ising, XY, Heisenberg) using periodic, NMR-like, pulse sequences. It allows one to encode the logical qubits without measurements and to protect them dynamically against the time evolution of the physical qubits. Thermal stability is achieved by weakly coupling the qubits to additional cavity modes that mediate long-range attractive interactions between the stabilizer operators of the toric code. We investigate how the fidelity, with which the toric code is realized, depends on the period length T of the pulse sequence and the magnitude of possible pulse errors. We derive an optimal period T_opt that maximizes the fidelity.

38.  An efficient decoding algorithm for stabilizer codes
Adrian Hutter, James R. Wootton, and Daniel Loss.
Phys. Rev. A 89, 022326 (2014); arXiv:1302.2669.

To date, the best classical algorithm for performing error correction in the surface code has been minimum-weight perfect matching. However, in this work we present a Markov chain Monte Carlo algorithm that achieves significantly lower logical error rates. It therefore allows any target logical error rate to be obtained using a significantly smaller code. This increase in performance does come at the cost of an increased runtime complexity, but only by a polynomial factor $O(L^\eps)$ for $\eps<2$. Our algorithm is based on an analytically exact rewriting of the probability of each logical equivalence class, which also suggests that for arbitrary stabilizer codes error correction can be performed to arbitrary accuracy in a runtime $O(\m{poly}(L))$. It is applicable to any stabilizer code, allows for parallelization, and can be used to correct in the case of imperfect stabilizer measurements.

39.  Fractional Fermions with Non-Abelian Statistics
Jelena Klinovaja and Daniel Loss.
Phys. Rev. Lett. 110, 126402 (2013); arXiv:1301.5822.

We introduce a novel class of low-dimensional topological tight-binding models that allow for bound states that are fractionally charged fermions and exhibit non-Abelian braiding statistics. The proposed model consists of a double (single) ladder of spinless (spinful) fermions in the presence of magnetic fields. We study the system analytically in the continuum limit as well as numerically in the tight-binding representation. We find a topological phase transition with a topological gap that closes and reopens as a function of system parameters and chemical potential. The topological phase is of the type BDI and carries two degenerate mid-gap bound states that are localized at opposite ends of the ladders. We show numerically that these bound states are robust against a wide class of perturbations.

40.  RKKY interaction in carbon nanotubes and graphene nanoribbons
Jelena Klinovaja and Daniel Loss.
Phys. Rev. B 87, 045422 (2013); arXiv:1211.3067.

We study Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction in carbon nanotubes (CNTs) and graphene nanoribbons in the presence of spin-orbit interactions and magnetic fields. For this, we evaluate the static spin susceptibility tensor in real space in various regimes at zero temperature. In metallic CNTs, the RKKY interaction depends strongly on the sublattice and, at the Dirac point, is purely ferromagnetic (antiferromagnetic) for the localized spins on the same (different) sublattice, whereas in semiconducting CNTs, the spin susceptibility depends only weakly on the sublattice and is dominantly ferromagnetic. The spin-orbit interactions break the SU(2) spin symmetry of the system, leading to an anisotropic RKKY interaction of Ising and Dzyaloshinskii-Moriya form, aside from the usual isotropic Heisenberg interaction. All these RKKY terms can be made of comparable magnitude by tuning the Fermi level close to the gap induced by the spin-orbit interaction. We further calculate the spin susceptibility also at finite frequencies and thereby obtain the spin noise in real space via the fluctuation-dissipation theorem.

41.  Giant spin orbit interaction due to rotating magnetic fields in graphene nanoribbons
Jelena Klinovaja and Daniel Loss.
Phys. Rev. X 3, 011008 (2013); arXiv:1211.2739.

We theoretically study graphene nanoribbons in the presence of spatially varying magnetic fields produced e.g. by nanomagnets. We show both analytically and numerically that an exceptionally large Rashba spin orbit interaction (SOI) of the order of 10 meV can be produced by the non-uniform magnetic field. As a consequence, helical modes exist in armchair nanoribbons that exhibit nearly perfect spin polarization and are robust against boundary defects. This paves the way to realizing spin filter devices in graphene nanoribbons in the temperature regime of a few Kelvins. If a nanoribbon in the helical regime is in proximity contact to an s-wave superconductor, the nanoribbon can be tuned into a topological phase sustaining Majorana fermions.

42.  Ultrafast magnon-transistor at room temperature
Kevin A. van Hoogdalem and Daniel Loss.
Phys. Rev. B 88, 024420 (2013); arXiv:1209.5594; See News and Views, SPINTRONICS: An insulator-based transistor, by Yaroslav Tserkovnyak; Nature Nanotechnology 8, 706 (2013).

We study sequential tunneling of magnetic excitations in nonitinerant systems (either magnons or spinons) through triangular molecular magnets. It is known that the quantum state of such molecular magnets can be controlled by application of an electric- or a magnetic field. Here, we use this fact to control the flow of a spin current through the molecular magnet by electric- or magnetic means. This allows us to design a system that behaves as a magnon-transistor. We show how to combine three magnon-transistors to form a NAND-gate, and give several possible realizations of the latter, one of which could function at room temperature using transistors with a 11 ns switching time.

43.  Effective quantum-memory Hamiltonian from local two-body interactions
Adrian Hutter, Fabio L. Pedrocchi, James R. Wootton, and Daniel Loss.
Phys. Rev. A 90, 012321 (2014); arXiv:1209.5289.

In Phys. Rev. A 88, 062313 (2013) we proposed and studied a model for a self-correcting quantum memory in which the energetic cost for introducing a defect in the memory grows without bounds as a function of system size. This positive behavior is due to attractive long-range interactions mediated by a bosonic field to which the memory is coupled. The crucial ingredients for the implementation of such a memory are the physical realization of the bosonic field as well as local five-body interactions between the stabilizer operators of the memory and the bosonic field. Here, we show that both of these ingredients appear in a low-energy effective theory of a Hamiltonian that involves only two-body interactions between neighboring spins. In particular, we consider the low-energy, long-wavelength excitations of an ordered Heisenberg ferromagnet (magnons) as a realization of the bosonic field. Furthermore, we present perturbative gadgets for generating the required five-spin operators. Our Hamiltonian involving only local two-body interactions is thus expected to exhibit self-correcting properties as long as the noise affecting it is in the regime where the effective low-energy description remains valid.

44.  Helical States in Curved Bilayer Graphene
Jelena Klinovaja, Gerson J. Ferreira, and Daniel Loss.
Phys. Rev. B 86, 235416 (2012); arXiv:1208.2601.

We study spin effects of quantum wires formed in bilayer graphene by electrostatic confinement. With a proper choice of the confinement direction, we show that in the presence of magnetic field, spin-orbit interaction induced by curvature, and intervalley scattering, bound states emerge that are helical. The localization length of these helical states can be modulated by the gate voltage which enables the control of the tunnel coupling between two parallel wires. Allowing for proximity effect via an s-wave superconductor, we show that the helical modes give rise to Majorana fermions in bilayer graphene.

45.  Magnetic texture-induced thermal Hall effects
Kevin A. van Hoogdalem, Yaroslav Tserkovnyak (UCLA), and Daniel Loss.
Phys. Rev. B 87, 024402 (2013); arXiv:1208.1646.

Magnetic excitations in ferromagnetic systems with a noncollinear ground state magnetization experience a fictitious magnetic field due to the equilibrium magnetic texture. Here, we investigate how such fictitious fields lead to thermal Hall effects in two-dimensional insulating magnets in which the magnetic texture is caused by spin-orbit interaction. We find that, besides the well-known geometric texture contribution to the fictitious magnetic field in such systems, there exists also an equally important but often neglected contribution due to the original spin-orbit term in the free energy. We consider the different possible ground states in the phase diagram of a two-dimensional ferromagnet with spin-orbit interaction: The spiral state and the skyrmion lattice, and find that thermal Hall effects can occur in certain domain walls as well as the skyrmion lattice.

46.  Transition from fractional to Majorana fermions in Rashba nanowires
Jelena Klinovaja, Peter Stano, and Daniel Loss.
Phys. Rev. Lett. 109, 236801 (2012); arXiv:1207.7322.

We study hybrid superconducting-semiconducting nanowires in the presence of Rashba spin-orbit interaction as well as helical magnetic fields. We show that the interplay between them leads to a competition of phases with two topological gaps closing and reopening, resulting in unexpected reentrance behavior. Besides the topological phase with localized Majorana fermions (MFs) we find new phases characterized by fractionally charged fermion (FF) bound states of Jackiw-Rebbi type. The system can be fully gapped by the magnetic fields alone, giving rise to FFs that transmute into MFs upon turning on superconductivity. We find explicit analytical solutions for MF and FF bound states and determine the phase diagram numerically by determining the corresponding Wronskian null space. We show by renormalization group arguments that electron-electron interactions enhance the Zeeman gaps opened by the fields.

47.  Realistic transport modeling for a superconducting nanowire with Majorana fermions
Diego Rainis, Luka Trifunovic, Jelena Klinovaja, and Daniel Loss.
Phys. Rev. B 87, 024515 (2013); arXiv:1207.5907.

Motivated by recent experiments searching for Majorana fermions (MFs) in hybrid semiconducting-superconducting nanostructures, we consider a realistic tight-binding model and analyze its transport behavior numerically. In particular, we take into account the presence of a superconducting contact, used in real experiments to extract the current, which is usually not included in theoretical calculations. We show that important features emerge that are absent in simpler models, such as the shift in energy of the proximity gap signal, and the enhanced visibility of the topological gap for increased spin-orbit interaction. We find oscillations of the zero bias peak as a function of the magnetic field and study them analytically. We argue that many of the experimentally observed features hint at an actual spin-orbit interaction larger than the one typically assumed. However, even taking into account all the known ingredients of the experiments and exploring many parameter regimes for MFs, we are not able to reach full agreement with the reported data. Thus, a different physical origin for the observed zero-bias peak cannot be excluded.

48.  Exchange-based CNOT gates for singlet-triplet qubits with spin orbit interaction
Jelena Klinovaja, Dimitrije Stepanenko, Bertrand I. Halperin (Harvard), and Daniel Loss.
Phys. Rev. B 86, 085423 (2012); arXiv:1206.2579.

We propose a scheme for implementing the CNOT gate over qubits encoded in a pair of electron spins in a double quantum dot. The scheme is based on exchange and spin orbit interactions and on local gradients in Zeeman fields. We find that the optimal device geometry for this implementation involves effective magnetic fields that are parallel to the symmetry axis of the spin orbit interaction. We show that the switching times for the CNOT gate can be as fast as a few nanoseconds for realistic parameter values in GaAs semiconductors. Guided by recent advances in surface codes, we also consider the perpendicular geometry. In this case, leakage errors due to spin orbit interaction occur but can be suppressed in strong magnetic fields.

49.  Self-correcting quantum memory with a boundary
Adrian Hutter, James R. Wootton, Beat Roethlisberger, and Daniel Loss.
Phys. Rev. A 86, 052340 (2012); arXiv:1206.0991.

We study the two-dimensional toric-code Hamiltonian with effective long-range interactions between its anyonic excitations induced by coupling the toric code to external fields. It has been shown that such interactions allow an arbitrary increase in the lifetime of the stored quantum information by making L, the linear size of the memory, larger [ Chesi et al. Phys. Rev. A 82 022305 (2010)]. We show that for these systems the choice of boundary conditions (open boundaries as opposed to periodic boundary conditions) is not a mere technicality; the influence of anyons produced at the boundaries becomes in fact dominant for large enough L. This influence can be either beneficial or detrimental. In particular, we study an effective Hamiltonian proposed by Pedrocchi et al. [ Phys. Rev. B 83 115415 (2011)] that describes repulsion between anyons and anyon holes. For this system, we find a lifetime of the stored quantum information that grows exponentially in L2 for both periodic and open boundary conditions, although the exponent in the latter case is found to be less favorable. However, L is upper bounded through the breakdown of the perturbative treatment of the underlying Hamiltonian.

50.  Decoherence of Majorana qubits by noisy gates
Manuel J. Schmidt (Aachen), Diego Rainis, and Daniel Loss.
Phys. Rev. B 86, 085414 (2012); arXiv:1206.0743.

We propose and study a realistic model for the decoherence of topological qubits, based on Majorana fermions in one-dimensional topological superconductors. The source of decoherence is the fluctuating charge on a capacitively coupled gate, modeled by non-interacting electrons. In this context, we clarify the role of quantum fluctuations and thermal fluctuations and find that quantum fluctuations do not lead to decoherence, while thermal fluctuations do. We explicitly calculate decay times due to thermal noise and give conditions for the gap size in the topological superconductor and the gate temperature. Based on this result, we provide simple rules for gate geometries and materials optimized for reducing the negative effect of thermal charge fluctuations on the gate.

51.  Composite Majorana Fermion Wavefunctions in Nanowires
Jelena Klinovaja and Daniel Loss.
Phys. Rev. B 86, 085408 (2012); arXiv:1205.7054.

We consider Majorana fermions (MFs) in quasi-one-dimensional nanowire systems containing normal and superconducting sections where the topological phase based on Rashba spin-orbit interaction can be tuned by magnetic fields. We derive explicit analytic solutions of the MF wave function in the weak and strong spin orbit interaction regimes. We find that the wave function for one single MF is a composite object formed by superpositions of different MF wave functions which have nearly disjoint supports in momentum space. These contributions are coming from the extrema of the spectrum, one centered around zero momentum and the other around the two Fermi points. As a result, the various MF wave functions have different localization lengths in real space and interference among them leads to pronounced oscillations of the MF probability density. For a transparent normal-superconducting junction we find that in the topological phase the MF leaks out from the superconducting into the normal section of the wire and is delocalized over the entire normal section, in agreement with numerical results obtained in previous studies.

52.  Hyperfine-induced decoherence in triangular spin-cluster qubits
Filippo Troiani (Modena), Dimitrije Stepanenko, and Daniel Loss.
Phys. Rev. B 86, 161409 (2012); arXiv:1205.5629.

We investigate hyperfine-induced decoherence in a triangular spin-cluster for different qubit encodings. Electrically controllable eigenstates of spin chirality (C_z) show decoherence times that approach milliseconds, two orders of magnitude longer than those estimated for the eigenstates of the total spin projection (S_z) and of the partial spin sum (S_{12}). The robustness of chirality is due to its decoupling from both the total- and individual-spin components in the cluster. This results in a suppression of the effective interaction between C_z and the nuclear spin bath.

53.  Prospects for Spin-Based Quantum Computing
Christoph Kloeffel and Daniel Loss.
Annu. Rev. Condens. Matter Phys. 4, 51 (2013); arXiv:1204.5917.

Experimental and theoretical progress toward quantum computation with spins in quantum dots (QDs) is reviewed, with particular focus on QDs formed in GaAs heterostructures, on nanowire-based QDs, and on self-assembled QDs. We report on a remarkable evolution of the field, where decoherence—one of the main challenges for realizing quantum computers—no longer seems to be the stumbling block it had originally been considered. General concepts, relevant quantities, and basic requirements for spin-based quantum computing are explained; opportunities and challenges of spin-orbit interaction and nuclear spins are reviewed. We discuss recent achievements, present current theoretical proposals, and make several suggestions for further experiments.

54.  Cotunneling in the 5/2 fractional quantum Hall regime
Robert Zielke, Bernd Braunecker, and Daniel Loss.
Phys. Rev. B 86, 235307 (2012); arXiv:1204.4400.

We show that cotunneling in the 5/2 fractional quantum Hall regime allows to test the Moore-Read wave function, proposed for this regime, and to probe the nature of the fractional charge carriers. We calculate the cotunneling current for electrons that tunnel between two quantum Hall edge states via a quantum dot and for quasiparticles with fractional charges e/4 and e/2 that tunnel via an antidot. While electron cotunneling is strongly suppressed, the quasiparticle tunneling shows signatures characteristic for the Moore-Read state. For comparison, we also consider cotunneling between Laughlin states, and find that electron-transport between Moore-Read states and the one between Laughlin states at filling factor 1/3 have identical voltage dependences.

55.  Non-abelian Majoranas and braiding in inhomogeneous spin ladders
Fabio L. Pedrocchi, Suhas Gangadharaiah (Bhopal), Stefano Chesi (Montreal), and Daniel Loss.
Phys. Rev. B 86, 205412 (2012); arXiv:1204.3044.

We propose an inhomogeneous open spin ladder, related to the Kitaev honeycomb model, which can be tuned between topological and nontopological phases. In extension of Lieb's theorem, we show numerically that the ground state of the spin ladder is either vortex free or vortex full. We study the robustness of Majorana end states (MES) which emerge at the boundary between sections in different topological phases and show that while the MES in the homogeneous ladder are destroyed by single-body perturbations, in the presence of inhomogeneities at least two-body perturbations are required to destabilize MES. Furthermore, we prove that x, y, or z inhomogeneous magnetic fields are not able to destroy the topological degeneracy. Finally, we present a trijunction setup where MES can be braided. A network of such spin ladders provides thus a promising platform for realization and manipulation of MES.

56.  Majorana qubit decoherence by quasiparticle poisoning
Diego Rainis and Daniel Loss.
Phys. Rev. B 85, 174533 (2012); arXiv:1204.3326.

We consider the problem of quasiparticle poisoning in a nanowire-based realization of a Majorana qubit, where a spin-orbit-coupled semiconducting wire is placed on top of a (bulk) superconductor. By making use of recent experimental data exhibiting evidence of a low-temperature residual nonequilibrium quasiparticle population in superconductors, we show by means of analytical and numerical calculations that the dephasing time due to the tunneling of quasiparticles into the nanowire may be problematically short to allow for qubit manipulation.

57.  Effect of strain on hyperfine-induced hole-spin decoherence in quantum dots
Franziska Maier and Daniel Loss.
Phys. Rev. B 85, 195323 (2012); arXiv:1203.3876.

We theoretically consider the effect of strain on the spin dynamics of a single heavy hole (HH) confined to a self-assembled quantum dot and interacting with the surrounding nuclei via hyperfine interaction. Confinement and strain hybridize the HH states, which show an exponential decay for a narrowed nuclear spin bath. For different strain configurations within the dot, the dependence of the spin decoherence time T2 on external parameters is shifted and the nonmonotonic dependence of the peak is altered. Application of external strain yields considerable shifts in the dependence of T2 on external parameters. We find that external strain affects mostly the effective hyperfine coupling strength of the conduction band (CB), indicating that the CB admixture of the hybridized HH states plays a crucial role in the sensitivity of T2 on strain.

58.  High threshold error correction for the surface code
James R. Wootton and Daniel Loss.
Phys. Rev. Lett. 109, 160503 (2012); arXiv:1202.4316.

An algorithm is presented for error correction in the surface code quantum memory. This is shown to correct depolarizing noise up to a threshold error rate of 18.5%, exceeding previous results and coming close to the upper bound of 18.9%. The time complexity of the algorithm is found to be sub-exponential, offering a significant speed-up over brute force methods and allowing efficient error correction for codes of realistic sizes.

59.  Frequency dependent transport through a spin chain
Kevin A. van Hoogdalem and Daniel Loss.
Phys. Rev. B 85, 054413 (2012); arXiv:1111.4803.

Motivated by potential applications in spintronics, we study frequency dependent spin transport in nonitinerant one-dimensional spin chains. We propose a system that behaves as a capacitor for the spin degree of freedom. It consists of a spin chain with two impurities a distance $d$ apart. We find that at low energy (frequency) the impurities flow to strong coupling, thereby effectively cutting the chain into three parts, with the middle island containing a discrete number of spin excitations. At finite frequency spin transport through the system increases. We find a strong dependence of the finite frequency characteristics both on the anisotropy of the spin chain and the applied magnetic field. We propose a method to measure the finite-frequency conductance in this system.

60.  Electric-Field Induced Majorana Fermions in Armchair Carbon Nanotubes
Jelena Klinovaja, Suhas Gangadharaiah, and Daniel Loss.
Phys. Rev. Lett. 108, 196804 (2012); arXiv:1201.0159.

We consider theoretically an armchair carbon nanotube (CNT) in the presence of an electric field and in contact with an s-wave superconductor. We show that the proximity effect opens up superconducting gaps in the CNT of different strengths for the exterior and interior branches of the two Dirac points. For strong proximity induced superconductivity the interior gap can be of the p-wave type, while the exterior gap can be tuned by the electric field to be of the s-wave type. Such a setup supports a single Majorana bound state at each end of the CNT. In the case of a weak proximity induced superconductivity, the gaps in both branches are of the p-wave type. However, the temperature can be chosen in such a way that the smallest gap is effectively closed. Using renormalization group techniques we show that the Majorana bound states exist even after taking into account electron-electron interactions.

61.  Thin-Film Magnetization Dynamics on the Surface of a Topological Insulator
Yaroslav Tserkovnyak (UCLA) and Daniel Loss.
Phys. Rev. Lett. 108, 187201 (2012); arXiv:1112.5884.

We theoretically study the magnetization dynamics of a thin ferromagnetic film exchange-coupled with a surface of a strong three-dimensional topological insulator. We focus on the role of electronic zero modes associated with domain walls (DW's) and other topological textures in the magnetic film. Thermodynamically reciprocal hydrodynamic equations of motion are derived for the DW responding to electronic spin torques, on the one hand, and fictitious electromotive forces in the electronic chiral mode fomented by the DW, on the other. An experimental realization illustrating this physics is proposed based on a ferromagnetic strip, which cuts the topological insulator surface into two gapless regions. In the presence of a ferromagnetic DW, a chiral mode transverse to the magnetic strip acts as a dissipative interconnect, which is itself a dynamic object that controls (and, inversely, responds to) the magnetization dynamics.

62.  Ferromagnetic order of nuclear spins coupled to conduction electrons: a combined effect of the electron-electron and spin-orbit interactions
Robert Andrzej Zak, Dmitrii L. Maslov (Gainesville), and Daniel Loss.
Phys. Rev. B 85, 115424 (2012); viewpoint; arXiv:1112.4786.

We analyze the ordered state of nuclear spins embedded in an interacting two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction (SOI). Stability of the ferromagnetic nuclear-spin phase is governed by nonanalytic dependences of the electron spin susceptibility $\chi^{ij}$ on the momentum ($\tilde{\mathbf{q}}$) and on the SOI coupling constant ($\alpha$). The uniform ($\tq=0$) spin susceptibility is anisotropic (with the out-of-plane component, $\chi^{zz}$, being larger than the in-plane one, $\chi^{xx}$, by a term proportional to $U^2(2k_F)|\alpha|$, where $U(q)$ is the electron-electron interaction). For $\tq \leq 2m^*|\alpha|$, corrections to the leading, $U^2(2k_F)|\alpha|$, term scale linearly with $\tq$ for $\chi^{xx}$ and are absent for $\chi^{zz}$. This anisotropy has important consequences for the ferromagnetic nuclear-spin phase: $(i)$ the ordered state--if achieved--is of an Ising type and $(ii)$ the spin-wave dispersion is gapped at $\tq=0$. To second order in $U(q)$, the dispersion a decreasing function of $\tq$, and anisotropy is not sufficient to stabilize long-range order. However, renormalization in the Cooper channel for $\tq\ll2m^*|\alpha|$ is capable of reversing the sign of the $\tq$-dependence of $\chi^{xx}$ and thus stabilizing the ordered state. We also show that a combination of the electron-electron and SO interactions leads to a new effect: long-wavelength Friedel oscillations in the spin (but not charge) electron density induced by local magnetic moments. The period of these oscillations is given by the SO length $\pi/m^*|\alpha|$.

63.  Singlet-triplet splitting in double quantum dots due to spin orbit and hyperfine interactions
Dimitrije Stepanenko, Mark Rudner (Harvard), Bertrand I. Halperin (Harvard), and Daniel Loss.
Phys. Rev. B 85, 075416 (2012); arXiv:1112.1644.

We analyze the low-energy spectrum of a two-electron double quantum dot under a potential bias in the presence of an external magnetic field. We focus on the regime of spin blockade, taking into account the spin-orbit interaction and hyperfine coupling of electron and nuclear spins. Starting from a model for two interacting electrons in a double dot, we derive an effective two-level Hamiltonian in the vicinity of an avoided crossing between singlet and triplet levels, which are coupled by the spin-orbit and hyperfine interactions. We evaluate the level splitting at the anticrossing, and show that it depends on a variety of parameters including the spin-orbit coupling strength, the orientation of the external magnetic field relative to an internal spin-orbit axis, the potential detuning of the dots, and the difference between hyperfine fields in the two dots. We provide a formula for the splitting in terms of the spin-orbit length, the hyperfine fields in the two dots, and the double dot parameters such as tunnel coupling and Coulomb energy. This formula should prove useful for extracting spin-orbit parameters from transport or charge sensing experiments in such systems. We identify a parameter regime where the spin-orbit and hyperfine terms can become of comparable strength, and discuss how this regime might be reached.

64.  Incoherent dynamics in the toric code subject to disorder
Beat Roethlisberger, James R. Wootton, Robert M. Heath (Leeds), Jiannis K. Pachos (Leeds), and Daniel Loss.
Phys. Rev. A 85, 022313 (2012); arXiv:1112.1613.

We numerically study the effects of two forms of quenched disorder on the anyons of the toric code. Firstly, a new class of codes based on random lattices of stabilizer operators is presented, and shown to be superior to the standard square lattice toric code for certain forms of biased noise. It is further argued that these codes are close to optimal, in that they tightly reach the upper bound of error thresholds beyond which no correctable CSS codes can exist. Additionally, we study the classical motion of anyons in toric codes with randomly distributed onsite potentials. In the presence of repulsive long-range interaction between the anyons, a surprising increase with disorder strength of the lifetime of encoded states is reported and explained by an entirely incoherent mechanism. Finally, the coherent transport of the anyons in the presence of both forms of disorder is investigated, and a significant suppression of the anyon motion is found.

65.  Localized end states in density modulated quantum wires and rings
Suhas Gangadharaiah, Luka Trifunovic, and Daniel Loss.
Phys. Rev. Lett. 108, 136803 (2012); arXiv:1111.5273.

We study finite quantum wires and rings in the presence of a charge-density wave gap induced by a periodic modulation of the chemical potential. We show that the Tamm-Shockley bound states emerging at the ends of the wire are stable against weak disorder and interactions, for discrete open chains and for continuum systems. The low-energy physics can be mapped onto the Jackiw-Rebbi equations describing massive Dirac fermions and bound end states. We treat interactions via the continuum model and show that they increase the charge gap and further localize the end states. The electrons placed in the two localized states on the opposite ends of the wire can interact via exchange interactions and this setup can be used as a double quantum dot hosting spin qubits. The existence of these states could be experimentally detected through the presence of an unusual 4\pi Aharonov-Bohm periodicity in the spectrum and persistent current as a function of the external flux.

66.  Rashba spin orbit interaction in a quantum wire superlattice
Gunnar Thorgilsson (Reykjavik), J. Carlos Egues (Sao Carlos), Daniel Loss, and Sigurdur I. Erlingsson (Reykjavik).
Phys. Rev. B 85, 045306 (2012); Phys. Rev. B 85, 039904(E) (2012); arXiv:1111.1534.

In this work we study the effects of a longitudinal periodic potential on a parabolic quantum wire defined in a two-dimensional electron gas with Rashba spin-orbit interaction. For an infinite wire superlattice we find, by direct diagonalization, that the energy gaps are shifted away from the usual Bragg planes due to the Rashba spin-orbit interaction. Interestingly, our results show that the location of the band gaps in energy can be controlled via the strength of the Rashba spin-orbit interaction. We have also calculated the charge conductance through a periodic potential of a finite length via the non-equilibrium Green's function method combined with the Landauer formalism. We find dips in the conductance that correspond well to the energy gaps of the infinite wire superlattice. From the infinite wire energy dispersion, we derive an equation relating the location of the conductance dips as a function of the (gate controllable) Fermi energy to the Rashba spin-orbit coupling strength. We propose that the strength of the Rashba spin-orbit interaction can be extracted via a charge conductance measurement.

67.  Long-distance spin-spin coupling via floating gates
Luka Trifunovic, Oliver Dial (Harvard), Mircea Trif, James R. Wootton, Rediet Abebe (Harvard), Amir Yacoby (Harvard), and Daniel Loss.
Synopsis; Phys. Rev. X 2, 011006 (2012); arXiv:1110.1342.

The electron spin is a natural two level system that allows a qubit to be encoded. When localized in a gate defined quantum dot, the electron spin provides a promising platform for a future functional quantum computer. The essential ingredient of any quantum computer is entanglement---between electron spin qubits---commonly achieved via the exchange interaction. Nevertheless, there is an immense challenge as to how to scale the system up to include many qubits. Here we propose a novel architecture of a large scale quantum computer based on a realization of long-distance quantum gates between electron spins localized in quantum dots. The crucial ingredients of such a long-distance coupling are floating metallic gates that mediate electrostatic coupling over large distances. We show, both analytically and numerically, that distant electron spins in an array of quantum dots can be coupled sel​ectively, with coupling strengths that are larger than the electron spin decay and with switching times on the order of nanoseconds.

68.  Crossed Andreev Reflection in Quantum Wires with Strong Spin-Orbit Interaction
Koji Sato (UCLA), Daniel Loss, and Yaroslav Tserkovnyak (UCLA).
Phys. Rev. B 85, 235433 (2012); arXiv:1109.6357.

We theoretically study tunneling of Cooper pairs from an s-wave superconductor into two semiconductor quantum wires with strong spin-orbit interaction under magnetic field, which approximate helical Luttinger liquids. The entanglement of electrons within a Cooper pair can be detected by the electric current cross correlations in the wires. By controlling the relative orientation of the wires, either lithographically or mechanically, on the substrate, the current correlations can be tuned, as dictated by the initial spin entanglement. This proposal of a spin-to-charge readout of quantum correlations is alternative to a recently proposed utilization of the quantum spin Hall insulator.

69.  Strong Spin-Orbit Interaction and Helical Hole States in Ge/Si Nanowires
Christoph Kloeffel, Mircea Trif, and Daniel Loss.
Phys. Rev. B 84, 195314 (2011); arXiv:1107.4870.

We study theoretically the low-energy hole states of Ge/Si core/shell nanowires. The low-energy valence band is quasi-degenerate, formed by two doublets of different orbital angular momentum, and can be controlled via the relative shell thickness and via external fields. We find that direct (dipolar) coupling to a moderate electric field leads to an unusually large spin-orbit interaction of Rashba-type on the order of meV which gives rise to pronounced helical states enabling electrical spin-control. The system allows for quantum dots and spin-qubits with energy levels that can vary from nearly zero to several meV, depending on the relative shell thickness.

70.  libCreme: An optimization library for evaluating convex-roof entanglement measures
Beat Roethlisberger, Joerg Lehmann (ABB Baden), and Daniel Loss.
Comput. Phys. Comm. 183, 155 (2012); arXiv:1107.4497.

We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the Matlab programming language, but is fully compatible to the free and open-source Octave platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focussing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems.

71.  Absence of spontaneous magnetic order of lattice spins coupled to itinerant interacting electrons in one and two dimensions
Daniel Loss, Fabio L. Pedrocchi, and Anthony J. Leggett (Urbana).
Phys. Rev. Lett. 107, 107201 (2011); arXiv:1107.1223; Synopsis.

We extend the Mermin-Wagner theorem to a system of lattice spins which are spin coupled to itinerant and interacting charge carriers. We use the Bogoliubov inequality to rigorously prove that neither (anti-) ferromagnetic nor helical long-range order is possible in one and two dimensions at any finite temperature. Our proof applies to a wide class of models including any form of electron-electron and single-electron interactions that are independent of spin. In the presence of Rashba or Dresselhaus spin-orbit interactions (SOI) magnetic order is not excluded and intimately connected to equilibrium spin currents. However, in the special case when Rashba and Dresselhaus SOIs are tuned to be equal, magnetic order is excluded again. This opens up a new possibility to control magnetism electrically.

72.  Carbon nanotubes in electric and magnetic fields
Jelena Klinovaja, Manuel J. Schmidt, Bernd Braunecker, and Daniel Loss.
Phys. Rev. B 84, 085452 (2011); arXiv:1106.3332.

We derive an effective low-energy theory for metallic (armchair and nonarmchair) single-wall nanotubes in the presence of an electric field perpendicular to the nanotube axis, and in the presence of magnetic fields, taking into account spin-orbit interactions and screening effects on the basis of a microscopic tight-binding model. The interplay between electric field and spin-orbit interaction allows us to tune armchair nanotubes into a helical conductor in both Dirac valleys. Metallic nonarmchair nanotubes are gapped by the surface curvature, yet helical conduction modes can be restored in one of the valleys by a magnetic field along the nanotube axis. Furthermore, we discuss electric dipole spin resonance in carbon nanotubes, and find that the Rabi frequency shows a pronounced dependence on the momentum along the nanotube.

73.  Low Bias Negative Differential Resistance in Graphene Nanoribbon Superlattices
Gerson J. Ferreira (S. Carlos), Michael N. Leuenberger (Orlando), Daniel Loss, and J. Carlos Egues (S. Carlos).
Phys. Rev. B 84, 125453 (2011); arXiv:1105.4850.

We theoretically investigate negative differential resistance (NDR) for ballistic transport in semiconducting armchair graphene nanoribbon (aGNR) superlattices (5 to 20 barriers) at low bias voltages $V_{SD} < 500$ mV. We combine the graphene Dirac hamiltonian with the Landauer-B\"uttiker formalism to calculate the current $I_{SD}$ through the system. We find three distinct transport regimes in which NDR occurs: (i) a "classical" regime for wide layers, through which the transport across bandgaps is strongly suppressed, leading to alternating regions of nearly unity and zero transmission probabilities as a function of $V_{SD}$ due to crossing of bandgaps from different layers. (ii) a quantum regime dominated by superlattice miniband conduction, with current suppression arising from the misalignment of miniband states with increasing $V_{SD}$; and (iii) a Wannier-Stark ladder regime with current peaks occurring at the crossings of Wannier-Stark rungs from distinct ladders. We observe NDR at voltage biases as low as 10 mV with a high current density, making the aGNR superlattices attractive for device applications.

74.  Physical solutions of the Kitaev honeycomb model
Fabio L. Pedrocchi, Stefano Chesi (McGill Univ.), and Daniel Loss.
Phys. Rev. B 84, 165414 (2011); arXiv:1105.4573.

We investigate the exact solution of the honeycomb model proposed by Kitaev and derive an explicit formula for the projector onto the physical subspace. The physical states are simply characterized by the parity of the total occupation of the fermionic eigenmodes. We consider a general lattice on a torus and show that the physical fermion parity depends in a nontrivial way on the vortex configuration and the choice of boundary conditions. In the vortex-free case with a constant gauge field we are able to obtain an analytical expression of the parity. For a general configuration of the gauge field the parity can be easily evaluated numerically, which allows the exact diagonalization of large spin models. We consider physically relevant quantities, as in particular the vortex energies, and show that their true value and associated states can be substantially different from the one calculated in the unprojected space, even in the thermodynamic limit.

75.  Schrieffer-Wolff transformation for quantum many-body systems
Sergey Bravyi (IBM Yorktown), David DiVincenzo (Julich), and Daniel Loss.
Annals of Physics 326, 2793-2826 (2011); arXiv:1105.0675.

The Schrieffer-Wolff (SW) method is a version of degenerate perturbation theory in which the low-energy effective Hamiltonian H_{eff} is obtained from the exact Hamiltonian by a unitary transformation decoupling the low-energy and high-energy subspaces. We give a self-contained summary of the SW method with a focus on rigorous results. We begin with an exact definition of the SW transformation in terms of the so-called direct rotation between linear subspaces. From this we obtain elementary proofs of several important properties of H_{eff} such as the linked cluster theorem. We then study the perturbative version of the SW transformation obtained from a Taylor series representation of the direct rotation. Our perturbative approach provides a systematic diagram technique for computing high-order corrections to H_{eff}. We then specialize the SW method to quantum spin lattices with short-range interactions. We establish unitary equivalence between effective low-energy Hamiltonians obtained using two different versions of the SW method studied in the literature. Finally, we derive an upper bound on the precision up to which the ground state energy of the n-th order effective Hamiltonian approximates the exact ground state energy.

76.  Universal quantum computation with topological spin-chain networks
Yaroslav Tserkovnyak (UCLA) and Daniel Loss.
Phys. Rev. A 84, 032333 (2011); arXiv:1104.1210.

It is shown that anisotropic spin chains with gapped bulk excitations and magnetically ordered ground states offer a promising platform for quantum computation, which bridges the conventional single-spin-based qubit concept with recently developed topological Majorana-based proposals. We show how to realize the single-qubit Hadamard, phase, and π/8 gates as well as the two-qubit controlled-not (cnot) gate, which together form a fault-tolerant universal set of quantum gates. The gates are implemented by judiciously controlling Ising exchange and magnetic fields along a network of spin chains, with each individual qubit furnished by a spin-chain segment. A subset of single-qubit operations is geometric in nature, relying on control of anisotropy of spin interactions rather than their strength. We contrast topological aspects of the anisotropic spin-chain networks to those of p-wave superconducting wires discussed in the literature.

77.  Rectification of spin currents in spin chains
Kevin A. van Hoogdalem and Daniel Loss.
Phys. Rev. B 84, 024402 (2011); arXiv:1102.4801.

We study spin transport in non-itinerant one-dimensional quantum spin chains. Motivated by possible applications in spintronics, we consider rectification effects in both ferromagnetic and antiferromagnetic systems. We find that the crucial ingredients in designing a system that displays a non-zero rectification current are an anisotropy in the exchange interaction of the spin chain combined with an offset magnetic field. For both ferromagnetic and antiferromagnetic systems we can exploit the gap in the excitation spectrum that is created by a bulk anisotropy to obtain a measurable rectification effect at realistic magnetic fields. For antiferromagnetic systems we also find that we can achieve a similar effect by introducing a magnetic impurity, obtained by altering two neighboring bonds in the spin Hamiltonian.

78.  Spectrum of an electron spin coupled to an unpolarized bath of nuclear spins
Oleksandr Tsyplyatyev (University of Sheffield) and Daniel Loss.
Phys. Rev. Lett. 106, 106803 (2011); arXiv:1102.2426.

The main source of decoherence for an electron spin confined to a quantum dot is the hyperfine interaction with nuclear spins. To analyze this process theoretically we diagonalize the central spin Hamiltonian in the high magnetic B-field limit. Then we project the eigenstates onto an unpolarized state of the nuclear bath and find that the resulting density of states has Gaussian tails. The level spacing of the nuclear sublevels is exponentially small in the middle of each of the two electron Zeeman levels but increases super-exponentially away from the center. This suggests to sel​ect states from the wings of the distribution when the system is projected on a single eigenstate by a measurement to reduce the noise of the nuclear spin bath. This theory is valid when the external magnetic field is larger than a typical Overhauser field at high nuclear spin temperature.

79.  Majorana edge states in interacting one-dimensional systems
Suhas Gangadharaiah, Bernd Braunecker, Pascal Simon (Orsay, Paris), and Daniel Loss.
Phys. Rev. Lett. 107, 036801 (2011); arXiv:1101.0094.

We show that one-dimensional electron systems in the proximity of a superconductor that support Majorana edge states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime in which the Majorana edge states persist. We present strategies of how this regime can be reached.

80.  Quantum memory coupled to cavity modes
Fabio L. Pedrocchi, Stefano Chesi, and Daniel Loss.
Phys. Rev. B.83, 115415 (2011); arXiv:1011.3762.

Inspired by spin-electric couplings in molecular magnets, we introduce in the Kitaev honeycomb model a linear modification of the Ising interactions due to the presence of quantized cavity fields. This allows to control the properties of the low-energy toric code Hamiltonian, which can serve as a quantum memory, by tuning the physical parameters of the cavity modes, like frequencies, photon occupations, and coupling strengths. We study the properties of the model perturbatively by making use of the Schrieffer-Wolff transformation and show that, depending on the specific setup, the cavity modes can be useful in several ways. They allow to detect the presence of anyons through frequency shifts and to prolong the lifetime of the memory by enhancing the anyon excitation energy or mediating long-range anyon-anyon interactions with tunable sign. We consider both resonant and largely detuned cavity modes.

81.  Helical modes in carbon nanotubes generated by strong electric fields
Jelena Klinovaja, Manuel J. Schmidt, Bernd Braunecker, and Daniel Loss.
Phys. Rev. Lett. 106, 156809 (2011); arXiv:1011.3630.

Helical modes, conducting opposite spins in opposite directions, are shown to exist in metallic armchair nanotubes in an all-electric setup. This is a consequence of the interplay between spin-orbit interaction and strong electric fields. The helical regime can also be obtained in chiral metallic nanotubes by applying an additional magnetic field. In particular, it is possible to obtain helical modes at one of the two Dirac points only, while the other one remains gapped. Starting from a tight-binding model we derive the effective low-energy Hamiltonian and the resulting spectrum.

82.  Controlling the electron spin-nuclear spin interaction of a quantum dot in the tunneling regime
C. Kloeffel, P. A. Dalgarno (Edinburgh), B. Urbaszek (Toulouse), B. D. Gerardot (Edinburgh), D. Brunner (Edinburgh), P. M. Petroff (UC Santa Barbara), D. Loss, and R. J. Warburton.
Phys. Rev. Lett. 106, 046802 (2011); arXiv:1010.3330.

We present a technique for manipulating the nuclear spins and the emission polarization from a single optically-active quantum dot. When the quantum dot is tunnel coupled to a Fermi sea, we have discovered a natural cycle in which an electron spin is repeatedly created with resonant optical excitation. The spontaneous emission polarization and the nuclear spin polarization exhibit a bistability. For a sigma(+) pump, the emission switches from sigma(+) to sigma(-) at a particular detuning of the laser. Simultaneously, the nuclear spin polarization switches from positive to negative. Away from the bistability, the nuclear spin polarization can be changed continuously from negative to positive, allowing precise control via the laser wavelength.

83.  Hybridization and spin decoherence in heavy-hole quantum dots
Jan Fischer and Daniel Loss.
Phys. Rev. Lett. 105, 266603 (2010); arXiv:1009.5195.

We theoretically investigate the spin dynamics of a heavy hole confined to a III-V semiconductor quantum dot interacting with a narrowed nuclear-spin bath. We show that band hybridization leads to an exponential decay of hole-spin superpositions due to hyperfine-mediated nuclear pair flips, and that the accordant single-hole-spin decoherence time T2 can be tuned over many orders of magnitude by changing external parameters. In particular, we show that, under experimentally accessible conditions, it is possible to suppress hyperfine-mediated nuclear-pair-flip processes so strongly that hole-spin quantum dots may be operated beyond the `ultimate limitation' set by the hyperfine interaction which is present in other spin-qubit candidate systems.

84.  Geometric Correlations and Breakdown of Mesoscopic Universality in Spin Transport
I. Adagideli (Istanbul), Ph. Jacquod (Tucson, AZ), M. Scheid (Regensburg), M. Duckheim (Berlin), D. Loss, and K. Richter (Regensburg).
Phys. Rev. Lett. 105, 246807 (2010); arXiv:1008.4656.

We construct a unified semiclassical theory of charge and spin transport in chaotic ballistic and disordered diffusive mesoscopic systems with spin-orbit interaction. Neglecting dynamic effects of spinorbit interaction, we reproduce the random matrix theory results that the spin conductance fluctuates universally around zero average. Incorporating these effects into the theory, we show that geometric correlations generate finite average spin conductances, but that they do not affect the charge conductance to leading order. The theory, which is confirmed by numerical transport calculations, allows us to investigate the entire range from the weak to the previously unexplored strong spin-orbit regime, where the spin rotation time is shorter than the momentum relaxation time.

85.  Poor man's derivation of the Bethe-Ansatz equations for the Dicke model
Oleksandr Tsyplyatyev, Jan von Delft (LMU Munich), and Daniel Loss.
Phys. Rev. B 82, 092203 (2010); arXiv:1008.1844.

We present an elementary derivation of the exact solution (Bethe-Ansatz equations) of the Dicke model, using only commutation relations and an informed Ansatz for the structure of its eigenstates.

86.  Energy spectra for quantum wires and 2DEGs in magnetic fields with Rashba and Dresselhaus spin-orbit interactions
Sigurdur I. Erlingsson (Reykjavik), J. Carlos Egues (Sao Carlos), and Daniel Loss.
Phys. Rev. B82, 155456 (2010); arXiv:1008.1317.

We introduce an analytical approximation scheme to diagonalize parabolically confined two dimensional electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and non-crossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k_Rl of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the n^th Landau-level g_n-factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g-factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.

87.  RKKY interaction in a disordered two-dimensional electron gas with Rashba and Dresselhaus spin-orbit couplings
Stefano Chesi and Daniel Loss.
Phys. Rev. B.82,165303 (2010); arXiv:1007.3506.

We study theoretically the statistical properties of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between localized magnetic moments in a disordered two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit couplings. Averaging over disorder, the static spin susceptibility tensor is evaluated diagrammatically in the mesoscopic (phase-coherent) regime. The disorder-averaged susceptibility leads to a twisted exchange interaction suppressed exponentially with distance, whereas the second-order correlations, which determine the fluctuations (variance) of the RKKY energy, decay with the same power-law as in the clean case. We obtain analytic expressions in the limits of large/small spin orbit interactions and for equal Rashba and Dresselhaus couplings. Beside these limiting cases, we study numerically the variance of the RKKY interaction in the presence of pure Rashba spin-orbit coupling. Our results are relevant for magnetic or nuclear moments embedded in III-V two-dimensional heterostructures or in contact with surface states of metals and metal alloys, which can display a sizable Rashba spin-orbit coupling.

88.  Spin susceptibility of interacting two-dimensional electrons in the presence of spin-orbit coupling
Robert Andrzej Zak, Dmitrii L. Maslov (Gainesville, FL), and Daniel Loss.
Phys. Rev. B 82, 115415 (2010); arXiv:1005.1913.

A long-range interaction via virtual particle-hole pairs between Fermi-liquid quasiparticles leads to a nonanalytic behavior of the spin susceptibility $\chi$ as a function of the temperature ($T$), magnetic field ($\mathbf{B}$), and wavenumber. In this paper, we study the effect of the Rashba spin-orbit interaction (SOI) on the nonanalytic behavior of $\chi$ for a two-dimensional electron liquid. Although the SOI breaks the $SU(2)$ symmetry, it does not eliminate nonanalyticity but rather makes it anisotropic: while the linear scaling of $\chi_{zz}$ with $T$ and $|\mathbf{B}|$ saturates at the energy scale set by the SOI, that of $\chi_{xx}$ ($=\chi_{yy}$) continues through this energy scale, until renormalization of the electron-electron interaction in the Cooper channel becomes important. We show that the Renormalization Group flow in the Cooper channel has a non-trivial fixed point, and study the consequences of this fixed point for the nonanalytic behavior of $\chi$. An immediate consequence of SOI-induced anisotropy in the nonanalytic behavior of $\chi$ is a possible instability of a second-order ferromagnetic quantum phase transition with respect to a first-order transition to an $XY$ ferromagnetic state.

89.  Tunable edge magnetism at graphene/graphane interfaces
Manuel J. Schmidt and Daniel Loss.
Phys. Rev. B 82, 085422 (2010); arXiv:1004.4363.

We study the magnetic properties of graphene edges and graphene/graphane interfaces under the influence of electrostatic gates. For this, an effective low-energy theory for the edge states, which is derived from the Hubbard model of the honeycomb lattice, is used. We first study the edge state model in a mean-field approximation for the Hubbard Hamiltonian and show that it reproduces the results of the extended 2D lattice theory. Quantum fluctuations around the mean-field theory of the effective one-dimensional model are treated by means of the bosonization technique in order to check the stability of the mean-field solution. We find that edge magnetism at graphene/graphane interfaces can be switched on and off by means of electrostatic gates. We describe a quantum phase transition between an ordinary and a ferromagnetic Luttinger liquid - a realization of itinerant one-dimensional ferromagnetism. This mechanism may provide means to experimentally discriminate between edge magnetism or disorder as the reason for a transport gap in very clean graphene nanoribbons.

90.  Spin-sel​ective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction
Bernd Braunecker, George I. Japaridze (Tbilisi, Georgia), Jelena Klinovaja, and Daniel Loss.
Phys. Rev. B 82, 045127 (2010); arXiv:1004.0467.

Interacting one-dimensional conductors with Rashba spin-orbit coupling are shown to exhibit a spin-sel​ective Peierls-like transition into a mixed spin-charge density wave state. The transition leads to a gap for one-half of the conducting modes, which is strongly enhanced by electron-electron interactions. The other half of the modes remains in a strongly renormalized gapless state and conducts opposite spins in opposite directions, thus providing a perfect spin filter. The transition is driven by magnetic field and by spin-orbit interactions. As an example we show for semiconducting quantum wires and carbon nanotubes that the gap induced by weak magnetic fields or intrinsic spin-orbit interactions can get renormalized by one order of magnitude up to 10-30 Kelvins.

91.  Cooper-Pair Injection into Topological Insulators
Koji Sato (UCLA), Daniel Loss, and Yaroslav Tserkovnyak (UCLA).
Phys. Rev. Lett. 105, 226401 (2010); arXiv:1003.4316.

We theoretically study tunneling of Cooper pairs (CP's) from a superconductor spanning a two-dimensional topological insulator strip into its helical edge states. The coherent low-energy electron-pair tunneling sets off positive nonlocal current cross-correlations along the edges, which reflect an interplay of two quantum-entanglement mechanisms. First of all, superconducting spin pairing dictates a CP partitioning into the helical edge liquids, which transport electrons in the opposite directions for opposite spin orientations. Luttinger-liquid (LL) correlations for the electron-density fluctuations are, furthermore, forcing paired electrons to enter into opposite insulator-strip edges, revealing CP spin entanglement in the inter-edge current correlations. At the same time, the LL behavior, in the absence of Fermi-liquid leads, fractionalizes electrons injected at a given edge into counter-propagating charge pulses carrying definite fractions of the elementary electron charge. The superconductivity as well as LL correlations thus introduce positive current cross-correlations, which reveal a wealth of information about both subsystems.

92.  The classical and quantum dynamics of the inhomogeneous Dicke model and its Ehrenfest time
Oleksandr Tsyplyatyev and Daniel Loss.
Phys. Rev. B 82, 024305 (2010); arXiv:1002.3932.

We show that in the few-excitation regime the classical and quantum time-evolution of the inhomogeneous Dicke model for N two-level systems coupled to a single boson mode agree for N>>1. In the presence of a single excitation only, the leading term in an 1/N-expansion of the classical equations of motion reproduces the result of the Schroedinger equation. For a small number of excitations, the numerical solutions of the classical and quantum problems become equal for N sufficiently large. By solving the Schroedinger equation exactly for two excitations and a particular inhomogeneity we obtain 1/N-corrections which lead to a significant difference between the classical and quantum solutions at a new time scale which we identify as an Ehrenferst time, given by tau_E=sqrt{N}, where sqrt{} is an effective coupling strength between the two-level systems and the boson.

93.  Spin electric effects in molecular antiferromagnets
Mircea Trif, Filippo Troiani (Modena), Dimitrije Stepanenko, and Daniel Loss.
Phys. Rev. B 82, 045429 (2010); arXiv:1001.3584.

Molecular nanomagnets show clear signatures of coherent behavior and have a wide variety of effective low-energy spin Hamiltonians suitable for encoding qubits and implementing spin-based quantum information processing. At the nanoscale, the preferred mechanism for the control of a quantum systems is the application of electric fields, which are strong, can be locally applied, and rapidly switched. In this work, we provide the theoretical tools for identifying molecular nanomagnets suitable for electric control. By group-theoretical symmetry analysis we find that the spin-electric coupling in triangular molecules is governed by the modification of the exchange interaction and is possible even in the absence of spin-orbit coupling. In pentagonal molecules the spin-electric coupling can exist only in the presence of spin-orbit interaction. This kind of coupling is allowed for both s=1/2 and s=3/2 spins at the magnetic centers. Within the Hubbard model, we find a relation between the spin-electric coupling and the properties of the chemical bonds in a molecule, suggesting that the best candidates for strong spin-electric coupling are molecules with nearly degenerate bond orbitals. We also investigate the possible experimental signatures of spin-electric coupling in nuclear magnetic resonance and electron spin resonance spectroscopy, as well as in the thermodynamic measurements of magnetization, electric polarization, and specific heat of the molecules.

94.  Free-induction decay and envelope modulations in a narrowed nuclear spin bath
W. A. Coish (Waterloo), Jan Fischer, and Daniel Loss.
Phys. Rev. B 81, 165315 (2010); arXiv:0911.4149.

We evaluate free-induction decay for the transverse components of a localized electron spin coupled to a bath of nuclear spins via the Fermi contact hyperfine interaction. Our perturbative treatment is valid for special (narrowed) bath initial conditions and when the Zeeman energy of the electron $b$ exceeds the total hyperfine coupling constant $A$: $b>A$. Using one unified and systematic method, we recover previous results reported at short and long times using different techniques. We find a new and unexpected modulation of the free-induction-decay envelope, which is present even for a purely isotropic hyperfine interaction without spin echoes and for a single nuclear species. We give sub-leading corrections to the decoherence rate, and show that, in general, the decoherence rate has a non-monotonic dependence on electron Zeeman splitting, leading to a pronounced maximum. These results illustrate the limitations of methods that make use of leading-order effective Hamiltonians and re-exponentiation of short-time expansions for a strongly-interacting system with non-Markovian (history-dependent) dynamics.

95.  One-step multi-qubit GHZ state generation in a circuit QED system
Ying-Dan Wang, Stefano Chesi, Daniel Loss, and Christoph Bruder.
Phys. Rev. B 81, 104524 (2010); arXiv:0911.1396.

We propose a one-step scheme to generate GHZ states for superconducting flux qubits or charge qubits in a circuit QED setup. The GHZ state can be produced within the coherence time of the multi-qubit system. Our scheme is independent of the initial state of the transmission line resonator and works in the presence of higher harmonic modes. Our analysis also shows that the scheme is robust to various operation errors and environmental noise.

96.  Edge states and enhanced spin-orbit interaction at graphene/graphane interfaces
Manuel J. Schmidt and Daniel Loss.
Phys. Rev. B 81, 165439 (2010); arXiv:0910.5333.

We study interfaces between graphene and graphane. If the interface is oriented along a zigzag direction, edge states are found which exhibit a strong amplification of effects related to the spin-orbit interaction. The enhanced spin splitting of the edge states allows a conversion between valley polarization and spin polarization at temperatures near one Kelvin. We show that these edge states give rise to quantum spin and/or valley Hall effects.

97.  Spin Accumulation in Diffusive Conductors with Rashba and Dresselhaus Spin-Orbit Interaction
Mathias Duckheim, Daniel Loss, Matthias Scheid (Regensburg), Klaus Richter (Regensburg), Inanc Adagideli (Istanbul), and Philippe Jacquod (Tucson).
Physical Review B 81 085303 (2010); arXiv:0909.4253.

We calculate the electrically induced spin accumulation in diffusive systems due to both Rashba (with strength $\alpha)$ and Dresselhaus (with strength $\beta)$ spin-orbit interaction. Using a diffusion equation approach we find that magnetoelectric effects disappear and that there is thus no spin accumulation when both interactions have the same strength, $\alpha=\pm \beta$. In thermodynamically large systems, the finite spin accumulation predicted by Chaplik, Entin and Magarill, [Physica E 13, 744 (2002)] and by Trushin and Schliemann [Phys. Rev. B 75, 155323 (2007)] is recovered an infinitesimally small distance away from the singular point $\alpha=\pm \beta$. We show however that the singularity is broadened and that the suppression of spin accumulation becomes physically relevant (i) in finite-sized systems of size $L$, (ii) in the presence of a cubic Dresselhaus interaction of strength $\gamma$, or (iii) for finite frequency measurements. We obtain the parametric range over which the magnetoelectric effect is suppressed in these three instances as (i) $|\alpha|-|\beta| \lesssim 1/mL$, (ii)$|\alpha|-|\beta| \lesssim \gamma p\rm F^2$, and (iii) $|\alpha|-|\beta| \lesssiM \sqrt{\omega/m p\rm F\ell}$ with $\ell$ the elastic mean free path and $p\rm F$ the Fermi momentum. We attribute the absence of spin accumulation close to $\alpha=\pm \beta$ to the underlying U (1) symmetry. We illustrate and confirm our predictions numerically.

98.  Dynamic spin-Hall effect and driven spin helix for linear spin-orbit interactions
Mathias Duckheim, Dmitrii L. Maslov (Gainesville, FL), and Daniel Loss.
Phys. Rev. B 80, 235327 (2009); arXiv:0909.1892.

We derive boundary conditions for the electrically induced spin accumulation in a finite 2D semiconductor channel. While for DC electric fields these boundary conditions sel​ect spatially constant spin profiles equivalent to a vanishing spin-Hall effect, we show that an in-plane ac electric field results in a non-zero ac spin-Hall effect, i.e., it generates a spatially non-uniform out-of-plane polarization even for linear intrinsic spin-orbit interactions. Analyzing different geometries in [001] and [110]-grown quantum wells, we find that although this out-of-plane polarization is typically confined to within a few spin-orbit lengths from the channel edges, it is also possible to generate spatially oscillating spin profiles which extend over the whole channel. The latter is due to the excitation of a driven spin-helix mode in the transverse direction of the channel. We show that while finite frequencies suppress this mode, it can be amplified by a magnetic field tuned to resonance with the frequency of the electric field. In this case, finite size effects at equal strengths of Rashba- and Dresselhaus SOI lead to an enhancement of the magnitude of this helix mode. We comment on the relation between spin currents and boundary conditions.

99.  A Self-Correcting Quantum Memory in a Thermal Environment
Stefano Chesi, Beat Röthlisberger, and Daniel Loss.
Phys. Rev. A 82, 022305 (2010); arXiv:0908.4264.

The ability to store information is of fundamental importance to any computer, be it classical or quantum. To identify systems for quantum memories, which rely, analogously to classical memories, on passive error protection (“self-correction”), is of greatest interest in quantum information science. While systems with topological ground states have been considered to be promising candidates, a large class of them was recently proven unstable against thermal fluctuations. Here, we propose two-dimensional (2D) spin models unaffected by this result. Specifically, we introduce repulsive long-range interactions in the toric code and establish a memory lifetime polynomially increasing with the system size. This remarkable stability is shown to originate directly from the repulsive long-range nature of the interactions. We study the time dynamics of the quantum memory in terms of diffusing anyons and support our analytical results with extensive numerical simulations. Our findings demonstrate that self-correcting quantum memories can exist in 2D at finite temperatures.

100.  Holonomic Quantum Computation with Electron Spins in Quantum Dots
Vitaly N. Golovach (LMU Munich), Massoud Borhani (Buffalo), and Daniel Loss.
Phys. Rev. A 81, 022315 (2010); arXiv:0908.2800.

With the help of the spin-orbit interaction, we propose a scheme to perform holonomic single qubit gates on the electron spin confined to a quantum dot. The manipulation is done in the absence (or presence) of an applied magnetic field. By adiabatic changing the position of the confinement potential, one can rotate the spin state of the electron around the Bloch sphere in semiconductor heterostructures. The dynamics of the system is equivalent to employing an effective non-Abelian gauge potential whose structure depends on the type of the spin-orbit interaction. As an example, we find an analytic expression for the electron spin dynamics when the dot is moved around a circular path (with radius R) on the two dimensional electron gas (2DEG), and show that all single qubit gates can be realized by tuning the radius and orientation of the circular paths. Moreover, using the Heisenberg exchange interaction, we demonstrate how one can generate two-qubit gates by bringing two quantum dots near each other, yielding a scalable scheme to perform quantum computing on arbitrary N qubits. This proposal shows a way of realizing holonomic quantum computers in solid-state systems.

101.  Nuclear magnetism and electron order in interacting one-dimensional conductors
Bernd Braunecker, Pascal Simon (Orsay, Paris), and Daniel Loss.
Phys. Rev. B 80, 165119 (2009); arXiv:0908.0904.

The interaction between localized magnetic moments and the electrons of a one-dimensional conductor can lead to an ordered phase in which the magnetic moments and the electrons are tightly bound to each other. We show here that this occurs when a lattice of nuclear spins is embedded in a Luttinger liquid. Experimentally available examples of such a system are single wall carbon nanotubes grown entirely from 13C and GaAs-based quantum wires. In these systems the hyperfine interaction between the nuclear spin and the conduction electron spin is very weak, yet it triggers a strong feedback reaction that results in an ordered phase consisting of a nuclear helimagnet that is inseparably bound to an electronic density wave combining charge and spin degrees of freedom. This effect can be interpreted as a strong renormalization of the nuclear Overhauser field and is a unique signature of Luttinger liquid physics. Through the feedback the order persists up into the millikelvin range. A particular signature is the reduction of the electric conductance by the universal factor 2.

102.  Spin Hall effect due to inter-subband-induced spin-orbit interaction in symmetric quantum well
Minchul Lee (Yongin, S. Korea), Marco O. Hachiya (Sao Carlos, Brazil), E. Bernardes (Sao Carlos, Brazil), J. Carlos Egues (Sao Carlos, Brazil), and Daniel Loss.
Phys. Rev. B 80, 155314 (2009); arXiv:0907.4078.

We investigate the intrinsic spin Hall effect in two-dimensional electron gases in quantum wells with two subbands, where a new intersubband-induced spin-orbit coupling is operative. The bulk spin Hall conductivity $\sigma^zxy$ is calculated in the ballistic limit within the standard Kubo formalism in the presence of a magnetic field $B$ and is found to remain finite in the B=0 limit, as long as only the lowest subband is occupied. Our calculated $\sigma^zxy$ exhibits a non-monotonic behavior and can change its sign as the Fermi energy (the carrier areal density $n2D$) is varied between the subband edges. We determine the magnitude of $\sigma^zxy$ for realistic InSb quantum wells by performing a self-consistent calculation of the intersubband-induced spin-orbit coupling.

103.  Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes
Stefano Chesi, Daniel Loss, Sergey Bravyi (IBM Yorktown), and Barbara M. Terhal (IBM Yorktown).
New J. Phys. 12 025013 (2010); arXiv:0907.2807.

We discuss and review several thermodynamic criteria that have been introduced to characterize the thermal stability of a self-correcting quantum memory. We first examine the use of symmetry-breaking fields in analyzing the properties of self-correcting quantum memories in the thermodynamic limit: we show that the thermal expectation values of all logical operators vanish for any stabilizer and any subsystem code in any spatial dimension. On the positive side, we generalize the results in [R. Alicki et al., arXiv:0811.0033] to obtain a general upper bound on the relaxation rate of a quantum memory at nonzero temperature, assuming that the quantum memory interacts via a Markovian master equation with a thermal bath. This upper bound is applicable to quantum memories based on either stabilizer or subsystem codes.

104.  Dicke model: entanglement as a finite size effect
Oleksandr Tsyplyatyev and Daniel Loss.
J. Phys.: Conf. Ser. 193, 012134(2009); arXiv:0907.2553v1.

We analyze Dicke model at zero temperature by matrix diagonalization to determine the entanglement in the ground state. In the infinite system limit the mean field approximation predicts a quantum phase transition from a non-interacting state to a Bose-Einstein condensate at a threshold coupling. We show that in a finite system the spin part of the ground state is a bipartite entangled state, which can be tested by probing two parts of the spin system separately, but only in a narrow regime around the threshold coupling. Around the resonance, the size of this regime is inversely proportional to the number of spins and shrinks down to zero for infinite systems. This spin entanglement is a non-perturbative effect and is also missed by the mean-field approximation.

105.  Quantum Computing with Electron Spins in Quantum Dots
Robert Andrzej Żak, Beat Röhlisberger, Stefano Chesi, and Daniel Loss.
Lecture notes for Course CLXXI "Quantum Coherence in Solid State Systems" Int. School of Physics "Enrico Fermi", Varenna, July 2008.
Rivista del Nuovo Cimento 033 (Issue 07), 345-399 (2010); arXiv:0906.4045.

Several topics on the implementation of spin qubits in quantum dots are reviewed. We first provide an introduction to the standard model of quantum computing and the basic criteria for its realization. Other alternative formulations such as measurement-based and adiabatic quantum computing are briefly discussed. We then focus on spin qubits in single and double GaAs electron quantum dots and review recent experimental achievements with respect to initialization, coherent manipulation and readout of the spin states. We extensively discuss the problem of decoherence in this system, with particular emphasis on its theoretical treatment and possible ways to overcome it.

106.  Hyperfine interaction and electron-spin decoherence in graphene and carbon nanotube quantum dots
Jan Fischer, Bjoern Trauzettel (Wuerzburg), and Daniel Loss.
Phys. Rev. B 80, 155401 (2009); arXiv:0906.2800.

We analytically calculate the nuclear-spin interactions of a single electron confined to a carbon nanotube or graphene quantum dot. While the conduction-band states in graphene are p-type, the accordant states in a carbon nanotube are sp-hybridized due to curvature. This leads to an interesting interplay between isotropic and anisotropic hyperfine interactions. By using only analytical methods, we are able to show how the interaction strength depends on important physical parameters, such as curvature and isotope abundances. We show that for the investigated carbon structures, the 13C hyperfine coupling strength is less than 1 mu-eV, and that the associated electron-spin decoherence time can be expected to be as long as several tens of microseconds, depending on the abundance of spin-carrying 13C nuclei. Furthermore, we find an unusual hyperfine-induced alignment of the 13C nuclear spins in nanotubes of any chirality.

107.  Dealing with Decoherence
Jan Fischer and Daniel Loss.
Perspective article
Science 324, 1277 (2009)

The dream of building computers that work according to the rules of quantum mechanics has strongly driven research over the past decade in many fields of basic and applied sciences, including physics, chemistry, and computer science. About 10 years ago, it was shown mathematically that the direct use of quantum phenomena such as interference and entanglement could crucially speed up data searching and prime factorization for encryption. To turn quantum computers into reality, however, many issues in engineering and in basic physics need to be addressed.

108.  Numerical evaluation of convex-roof entanglement measures with applications to spin rings
Beat Röthlisberger, Jörg Lehmann (ABB Baden), and Daniel Loss.
Phys. Rev. A 80, 042301 (2009); arXiv:0905.3106.

We present two ready-to-use numerical algorithms to evaluate convex-roof extensions of arbitrary pure-state entanglement monotones. Their implementation leaves the user merely with the task of calculating derivatives of the respective pure-state measure. We provide numerical tests of the algorithms and demonstrate their good convergence properties. We further employ them in order to investigate the entanglement in particular few-spins systems at finite temperature. Namely, we consider ferromagnetic Heisenberg exchange-coupled spin-1/2 rings subject to an inhomogeneous in-plane field geometry obeying full rotational symmetry around the axis perpendicular to the ring through its center. We demonstrate that highly entangled states can be obtained in these systems at sufficiently low temperatures and by tuning the strength of a magnetic field configuration to an optimal value which is identified numerically.

109.  Nanotubes: Carbon surprises again
Björn Trauzettel (Wuerzburg) and Daniel Loss.
News and Views
Nature Physics 5, 317 (2009)

Experiments in 13C nanotubes reveal surprisingly strong nuclear spin effects that, if properly harnessed, could provide a mechanism for manipulation and storage of quantum information.

110.  Spin interactions, relaxation and decoherence in quantum dots
Jan Fischer, Mircea Trif, W. A. Coish (Waterloo), and Daniel Loss.
Solid State Communications 149, 1443 (2009); arXiv:0903.0527.

We review recent studies on spin decoherence of electrons and holes in quasi-two-dimensional quantum dots, as well as electron-spin relaxation in nanowire quantum dots. The spins of confined electrons and holes are considered major candidates for the realization of quantum information storage and processing devices, provided that sufficently long coherence and relaxation times can be achieved. The results presented here indicate that this prerequisite might be realized in both electron and hole quantum dots, taking one large step towards quantum computation with spin qubits.

111.  Spin orbit-induced anisotropic conductivity of a disordered 2DEG
Oleg Chalaev and Daniel Loss.
Phys. Rev. B 80, 035305 (2009); arXiv:0902.3277.

We present a semi-automated computer-assisted method to generate and calculate diagrams in the disorder averaging approach to disordered 2D conductors with intrinsic spin-orbit interaction (SOI). As an application, we calculate the effect of the SOI on the charge conductivity for disordered 2D systems and rings in the presence of Rashba and Dresselhaus SOI. In an infinite-size 2D system, anisotropic corrections to the conductivity tensor arise due to phase-coherence and the interplay of Rashba and Dresselhaus SOI. The effect is more pronounced in the quasi-onedimensional case, where the conductivity becomes anisotropic already in the presence of only one type of SOI. The anisotropy further increases if the time-reversal symmetry of the Hamiltonian is broken.

112.  Relaxation of hole spins in quantum dots via two-phonon processes
Mircea Trif, Pascal Simon (Orsay), and Daniel Loss.
Phys. Rev. Lett. 103, 106601 (2009); arXiv:0902.2457.

We investigate theoretically spin relaxation in heavy hole quantum dots in low external magnetic fields. We demonstrate that two-phonon processes and spin-orbit interaction are experimentally relevant and provide an explanation for the recently observed saturation of the spin relaxation rate in heavy hole quantum dots with vanishing magnetic fields. We propose further experiments to identify the relevant spin relaxation mechanisms in low magnetic fields.

113.  Undoing a quantum measurement
Christoph Bruder and Daniel Loss.
Physics 1, 34 (2008)

Quantum measurements are conventionally thought of as irretrievably "collapsing" a wave function to the observed state. However, experiments with superconducting qubits show that the partial collapse resulting from a weak continuous measurement can be restored.

114.  Interference of heavy holes in an Aharonov-Bohm ring
Dimitrije Stepanenko, Minchul Lee (Marseille), Guido Burkard (Konstanz), and Daniel Loss.
Phys. Rev. B 79, 235301 (2009); arXiv:0811.4566.

We study the coherent transport of heavy holes through a one-dimensional ring in the presence of spin-orbit coupling. Spin-orbit interaction of holes, cubic in the in-plane components of momentum, gives rise to an angular momentum dependent spin texture of the eigenstates and influences transport. We analyze the dependence of the resulting differential conductance of the ring on hole polarization of the leads and the signature of the textures in the Aharonov-Bohm oscillations when the ring is in a perpendicular magnetic field. We find that the polarization-resolved conductance reveals whether the dominant spin-orbit coupling is of Dresselhaus or Rashba type, and that the cubic spin-orbit coupling can be distinguished from the conventional linear coupling by observing the four-peak structure in the Aharonov-Bohm oscillations.

115.  Exact quantum dynamics of the inhomogeneous Dicke model
Oleksandr Tsyplyatyev and Daniel Loss.
Phys. Rev. A 80, 023803 (2009); arXiv:0811.2386.

We study the time dynamics of a single boson coupled to a bath of two-level systems (spins 1/2) with different excitation energies, described by an inhomogeneous Dicke model. Solving the time-dependent Schroedinger equation exactly we find that at resonance the boson decays in time to an oscillatory state characterized by a single Rabi frequency. In the limit of small inhomogeneity, the decay is suppressed and exhibits a complex (mainly Gaussian-like) behavior, whereas the decay is complete and of exponential form in the opposite limit. For intermediate inhomogeneity, the boson decay is partial and governed by a combination of exponential and power laws.

116.  Momentum dependence of the spin-susceptibility in two dimensions: nonanalytic corrections in the Cooper channel
Stefano Chesi, Robert Andrzej Żak, Pascal Simon (Orsay), and Daniel Loss.
Phys. Rev. B 79, 115445 (2009); arXiv:0811.0996.

We consider the effect of rescattering of pairs of quasiparticles in the Cooper channel resulting in the strong renormalization of second order corrections to the spin susceptibility in a two-dimensional electron system. We use the Fourier expansion of the scattering potential in the vicinity of the Fermi surface to find that each harmonic becomes renormalized independently. Since some of those harmonics are negative, the slope of the spin susceptibility is bound to be negative at small momenta, in contrast to the lowest order perturbation theory result, which predicts a positive slope. We present in detail an effective method to calculate diagrammatically corrections to the spin susceptibility to infinite order.

117.  Semiconductor spintronics: Snapshots of spins separating
Mathias Duckheim and Daniel Loss.
News and Views
Nature Physics 4, 836-837 (2008)

Theories of the spin Hall effect suggest that spin currents generated by electric fields accumulate spin polarization at the sample edges. Now an experiment has observed this conversion in real time.

118.  Magnetic Order in Kondo-Lattice Systems due to Electron-Electron Interactions
Bernd Braunecker, Pascal Simon (Orsay), and Daniel Loss.
AIP Conf. Proc. 1074, 62 (2008); arXiv:0808.4063.

The hyperfine interaction between the electron spin and the nuclear spins is one of the main sources of decoherence for spin qubits when the nuclear spins are disordered. An ordering of the latter largely suppresses this source of decoherence. Here we show that such an ordering can occur through a thermodynamic phase transition in two-dimensional (2D) Kondo-lattice type systems. We specifically focus on nuclear spins embedded in a 2D electron gas. The nuclear spins interact with each other through the RKKY interaction, which is carried by the electron gas. We show that a nuclear magnetic order at finite temperature relies on the anomalous behavior of the 2D static electron spin susceptibility due to electron-electron interactions. This provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. We discuss the conditions for nuclear magnetism, and show that the associated Curie temperature increases with the electron-electron interactions and may reach up into the millikelvin regime. The further reduction of dimensionality to one dimension is shortly discussed.

119.  Nuclear Magnetism and Electronic Order in 13C Nanotubes
Bernd Braunecker, Pascal Simon, and Daniel Loss.
Phys. Rev. Lett. 102, 116403 (2009);

Nuclear spins embedded in correlated metals offer an ideal platform to investigate the effect of electron-electron interactions on magnetism of localized moments. Here we focus on a one-dimensional realization of such a system: Single wall carbon nanotubes grown entirely from the 13C isotope. With this isotope the nanotube forms a nuclear spin lattice which couples through the hyperfine interaction to a Luttinger liquid if the nanotube is in the metallic regime. Even though the hyperfine interaction is very weak, the system is driven into an ordered phase which combines electron and nuclear spin degrees of freedom. This phase persists up into the millikelvin regime and leads to a reduction of the nanotube conductance by a universal factor of 2, allowing for an experimental detection by standard transport measurements.

120.  Spin Stiffness of Mesoscopic Quantum Antiferromagnets
Daniel Loss and Dmitrii L. Maslov.
Phys. Rev. Lett. 74, 178 (1995)

We study the spin stiffness of a one-dimensional quantum antiferromagnet in the whole range of system sizes L and temperatures T. We show that for integer and half-odd integer spin cases the stiffness differs fundamentally in its L and T dependences, and that in the latter case the stiffness exhibits a striking dependence on the parity of the number of sites. Integer spin chains are treated in terms of the nonlinear sigma model, while half-odd integer spin chains are discussed in a renormalization group approach leading to a Luttinger liquid with Aharonov-Bohm-type boundary conditions.

121.  Intersubband-induced spin-orbit interaction in quantum wells
Rafael S. Calsaverini, Esmerindo Bernardes, J. Carlos Egues, and Daniel Loss.
Phys. Rev. B 78, 155313 (2008); arXiv:0807.0771.

Recently, we have found an additional spin-orbit (SO) interaction in quantum wells with two subbands [Phys. Rev. Lett. 99, 076603 (2007)]. This new SO term is non-zero even in symmetric geometries, as it arises from the intersubband coupling between confined states of distinct parities, and its strength is comparable to that of the ordinary Rashba. Starting from the $8 \times 8$ Kane model, here we present a detailed derivation of this new SO Hamiltonian and the corresponding SO coupling. In addition, within the self-consistent Hartree approximation, we calculate the strength of this new SO coupling for realistic symmetric modulation-doped wells with two subbands. We consider gated structures with either a constant areal electron density or a constant chemical potential. In the parameter range studied, both models give similar results. By considering the effects of an external applied bias, which breaks the structural inversion symmetry of the wells, we also calculate the strength of the resulting induced Rashba couplings within each subband. Interestingly, we find that for double wells the Rashba couplings for the first and second subbands interchange signs abruptly across the zero bias, while the intersubband SO coupling exhibits a resonant behavior near this symmetric configuration. For completeness we also determine the strength of the Dresselhaus couplings and find them essentially constant as function of the applied bias.

122.  Spin decoherence of a heavy hole coupled to nuclear spins in a quantum dot
Jan Fischer, W. A. Coish (Waterloo), D. V. Bulaev (Chernogolovka), and Daniel Loss.
Phys. Rev. B 78, 155329 (2008); arXiv:0807.0368.

We theoretically study the interaction of a heavy hole with nuclear spins in a quasi-two-dimensional III-V semiconductor quantum dot and the resulting dephasing of heavy-hole spin states. It has frequently been stated in the literature that heavy holes have a negligible interaction with nuclear spins. We show that this is not the case. In contrast, the interaction can be rather strong and will be the dominant source of decoherence in some cases. We also show that the form of the interaction is Ising-like, resulting in unique and interesting decoherence properties, which might provide a crucial advantage to using dot-confined hole spins for quantum information processing, as compared to electron spins.

123.  Mesoscopic fluctuations in the spin-electric susceptibility due to Rashba spin-orbit interaction
Mathias Duckheim and Daniel Loss.
Phys. Rev. Lett. 101, 226602 (2008); arXiv:0805.4143.

We investigate mesoscopic fluctuations in the spin polarization generated by a static electric field and by Rashba spin-orbit interaction in a disordered 2D electron gas. In a diagrammatic approach we find that the out-of-plane polarization -- while being zero for self-averaging systems -- exhibits large sample-to-sample fluctuations which are shown to be well within experimental reach. We evaluate the disorder-averaged variance of the susceptibility and find its dependence on magnetic field, spin-orbit interaction, dephasing, and chemical potential difference.

124.  Spin-Electric Coupling in Molecular Magnets
Mircea Trif, Filippo Troiani (Modena), Dimitrije Stepanenko, and Daniel Loss.
Phys. Rev. Lett. 101, 217201 (2008); arXiv:0805.1158.

We study the triangular antiferromagnet Cu$_3$ in external electric fields, using symmetry group arguments and a Hubbard model approach. We identify a spin-electric coupling caused by an interplay between spin exchange, spin-orbit interaction, and the chirality of the underlying spin texture of the molecular magnet. This coupling allows for the electric control of the spin (qubit) states, e.g. by using an STM tip or a microwave cavity. We propose an experimental test for identifying molecular magnets exhibiting spin-electric effects.

125.  AC magnetization transport and power absorption in non-itinerant spin chains
Bjoern Trauzettel (Wuerzburg), Pascal Simon (Grenoble), and Daniel Loss.
Phys. Rev. Lett. 101, 017202 (2008); arXiv:0804.3697.

We investigate the ac transport of magnetization in non-itinerant quantum systems such as spin chains described by the XXZ Hamiltonian. Using linear response theory, we calculate the ac magnetization current and the power absorption of such magnetic systems. Remarkably, the difference in the exchange interaction of the spin chain itself and the bulk magnets (i.e. the magnetization reservoirs), to which the spin chain is coupled, strongly influences the absorbed power of the system. This feature can be used in future spintronic devices to control power dissipation. Our analysis allows to make quantitative predictions about the power absorption and we show that magnetic systems are superior to their electronic counter parts.

126.  Quantum Hall ferromagnetic states and spin-orbit interactions in the fractional regime
Stefano Chesi and Daniel Loss.
Phys. Rev. Lett. 101, 146803 (2008); arXiv:0804.3332.

The competition between the Zeeman energy and the Rashba and Dresselhaus spin-orbit couplings is studied for fractional quantum Hall states by including correlation effects. A transition of the direction of the spin-polarization is predicted at specific values of the Zeeman energy. We show that these values can be expressed in terms of the pair-correlation function, which thus provides a way to obtain experimental access to the corresponding ground state. As specific examples, we consider the Laughlin wavefunctions and the 5/2-Pfaffian state and find indications of non-analytic features around the fractional states. We also include effects of the nuclear bath, becoming relevant in the mK-regime.

127.  Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions
Sergey Bravyi, David P. DiVincenzo, Daniel Loss, and Barbara M. Terhal.
Phys. Rev. Lett. 101, 070503 (2008); arXiv:0803.2686; News & Views, M.M. Wolf, Nature Physics 4, 834 (2008).

We show how to map a given n-qubit target Hamiltonian with bounded-strength k-body interactions onto a simulator Hamiltonian with two-body interactions, such that the ground-state energy of the target and the simulator Hamiltonians are the same up to an extensive error O(epsilon n) for arbitrary small epsilon. The strength of interactions in the simulator Hamiltonian depends on epsilon and k but does not depend on n. We accomplish this reduction using a new way of deriving an effective low-energy Hamiltonian which relies on the Schrieffer-Wolff transformation of many-body physics.

128.  Nuclear spin dynamics and Zeno effect in quantum dots and defect centers
D. Klauser, W. A. Coish (Waterloo), and Daniel Loss.
Phys. Rev. B 78, 205301 (2008); arXiv:0802.2463.

We analyze nuclear spin dynamics in quantum dots and defect centers with a bound electron under electron-mediated coupling between nuclear spins due to the hyperfine interaction ("J-coupling" in NMR). Our analysis shows that the Overhauser field generated by the nuclei at the position of the electron has short-time dynamics quadratic in time for an initial nuclear spin state without transverse coherence. The quadratic short-time behavior allows for an extension of the Overhauser field lifetime through a sequence of projective measurements (quantum Zeno effect). We analyze the requirements on the repetition rate of measurements and the measurement accuracy to achieve such an effect. Further, we calculate the long-time behavior of the Overhauser field for effective electron Zeeman splittings larger than the hyperfine coupling strength and find, both in a Dyson series expansion and a generalized master equation approach, that for a nuclear spin system with a sufficiently smooth polarization the electron-mediated interaction alone leads only to a partial decay of the Overhauser field by an amount on the order of the inverse number of nuclear spins interacting with the electron.

129.  Spin-orbit interaction and anomalous spin relaxation in carbon nanotube quantum dots
Denis V. Bulaev, Bjoern Trauzettel (Wuerzburg), and Daniel Loss.
Phys. Rev. B 77, 235301 (2008); arXiv:0712.3767 [cond-mat.mes-hall].

We study spin relaxation and decoherence caused by electron-lattice and spin-orbit interaction and predict striking effects induced by magnetic fields B. For particular values of B, destructive interference occurs resulting in ultralong spin relaxation times T1 exceeding tens of seconds. For small phonon frequencies \omega, we find a 1/\sqrt{\omega} spin-phonon noise spectrum --a novel dissipation channel for spins in quantum dots --which can reduce T1 by many orders of magnitude. We show that nanotubes exhibit zero-field level splitting caused by spin-orbit interaction. This enables an all-electrical and phase-coherent control of spin.

130.  Exponential decay in a spin bath
W. A. Coish (Waterloo), Jan Fischer, and Daniel Loss.
Phys. Rev. B 77, 125329 (2008); arXiv:0710.3762 [cond-mat.mes-hall].

We show that the coherence of an electron spin interacting with a bath of nuclear spins can exhibit a well-defined purely exponential decay for special (`narrowed') bath initial conditions in the presence of a strong applied magnetic field. This is in contrast to the typical case, where spin-bath dynamics have been investigated in the non-Markovian limit, giving super-exponential or power-law decay of correlation functions. We calculate the relevant decoherence time T_2 explicitly for free-induction decay and find a simple expression with dependence on bath polarization, magnetic field, the shape of the electron wave function, dimensionality, total nuclear spin I, and isotopic concentration for experimentally relevant heteronuclear spin systems.

131.  Magnetic Ordering of Nuclear Spins in an Interacting 2D Electron Gas
Pascal Simon, Bernd Braunecker, and Daniel Loss.
Phys. Rev. B 77, 045108 (2008); arXiv:0709.0164.

We investigate the magnetic behavior of nuclear spins embedded in a 2D interacting electron gas using a Kondo lattice model description. We derive an effective magnetic Hamiltonian for the nuclear spins which is of the RKKY type and where the interactions between the nuclear spins are strongly modified by the electron-electron interactions. We show that the nuclear magnetic ordering at finite temperature relies on the (anomalous) behavior of the 2D static electron spin susceptibility, and thus provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. Using various perturbative and non-perturbative approximation schemes in order to establish the general shape of the electron spin susceptibility as function of its wave vector, we show that the nuclear spins locally order ferromagnetically, and that this ordering can become global in certain regimes of interest. We demonstrate that the associated Curie temperature for the nuclear system increases with the electron-electron interactions up to the millikelvin range.

132.  Anisotropic conductivity of disordered 2DEGs due to spin-orbit interactions
Oleg Chalaev and Daniel Loss.
Phys. Rev. B 77, 115352 (2008); arXiv:0708.3504.

We show that the conductivity tensor of a disordered two-dimensional electron gas becomes anisotropic in the presence of both Rashba and Dresselhaus spin-orbit interactions (SOI). This anisotropy is a mesoscopic effect and vanishes with vanishing charge dephasing time. Using a diagrammatic approach including zero, one, and two-loop diagrams, we show that a consistent calculation needs to go beyond a Boltzmann equation approach. In the absence of charge dephasing and for zero frequency, a finite anisotropy \sigmaxy~ e^2/lhpf arises even for infinitesimal SOI.

133.  Spin dynamics in InAs-nanowire quantum-dots coupled to a transmission line
Mircea Trif, Vitaly N. Golovach (LMU Munich), and Daniel Loss.
Phys. Rev. B 77, 045434 (2008); arXiv:0708.2091v1.

We study theoretically electron spins in nanowire quantum dots placed inside a transmission line resonator. Because of the spin-orbit interaction, the spins couple to the electric component of the resonator electromagnetic field and enable coherent manipulation, storage, and read-out of quantum information in an all-electrical fashion. Coupling between distant quantum-dot spins, in one and the same or different nanowires, can be efficiently performed via the resonator mode either in real time or through virtual processes. For the latter case we derive an effective spin-entangling interaction and suggest means to turn it on and off. We consider both transverse and longitudinal types of nanowire quantum-dots and compare their manipulation timescales against the spin relaxation times. For this, we evaluate the rates for spin relaxation induced by the nanowire vibrations (phonons) and show that, as a result of phonon confinement in the nanowire, this rate is a strongly varying function of the spin operation frequency and thus can be drastically reduced compared to lateral quantum dots in GaAs. Our scheme is a step forward to the formation of hybrid structures where qubits of different nature can be integrated in a single device.

134.  CNOT for Multi-Particle Qubits and Topological Quantum Computation based on Parity Measurements
Oded Zilberberg, Bernd Braunecker, and Daniel Loss.
Phys. Rev. A 77, 012327 (2008); arXiv:0708.1062v1.

We discuss a measurement-based implementation of a Controlled-NOT (CNOT) quantum gate. Such a gate has recently been discussed for free electron qubits. Here we extend this scheme for qubits encoded in product states of two (or more) spins-1/2 or in equivalent systems. The key to such an extension is to find a feasible qubit-parity meter. We present a general scheme for reducing this meter to a local spin-parity measurement performed on two spins, one from each qubit. Two possible realizations of a multi-particle CNOT are further discussed: Electron spins in double quantum dots in the singlet-triplet encoding and nu=5/2 Ising non-Abelian anyons using topological quantum computation braiding operations and nontopological charge measurements.

135.  Polynomial-time algorithm for simulation of weakly interacting quantum spin systems
Sergey Bravyi (IBM Yorktown), David DiVincenzo (IBM Yorktown), and Daniel Loss.
Commun. Math. Phys. 284, 481 (2008); arXiv:0707.1894.

We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial in the number of qubits and the required precision. Specifically, we consider Hamiltonians of the form $H=H_0+\epsilon V$, where H_0 describes non-interacting qubits, V is a perturbation that involves arbitrary two-qubit interactions on a graph of bounded degree, and $\epsilon$ is a small parameter. The algorithm works if $|\epsilon|$ is below a certain threshold value that depends only upon the spectral gap of H_0, the maximal degree of the graph, and the maximal norm of the two-qubit interactions. The main technical ingredient of the algorithm is a generalized Kirkwood-Thomas ansatz for the ground state. The parameters of the ansatz are computed using perturbative expansions in powers of $\epsilon$. Our algorithm is closely related to the coupled cluster method used in quantum chemistry.

136.  Electron and hole spin dynamics and decoherence in quantum dots
D. Klauser, D. V. Bulaev, W. A. Coish, and Daniel Loss.
Chapter 10 in Semiconductor Quantum Bits, eds. O. Benson and F. Henneberger, World Scientific, 2008. ISBN 978-981-4241-05-2

In this article we review our work on the dynamics and decoherence of electron and hole spins in single and double quantum dots. The first part, on electron spins, focuses on decoherence induced via the hyperfine interaction while the second part covers decoherence and relaxation of heavy-hole spins due to spin-orbit interaction as well as the manipulation of heavy-hole spin using electric dipole spin resonance.

137.  Theory of spin qubits in nanostructures
B. Trauzettel, M. Borhani, M. Trif, and D. Loss.
J. Phys. Soc. Jpn. 77 (2008) 031012; arXiv:0707.4622v1.

We review recent advances on the theory of spin qubits in nanostructures. We focus on four sel​ected topics. First, we show how to form spin qubits in the new and promising material graphene. Afterwards, we discuss spin relaxation and decoherence in quantum dots. In particular, we demonstrate how charge fluctations in the surrounding environment cause spin decay via spin--orbit coupling. We then turn to a brief overview of how one can use electron-dipole spin resonance (EDSR) to perform single spin rotations in quantum dots using an oscillating electric field. The final topic we cover is the spin-spin coupling via spin-orbit interaction which is an alternative to the usual spin-spin coupling via the Heisenberg exchange interaction.

138.  Highly Entangled Ground States in Tripartite Qubit Systems
Beat Röthlisberger, Jörg Lehmann, D. S. Saraga, Philipp Traber, and Daniel Loss.
Phys. Rev. Lett. 100, 100502 (2008); arXiv:0705.1710v1 [quant-ph].

We investigate the creation of highly entangled ground states in a system of three exchange-coupled qubits arranged in a ring geometry. Suitable magnetic field configurations yielding approximate GHZ and exact W ground states are identified. The entanglement in the system is studied at finite temperature in terms of the mixed-state tangle tau. By adapting a steepest-descent optimization algorithm we demonstrate that tau can be evaluated efficiently and with high precision. We identify the parameter regime for which the equilibrium entanglement of the tripartite system reaches its maximum.

139.  Spin qubits with electrically gated polyoxometalate molecules
Jörg Lehmann, Alejandro Gaita-Ariño, Eugenio Coronado (Valencia), and Daniel Loss.
Nature Nanotech. 2, 312 (2007); News and Views, Nature Nanotech. 2, 271 (2007); cond-mat/0703501.

Spin qubits offer one of the most promising routes to the implementation of quantum computers. Very recent results in semiconductor quantum dots show that electrically-controlled gating schemes are particularly well-suited for the realization of a universal set of quantum logical gates. Scalability to a larger number of qubits, however, remains an issue for such semiconductor quantum dots. In contrast, a chemical bottom-up approach allows one to produce identical units in which localized spins represent the qubits. Molecular magnetism has produced a wide range of systems with tailored properties, but molecules permitting electrical gating have been lacking. Here we propose to use the polyoxometalate [PMo12O40(VO)2]q-, where two localized spins-1/2 can be coupled through the electrons of the central core. Via electrical manipulation of the molecular redox potential, the charge of the core can be changed. With this setup, two-qubit gates and qubit readout can be implemented.

140.  Observation of extremely slow hole spin relaxation in self-assembled quantum dots
D. Heiss (1), S. Schaeck (1), H. Huebl (1), M. Bichler (1), G. Abstreiter (1), J. J. Finley (1), D. V. Bulaev, Daniel Loss ((1), and Technische Universität München).
Phys. Rev. B 76, 241306 (2007); cond-mat/0705.1466.

We report the measurement of extremely slow hole spin relaxation dynamics in self-assembled InGaAs quantum dots. Individual spin orientated holes are optically created in the lowest orbital state of each dot and read out after a defined storage time using spin memory devices. The hole spin relaxation time (T_1h) is measured as a function of the external magnetic field and lattice temperature. As predicted by theory, hole spin relaxation can occur over remarkably long timescales in strongly confined quantum dots (up to T_1h ~270 \mus) comparable to the corresponding time for electrons. Our findings are supported by calculations that reproduce both the observed magnetic field and temperature dependencies. The results show that hole spin relaxation in strongly confined quantum dots is governed by spin-lattice interaction, in marked contrast to higher dimensional nanostructures where it is limited by spin-orbit coupling between valence bands.

141.  Nuclear spin ferromagnetic phase transition in an interacting 2D electron gas
Pascal Simon and Daniel Loss.
Phys. Rev. Lett. 98, 156401 (2007); cond-mat/0611292.

Electrons in a two-dimensional semiconducting heterostructure interact with nuclear spins via the hyperfine interaction. Using a a Kondo lattice formulation of the electron-nuclear spin interaction, we show that the nuclear spin system within an interacting two-dimensional electron gas undergoes a ferromagnetic phase transition at finite temperatures. We find that electron-electron interactions and non-Fermi liquid behavior substantially enhance the nuclear spin Curie temperature into the $mK$ range with decreasing electron density.

142.  Universal phase shift and non-exponential decay of driven single-spin oscillations
F.H.L. Koppens (TU Delft), D. Klauser, W. A. Coish, K. C. Nowack (TU Delft), L.P. Kouwenhoven (TU Delft), D. Loss, and L.M.K. Vandersypen (TU Delft).
Phys. Rev. Lett. 99, 106803 (2007); cond-mat/0703640.

We study, both theoretically and experimentally, driven Rabi oscillations of a single electron spin coupled to a nuclear spin bath. Due to the long correlation time of the bath, two unusual features are observed in the oscillations. The decay follows a power law, and the oscillations are shifted in phase by a universal value of ~pi/4. These properties are well understood from a theoretical expression that we derive here in the static limit for the nuclear bath. This improved understanding of the coupled electron-nuclear system is important for future experiments using the electron spin as a qubit.

143.  Spin relaxation at the singlet-triplet transition in a quantum dot
Vitaly N. Golovach (LMU Munich), Alexander Khaetskii (Chernogolovka), and Daniel Loss.
Phys. Rev. B 77, 045328 (2008); cond-mat/0703427.

We study spin relaxation in a two-electron quantum dot in the vicinity of the singlet-triplet transition. The spin relaxation occurs due to a combined effect of the spin-orbit, Zeeman, and electron-phonon interactions. The singlet-triplet relaxation rates exhibit strong variations as a function of the singlet-triplet splitting. We show that the Coulomb interaction between the electrons has two competing effects on the singlet-triplet spin relaxation. One effect is to enhance the relative strength of spin-orbit coupling in the quantum dot, resulting in larger spin-orbit splittings and thus in a stronger coupling of spin to charge. The other effect is to make the charge density profiles of the singlet and triplet look similar to each other, thus diminishing the ability of charge environments to discriminate between singlet and triplet states. We thus find essentially different channels of singlet-triplet relaxation for the case of strong and weak Coulomb interaction. Finally, for the linear in momentum Dresselhaus and Rashba spin-orbit interactions, we calculate the singlet-triplet relaxation rates to leading order in the spin-orbit interaction, and find that they are proportional to the second power of the Zeeman energy, in agreement with recent experiments on triplet-to-singlet relaxation in quantum dots.

144.  Sequential Tunneling through Molecular Spin Rings
Jörg Lehmann and Daniel Loss.
Phys. Rev. Lett. 98, 117203 (2007); cond-mat/0608642.

We consider electrical transport through molecules with Heisenberg-coupled spins arranged in a ring structure in the presence of an easy-axis anisotropy. The molecules are coupled to two metallic leads and a gate. In the charged state of the ring, a Zener double-exchange mechanism links transport properties to the underlying spin structure. This leads to a remarkable contact-site dependence of the current, which for an antiferromagnetic coupling of the spins can lead to a total suppression of the zero-bias conductance when the molecule is contacted at adjacent sites.

145.  Spin qubits in graphene quantum dots
B. Trauzettel, Denis V. Bulaev, Daniel Loss, and Guido Burkard.
Nature Physics 3, 192 (2007); News and Views; Research Highlights; cond-mat/0611252.

We propose how to form spin qubits in graphene. A crucial requirement to achieve this goal is to find quantum dot states where the usual valley degeneracy in bulk graphene is lifted. We show that this problem can be avoided in quantum dots based on ribbons of graphene with semiconducting armchair boundaries. For such a setup, we find the energies and the exact wave functions of bound states, which are required for localized qubits. Additionally, we show that spin qubits in graphene can not only be coupled between nearest neighbor quantum dots via Heisenberg exchange interaction but also over long distances. This remarkable feature is a direct consequence of the quasi-relativistic spectrum of graphene. See also

146.  Exchange-controlled single-electron-spin rotations in quantum dots
W. A. Coish and Daniel Loss.
Phys. Rev. B 75, 161302 (2007) (R); cond-mat/0610443.

We show theoretically that arbitrary coherent rotations can be performed quickly (with a gating time ~1 ns) and with high fidelity on the spin of a single electron confined to a quantum dot using exchange. These rotations can be performed using experimentally proven techniques for rapid exchange control, without the need for spin-orbit interaction or ac electromagnetic fields. We expect that implementations of this scheme would achieve gate error rates on the order of $\eta\lesssim 10-3$, within reach of several known error-correction schemes.

147.  Electric Dipole Spin Resonance for Heavy Holes in Quantum Dots
Denis V. Bulaev and Daniel Loss.
Phys. Rev. Lett. 98, 097202 (2007); cond-mat/0608410.

We propose and analyze a new method for manipulation of a heavy hole spin in a quantum dot. Due to spin-orbit coupling between states with different orbital momenta and opposite spin orientations, an applied rf electric field induces transitions between spin-up and spin-down states. This scheme can be used for detection of heavy-hole spin resonance signals, for the control of the spin dynamics in two-dimensional systems, and for determining important parameters of heavy-holes such as the effective $g$-factor, mass, spin-orbit coupling constants, spin relaxation and decoherence times.

148.  Resonant spin polarization and spin current in a two-dimensional electron gas
Mathias Duckheim and Daniel Loss.
Phys. Rev. B 75, 201305 (2007); cond-mat/0701559.

We study the spin polarization and its associated spin-Hall current due to EDSR in disordered two-dimensional electron systems. We show that the disorder induced damping of the resonant spin polarization can be strongly reduced by an optimal field configuration that exploits the interference between Rashba and Dresselhaus spin-orbit interaction. This leads to a striking enhancement of the spin susceptibility while the spin-Hall current vanishes at the same time. We give an interpretation of the spin current in geometrical terms which are associated with the trajectories the polarization describes in spin space.

149.  Quantum Information is Physical
David P. DiVincenzo (IBM Yorktown) and Daniel Loss.
Superlattices and Microstructures 23, 419 (1998); cond-mat/9710259.

We discuss a few current developments in the use of quantum mechanically coherent systems for information processing. In each of these developments, Rolf Landauer has played a crucial role in nudging us and other workers in the field into asking the right questions, some of which we have been lucky enough to answer. A general overview of the key ideas of quantum error correction is given. We discuss how quantum entanglement is the key to protecting quantum states from decoherence in a manner which, in a theoretical sense, is as effective as the protection of digital data from bit noise. We also discuss five general criteria which must be satisfied to implement a quantum computer in the laboratory, and we illustrate the application of these criteria by discussing our ideas for creating a quantum computer out of the spin states of coupled quantum dots. [Special Issue on the Occasion of Rolf Landauer's 70th Birthday.]

150.  Direct Measurement of the Spin-Orbit Interaction in a Two-Electron InAs Nanowire Quantum Dot
C. Fasth, A. Fuhrer, L. Samuelson (Lund University), Vitaly N. Golovach (LMU Munich), and Daniel Loss.
Phys. Rev. Lett. 98, 266801 (2007); cond-mat/0701161.

We demonstrate control of the electron number down to the last electron in tunable few-electron quantum dots defined in catalytically grown InAs nanowires. Using low temperature transport spectroscopy in the Coulomb blockade regime we propose a simple method to directly determine the magnitude of the spin-orbit interaction in a two-electron artificial atom with strong spin-orbit coupling. Due to a large effective g-factor |g*|=8+/-1 the transition from singlet S to triplet T+ groundstate with increasing magnetic field is dominated by the Zeeman energy rather than by orbital effects. We find that the spin-orbit coupling mixes the T+ and S states and thus induces an avoided crossing with magnitude $\DeltaSO$=0.25+/-0.05 meV. This allows us to calculate the spin-orbit length $\lambdaSO\approx$127 nm in such systems using a simple model.

151.  Spin orbit interaction and zitterbewegung in symmetric wells
E Bernardes (São Paulo), J. Schliemann (Regensburg), J. C. Egues (São Paulo), and D. Loss.
Phys. Stat. Sol. (c) 3, No. 12, 4330 - 4333 (2006); (PASPS IV Proceedings).

Recently, we have introduced a novel inter-subband-induced spin-orbit (s-o) coupling (cond-mat/0607218) arising in symmetric wells with at least two subbands. This new s-o coupling gives rise to an usual zitterbewegung -- i.e. the semiconductor analog to the relativistic trembling motion of electrons -- with cycloidal motion without magnetic fields. Here we complement these findings by explicitly deriving expressions for the corresponding zitterbewegung in spin space.

152.  Spin densities in parabolic quantum wires with Rashba spin-orbit interaction
S. I. Erlingsson (Reykjavik), J. C. Egues (Sao Paulo), and D. Loss.
Phys. Stat. Sol. (c) 3, 4317 (2006) (PASPS IV Proceedings); cond-mat/0701564.

Using canonical transformations we diagonalize approximately the Hamiltonian of a gaussian wire with Rashba spin-orbit interaction. This proceedure allows us to obtain the energy dispersion relations and the wavefunctions with good accuracy, even in systems with relatively strong Rashba coupling. With these eigenstates one can calculate the non-equilibrium spin densities induced by applying bias voltages across the sample. We focus on the $z$-component of the spin density, which is related to the spin Hall effect.

153.  Quantum vs. classical hyperfine-induced dynamics in a quantum dot
W. A. Coish, E. A. Yuzbashyan (Rutgers University), B. L. Altshuler (Columbia University), and Daniel Loss.
J. Appl. Phys. 101, 081715 (2007); cond-mat/0610633.

In this article we analyze spin dynamics for electrons confined to semiconductor quantum dots due to the contact hyperfine interaction. We compare mean-field (classical) evolution of an electron spin in the presence of a nuclear field with the exact quantum evolution for the special case of uniform hyperfine coupling constants. We find that (in this special case) the zero-magnetic-field dynamics due to the mean-field approximation and quantum evolution are similar. However, in a finite magnetic field, the quantum and classical solutions agree only up to a certain time scale t<\tau_c, after which they differ markedly.

154.  Transport through a quantum dot with SU(4) Kondo entanglement
Karyn Le Hur (Yale), Pascal Simon, and Daniel Loss.
Phys. Rev. B 75, 035332 (2007); cond-mat/0609298.

We investigate a mesoscopic setup composed of a small electron droplet (dot) coupled to a larger quantum dot (grain) also subject to Coulomb blockade as well as two macroscopic leads used as source and drain. An exotic Kondo ground state other than the standard SU(2) Fermi liquid unambiguously emerges: an SU(4) Kondo correlated liquid. The transport properties through the small dot are analyzed for this regime, through boundary conformal field theory, and allow a clear distinction with other regimes such as a two-channel spin state or a two-channel orbital state.

155.  Measurement, control, and decay of quantum-dot spins
W. A. Coish, Vitaly N. Golovach, J. Carlos Egues, and Daniel Loss.
Physica Status Solidi (b) 243, 3658 (2006); cond-mat/0606782.

In this review we discuss a recent proposal to perform partial Bell-state (parity) measurements on two-electron spin states for electrons confined to quantum dots. The realization of this proposal would allow for a physical implementation of measurement-based quantum computing. In addition, we consider the primary sources of energy relaxation and decoherence which provide the ultimate limit to all proposals for quantum information processing using electron spins in quantum dots. We give an account of the Hamiltonians used for the most important interactions (spin-orbit and hyperfine) and survey some of the recent work done to understand dynamics, control, and decoherence under the action of these Hamiltonians. We conclude the review with a table of important decay times found in experiment, and relate these time scales to the potential viability of measurement-based quantum computing.

156.  Spin-spin coupling in electrostatically coupled quantum dots
Mircea Trif, Vitaly N. Golovach, and Daniel Loss.
Phys. Rev. B 75, 085307 (2007); cond-mat/0608512.

We study the spin-spin coupling between two single-electron quantum dots due to the Coulomb and spin-orbit interactions, in the absence of tunneling between the dots. We find an anisotropic XY spin-spin interaction that is proportional to the Zeeman splitting produced by the external magnetic field. This interaction is studied both in the limit of weak and strong Coulomb repulsion with respect to the level spacing of the dot. The interaction is found to be a non-monotonic function of inter-dot distance $a_0$ and external magnetic field, and, moreover, vanishes for some special values of $a_0$ and/or magnetic field orientation. This mechanism thus provides a new way to generate and tune spin interaction between quantum dots. We propose a scheme to measure this spin-spin interaction based on the spin-relaxation-measurement technique.

157.  Spin-orbit interaction in symmetric wells and cycloidal orbits without magnetic fields
Esmerindo S. Bernardes, John Schliemann (Regensburg), J. Carlos Egues, and Daniel Loss.
Phys. Rev. Lett. 99, 076603 (2007); cond-mat/0607218.

We investigate the spin-orbit (s-o) interaction in two-dimensional electron gases (2DEGs) in quantum wells with two subbands. From the $8\times 8$ Kane model, we derive a new inter-subband-induced s-o coupling which resembles the functional form of the Rashba s-o -- but is non-zero even in \emph{symmetric} structures. This follows from the distinct parity of the confined states (even/odd) which obliterates the need for asymmetric potentials. Interestingly, our s-o interaction gives rise to an unusual \emph{zitterbewegung} of spin-polarized electrons with cycloidal trajectories \textit{without} magnetic fields. We also predict a sizable effective-mass renormalization due to the s-o--induced subband warping.

158.  Quantum computing with spins in solids
W. A. Coish and Daniel Loss.
Handbook of Magnetism and Advanced Magnetic Materials. Helmut Kronmüller (editor) and Stuart Parkin (editor). Volume 5: Spintronics and Magnetoelectronics. ; 2007 John Wiley & Sons, Ltd. ISBN: 978-0-470-02217-7; cond-mat/0606550.

The ability to perform high-precision one- and two-qubit operations is sufficient for universal quantum computation. For the Loss-DiVincenzo proposal to use single electron spins confned to quantum dots as qubits, it is therefore sufficient to analyze only single- and coupled double-dot structures, since the strong Heisenberg exchange coupling between spins in this proposal falls off exponentially with distance and long-ranged dipolar coupling mechanisms can be made significantly weaker. This scalability of the Loss-DiVincenzo design is both a practical necessity for eventual applications of multi-qubit quantum computing and a great conceptual advantage, making analysis of the relevant components relatively transparent and systematic. We review the Loss-DiVincenzo proposal for quantum-dot-confned electron spin qubits, and survey the current state of experiment and theory regarding the relevant single- and double- quantum dots, with a brief look at some related alternative schemes for quantum computing.

159.  Quantum-dot spin qubit and hyperfine interaction
D. Klauser, W. A. Coish, and Daniel Loss.
Advances in Solid State Physics 46, p.17-29, (2007); cond-mat/0604252.

We review our investigation of the spin dynamics for two electrons confined to a double quantum dot under the influence of the hyperfine interaction between the electron spins and the surrounding nuclei. Further we propose a scheme to narrow the distribution of difference in polarization between the two dots in order to suppress hyperfine induced decoherence.

160.  Molecular states in carbon nanotube double quantum dots
M.R. Graeber, W.A. Coish, C. Hoffmann, M. Weiss, J. Furer, S. Oberholzer, D. Loss, and C. Schoenenberger.
Phys. Rev. B 74, 075427 (2006); cond-mat/0603367.

We report electrical transport measurements through a semiconducting single-walled carbon nanotube (SWNT) with three additional top-gates. At low temperatures the system acts as a double quantum dot with large inter-dot tunnel coupling allowing for the observation of tunnel-coupled molecular states extending over the whole double-dot system. We precisely extract the tunnel coupling and identify the molecular states by the sequential-tunneling line shape of the resonances in differential conductance.

161.  Electric-dipole-induced spin resonance in disordered semiconductors (Article)
Mathias Duckheim and Daniel Loss.
Nature Physics 2, 195-199 (2006); Supplementary Information; cond-mat/0605735.

One of the hallmarks of spintronics is the control of magnetic moments by electric fields enabled by strong spin-orbit interaction (SOI) in semiconductors. A powerful way of manipulating spins in such structures is electric-dipole-induced spin resonance (EDSR), where the radio-frequency fields driving the spins are electric, not magnetic as in standard paramagnetic resonance. Here, we present a theoretical study of EDSR for a two-dimensional electron gas in the presence of disorder, where random impurities not only determine the electric resistance but also the spin dynamics through SOI. Considering a specific geometry with the electric and magnetic fields parallel and in-plane, we show that the magnetization develops an out-of-plane component at resonance that survives the presence of disorder. We also discuss the spin Hall current generated by EDSR. These results are derived in a diagrammatic approach, with the dominant effects coming from the spin vertex correction, and the optimal parameter regime for observation is identified. See also, 'Semiconductor physics: Electric fields drive spins', by Emmanuel I. Rashba, Nature Physics 2, 149-150 (01 Mar 2006) News and Views

162.  Electric Dipole Induced Spin Resonance in Quantum Dots
Vitaly N. Golovach, Massoud Borhani, and Daniel Loss.
Phys. Rev. B 74, 165319 (2006); cond-mat/0601674.

An alternating electric field, applied to a ``spin 1/2'' quantum dot, couples to the electron spin via the spin-orbit interaction. We analyze different types of spin-orbit couplings known in the literature and find that an electric dipole spin resonance (EDSR) scheme for spin manipulation can be realized with the up-to-date experimental setups. In particular, for the Rashba and Dresselhaus spin-orbit couplings, a fully transverse effective magnetic field arises in the presence of a Zeeman splitting in the lowest order of spin-orbit interaction. Spin manipulation and measurement of the spin decoherence time $T_2$ are straightforward in lateral GaAs quantum dots through the use of EDSR.

163.  Zitterbewegung of electrons and holes in III-V semiconductor quantum wells
John Schliemann (Regensburg), Daniel Loss, and R.M. Westervelt (Harvard).
Phys. Rev. B 73, 085323 (2006); cond-mat/0512148.

The notion of zitterbewegung is a long-standing prediction of relativistic quantum mechanics. Here we extend earlier theoretical studies on this phenomenon for the case of III-V zinc-blende semiconductors which exhibit particularly strong spin-orbit coupling. This property makes nanostructures made of these materials very favorable systems for possible experimental observations of zitterbewegung. Our investigations include electrons in n-doped quantum wells under the influence of both Rashba and Dresselhaus spin-orbit interaction, and also the two-dimensional hole gas. Moreover, we give a detailed anaysis of electron zitterbewegung in quantum wires which appear to be particularly suited for experimentally observing this effect.

164.  Dynamics of Coupled Qubits Interacting with an Off-Resonant Cavity
Oliver Gywat (UCSB), Florian Meier (UCSB), Daniel Loss, and D. D. Awschalom (UCSB).
Phys. Rev. B 73, 125336 (2006); cond-mat/0511592.

We study a model for a pair of qubits which interact with a single off-resonant cavity mode and, in addition, exhibit a direct inter-qubit coupling. Possible realizations for such a system include coupled superconducting qubits in a line resonator as well as exciton states or electron spin states of quantum dots in a cavity. The emergent dynamical phenomena are strongly dependent on the relative energy scales of the inter-qubit coupling strength, the coupling strength between qubits and cavity mode, and the cavity mode detuning. We show that the cavity mode dispersion enables a measurement of the state of the coupled-qubit system in the perturbative regime. We discuss the effect of the direct inter-qubit interaction on a cavity-mediated two-qubit gate. Further, we show that for asymmetric coupling of the two qubits to the cavity, the direct inter-qubit coupling can be controlled optically via the ac Stark effect.

165.  A Mesoscopic Resonating Valence Bond system on a triple dot
Karyn Le Hur (Sherbrooke), Patrik Recher (Stanford), Emilie Dupont (Sherbrooke), and Daniel Loss.
Phys. Rev. Lett. 96, 106803 (2006); cond-mat/0510450.

We theoretically introduce a mesoscopic pendulum from a triple dot. The pendulum is fastened through a singly-occupied dot (spin qubit). Two other strongly capacitively coupled islands form a double-dot charge qubit with one electron in excess oscillating between the two low-energy charge states (1, 0) and (0, 1). The triple dot is placed between two superconducting leads. Under realistic conditions, the main proximity effect stems from the injection of resonating singlet (valence) bonds on the triple dot. This gives rise to a Josephson current that is charge- and spin-dependent and, as a consequence, exhibits a distinct resonance as a function of the superconducting phase difference.

166.  Spin Decay in a Quantum Dot Coupled to a Quantum Point Contact
Massoud Borhani, Vitaly N. Golovach, and Daniel Loss.
Phys. Rev. B 73, 155311 (2006); cond-mat/0510758.

We consider a mechanism of spin decay for an electron spin in a quantum dot due to coupling to a nearby quantum point contact (QPC) with and without an applied bias voltage. The coupling of spin to charge is induced by the spin-orbit interaction in the presence of a magnetic field. We perform a microscopic calculation of the effective Hamiltonian coupling constants to obtain the QPC-induced spin relaxation and decoherence rates in a realistic system. This rate is shown to be proportional to the shot noise of the QPC in the regime of large bias voltage and scales as $a-6$ where $a$ is the distance between the quantum dot and the QPC. We find that, for some specific orientations of the setup with respect to the crystallographic axes, the QPC-induced spin relaxation and decoherence rates vanish, while the charge sensitivity of the QPC is not changed. This result can be used in experiments to minimize QPC-induced spin decay in read-out schemes.

167.  Nuclear spin state narrowing via gate--controlled Rabi oscillations in a double quantum dot
D. Klauser, W.A. Coish, and Daniel Loss.
Phys. Rev. B 73, 205302 (2006); cond-mat/0510177.

We study spin dynamics for two electrons confined to a double quantum dot under the influence of an oscillating exchange interaction. This leads to driven Rabi oscillations between the $\ket{\uparrow\downarrow}$--state and the $\ket{\downarrow\uparrow}$--state of the two--electron system. The width of the Rabi resonance is proportional to the amplitude of the oscillating exchange. A measurement of the Rabi resonance allows one to narrow the distribution of nuclear spin states and thereby to prolong the spin decoherence time. Further, we study decoherence of the two-electron states due to the hyperfine interaction and give requirements on the parameters of the system in order to initialize in the $\ket{\uparrow\downarrow}$--state and to perform a $\sqrt{\mathrm{SWAP}}$ operation with unit fidelity.

168.  Cotunneling current through quantum dots with phonon-assisted spin-flip processes
Jörg Lehmann and Daniel Loss.
Phys. Rev. B 73, 045328 (2006); cond-mat/0509420.

We consider cotunneling through a quantum dot in the presence of spin-flip processes induced by the coupling to acoustic phonons of the surrounding. An expression for the phonon-assisted cotunneling current is derived by means of a generalized Schrieffer-Wolff transformation. The influence of the spin-phonon coupling on the heating of the dot is considered. The result is evaluated for the case of a parabolic semiconductor quantum dot with Rashba and Dresselhaus spin-orbit coupling and a novel method for the determination of the spin-phonon relaxation rate is proposed.

169.  Shot noise and spin-orbit coherent control of entangled and spin polarized electrons
J. Carlos Egues (Sao Paulo), Guido Burkard, D. Saraga, John Schliemann, and Daniel Loss.
Phys. Rev. B 72, 235326 (2005); cond-mat/0509038.

We extend our previous work on shot noise for entangled and spin polarized electrons in a beam-splitter geometry with spin-orbit (\textit{s-o}) interaction in one of the incoming leads (lead 1). Besides accounting for both the Dresselhaus and the Rashba spin-orbit terms, we present general formulas for the shot noise of singlet and triplets states derived within the scattering approach. We determine the full scattering matrix of the system for the case of leads with \textit{two} orbital channels coupled via weak \textit{s-o} interactions inducing channel anticrossings. We show that this interband coupling coherently transfers electrons between the channels and gives rise to an additional modulation angle -- dependent on both the Rashba and Dresselhaus interaction strengths -- which allows for further independent coherent control of the electrons traversing the incoming leads. We derive explicit shot noise formulas for a variety of correlated pairs (e.g., Bell states) and lead spin polarizations. Interestingly, the singlet and \textit{each} of the triplets defined along the quantization axis perpendicular to lead 1 (with the local \textit{s-o} interaction) and in the plane of the beam splitter display distinctive shot noise for injection energies near the channel anticrossings; hence, one can tell apart all the triplets, in addition to the singlet, through noise measurements. We also find that spin-orbit induced backscattering within lead 1 reduces the visibility of the noise oscillations, due to the additional partition noise in this lead. Finally, we consider injection of two-particle wavepackets into leads with multiple discrete states and find that two-particle entanglement can still be observed via noise bunching and antibunching.

170.  Quantum information processing and communication - Strategic report on current status, visions and goals for research in Europe
Zoller P, Beth T, Binosi D, Blatt R, Briegel H, Bruss D, Calarco T, Cirac JI, Deutsch D, Eisert J, Ekert A, Fabre C, Gisin N, Grangiere P, Grassl M, Haroche S, Imamoglu A, Karlson A, Kempe J, Kouwenhoven L, Kroll S, Leuchs G, Lewenstein M, Loss D, Lutkenhaus N, Massar S, Mooij JE, Plenio MB, Polzik E, Popescu S, Rempe G, Sergienko A, Suter D, Twamley J, Wendin G, Werner R, Winter A, Wrachtrup J, and Zeilinger A.
Eur. Phys. J. D 36, 203 (2005); DOI:10.1140/epjd/e2005-00251-1.

We present an excerpt of the document "Quantum Information Processing and Communication: Strategic report on current status, visions and goals for research in Europe", which has been recently published in electronic form at the website of FET (the Future and Emerging Technologies Unit of the Directorate General Information Society of the European Commission, This document has been elaborated, following a former suggestion by FET, by a committee of QIPC scientists to provide input towards the European Commission for the preparation of the Seventh Framework Program. Besides being a document addressed to policy makers and funding agencies (both at the European and national level), the document contains a detailed scientific assessment of the state-of-the-art, main research goals, challenges, strengths, weaknesses, visions and perspectives of all the most relevant QIPC sub-fields, that we report here.

171.  Fermionic Bell-State Analyzer for Spin Qubits
Hans-Andreas Engel (Harvard Univ.) and Daniel Loss.
Science 309, 586 (2005)

We propose a protocol and physical implementation for partial Bell-state measurements of Fermionic qubits, allowing for deterministic quantum computing in solid-state systems without the need for two-qubit gates. Our scheme consists of two spin qubits in a double quantum dot where the two dots have different Zeeman splittings and resonant tunneling between the dots is only allowed when the spins are antiparallel. This converts spin parity into charge information by means of a projective measurement and can be implemented with established technologies. This measurement-based qubit scheme greatly simplifies the experimental realization of scalable quantum computers in electronic nanostructures. [See also Science Perspective, Fingerprinting Spin Qubits, J. Carlos Egues, Science , Vol 309, Issue 5734, 565 (2005); Philip Ball, Nature news: Quantum computers go for a spin. ]

172.  Phase coherence in the inelastic cotunneling regime
M. Sigrist, T. Ihn, K. Ensslin (ETH Zurich), D. Loss, M. Reinwald, and W. Wegscheider (Regensburg).
Phys. Rev. Lett. 96, 036804 (2006); cond-mat/0508757.

Two quantum dots with tunable mutual tunnel coupling have been embedded in a two-terminal Aharonov-Bohm geometry. Aharonov-Bohm oscillations are investigated in the cotunneling regime. Visibilities of more than 0.8 are measured indicating that phase-coherent processes are involved in the elastic and inelastic cotunneling. An oscillation-phase change of pi is detected as a function of bias voltage at the inelastic cotunneling onset.

173.  Singlet-triplet decoherence due to nuclear spins in a double quantum dot
W. A. Coish and Daniel Loss.
Phys. Rev. B 72, 125337 (2005); cond-mat/0506090.

We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ensemble averaging over initial conditions. In contrast to an earlier semiclassical calculation, which neglects the exchange interaction, we find that the singlet-triplet correlator shows a long-time saturation value that differs from 1/2, even in the presence of a strong magnetic field. Furthermore, we find that the form of the long-time decay undergoes a transition from a rapid Gaussian to a slow power law ($\sim 1/t3/2$) when the exchange interaction becomes nonzero and the singlet-triplet correlator acquires a phase shift given by a universal (parameter independent) value of $3\pi/4$ at long times. The oscillation frequency and time-dependent phase shift of the singlet-triplet correlator can be used to perform a precision measurement of the exchange interaction and Overhauser field fluctuations in an experimentally accessible system. We also address the effect of orbital dephasing on singlet-triplet decoherence, and find that there is an optimal operating point where orbital dephasing becomes negligible.

174.  Fermi liquid parameters in 2D with spin-orbit interaction
D. S. Saraga and Daniel Loss.
Phys. Rev. B 72, 195319 (2005); cond-mat/0504661.

We derive analytical expressions for the quasiparticle lifetime \tau, the effective mass m^*, and the Green's function renormalization factor Z for a 2D Fermi liquid with electron-electron interaction in the presence of the Rashba spin-orbit interaction. For the lifetime \tau and the renormalization Z, we find that the modification is independent of the Rashba band index \rho, and occurs in second order of the spin-orbit coupling \alpha . On the contrary, the modification of the effective mass m^* is linear in \alpha and is different for the two Rashba bands, yielding a spin-dependent effective mass. In the derivation of these results, we also discuss the screening of the Coulomb interaction, and the susceptibility.

175.  Zitterbewegung of electronic wave packets in semiconductor nanostructures
John Schliemann, Daniel Loss, and R.M. Westervelt (Harvard Univ.).
Phys. Rev. Lett. 94, 206801 (2005); cond-mat/0410321.

We study the zitterbewegung of electronic wave packets in III-V zinc-blende semiconductor quantum wells due to spin-orbit coupling. Our results suggest a direct experimental proof of this fundamental effect, confirming a long-standing theoretical prediction. For electron motion in a harmonic quantum wire, we numerically and analytically find a resonance condition maximizing the zitterbewegung. See also, 'Dirac gets the jitters', M. Buchanan, Nature Physics 1, 5 (2005);

176.  Determining the spin Hall conductance via charge transport
Sigurdur I. Erlingsson and Daniel Loss.
Phys. Rev. B 72, 121310 (2005); cond-mat/0503605.

We propose a scheme where transport measurements of charge current and its noise can be used to determine the spin Hall conductance in a four-terminal setup. Starting from the scattering formalism we express the spin current and spin Hall conductance in terms of spin-dependent transmission coefficients. These coefficients are then expressed in terms of charge current and noise. We use the scheme to characterize the spin injection efficiency of a ferromagnetic/semiconductor interface.

177.  Spin relaxation and decoherence of holes in quantum dots
Denis V. Bulaev and Daniel Loss.
Phys. Rev. Lett. 95, 076805 (2005); cond-mat/0503181.

We investigate heavy-hole spin relaxation and decoherence in quantum dots in perpendicular magnetic fields. We show that at low temperatures the spin decoherence time is two times longer than the spin relaxation time. We find that the spin relaxation time for heavy holes can be comparable to or even longer than that for electrons in strongly two-dimensional quantum dots. We discuss the difference in the magnetic-field dependence of the spin relaxation rate due to Rashba or Dresselhaus spin-orbit coupling for systems with positive (i.e., GaAs quantum dots) or negative (i.e., InAs quantum dots) $g$-factor.

178.  Phonon Bottleneck Effect Leads to Observation of Quantum Tunneling of the Magnetization and Butterfly Hysteresis Loops in (Et4N)3Fe2F9
Ralph Schenker, Michael N. Leuenberger (UC San Diego), Gregory Chaboussant (Uni Bern), Daniel Loss, and Hans U. Gudel (Uni Bern).
Phys. Rev. B 72, 184403 (2005); cond-mat/0502548.

A detailed investigation of the unusual dynamics of the magnetization of (Et4N)3Fe2F9 (Fe2), containing isolated [Fe2F9]3- dimers, is presented and discussed. Fe2 possesses an S=5 ground state with an energy barrier of 2.40 K due to an axial anisotropy. Poor thermal contact between sample and bath leads to a phonon bottleneck situation, giving rise to butterfly-shaped hysteresis loops below 5 K concomitant with slow decay of the magnetization for magnetic fields Hz applied along the Fe--Fe axis. The butterfly curves are reproduced using a microscopic model based on the interaction of the spins with resonant phonons. The phonon bottleneck allows for the observation of resonant quantum tunneling of the magnetization at 1.8 K, far above the blocking temperature for spin-phonon relaxation. The latter relaxation is probed by AC magnetic susceptibility experiments at various temperatures and bias fields. At H=0, no out-of-phase signal is detected, indicating that at T smaller than 1.8 K Fe2 does not behave as a single-molecule magnet. At 1 kG, relaxation is observed, occurring over the barrier of the thermally accessible S=4 first excited state that forms a combined system with the S=5 state.

179.  Recipes for spin-based quantum computing
Veronica Cerletti, W. A. Coish, Oliver Gywat, and Daniel Loss.
Nanotechnology 16, R27 (2005); cond-mat/0412028.

Technological growth in the electronics industry has historically been measured by the number of transistors that can be crammed onto a single microchip. Unfortunately, all good things must come to an end; spectacular growth in the number of transistors on a chip requires spectacular reduction of the transistor size. For electrons in semiconductors, the laws of quantum mechanics take over at the nanometre scale, and the conventional wisdom for progress (transistor cramming) must be abandoned. This realization has stimulated extensive research on ways to exploit the spin (in addition to the orbital) degree of freedom of the electron, giving birth to the field of spintronics. Perhaps the most ambitious goal of spintronics is to realize complete control over the quantum mechanical nature of the relevant spins. This prospect has motivated a race to design and build a spintronic device capable of complete control over its quantum mechanical state, and ultimately, performing computations: a quantum computer.
In this tutorial we summarize past and very recent developments which point the way to spin-based quantum computing in the solid-state. After introducing a set of basic requirements for any quantum computer proposal, we offer a brief summary of some of the many theoretical proposals for solid-state quantum computers. We then focus on the Loss-DiVincenzo proposal for quantum computing with the spins of electrons confined to quantum dots. There are many obstacles to building such a quantum device. We address these, and survey recent theoretical, and then experimental progress in the field. To conclude the tutorial, we list some as-yet unrealized experiments, which would be crucial for the development of a quantum-dot quantum computer.

180.  Spin-Hall conductivity due to Rashba spin-orbit interaction in disordered systems
Oleg Chalaev and Daniel Loss.
Phys. Rev. B 71, 245318 (2005); cond-mat/0407342.

We consider the spin-Hall current in a disordered two-dimensional electron gas in the presence of Rashba spin-orbit interaction. We derive a generalized Kubo-Greenwood formula for the spin-Hall conductivity $\sigma$ and evaluate it in an systematic way using standard diagrammatic techniques for disordered systems. We find that in the diffusive regime both Boltzmann and the weak localization contributions to the $\sigma$ vanish in the zero frequency limit. We show that the uniform spin current is given by the total time derivative of the magnetization from which we can conclude that the spin current vanishes exactly in the stationary limit. This conclusion is valid for arbitrary spin-independent disorder, external electric field strength, and also for interacting electrons.

181.  Cluster States From Heisenberg Interaction
Massoud Borhani and Daniel Loss.
Phys. Rev. A 71, 034308 (2005); quant-ph/0410145.

We show that a special type of entangled states, cluster states, can be created with Heisenberg interactions and local rotations in 2d steps where d is the dimension of the lattice. We find that, by tuning the coupling strengths, anisotropic exchange interactions can also be employed to create cluster states. Finally, we propose electron spins in quantum dots as a possible realization of a one-way quantum computer based on cluster states.

182.  Entanglement transfer from electron spins to photons
Veronica Cerletti, Oliver Gywat, and Daniel Loss.
Phys. Rev. B 72, 115316 (2005); cond-mat/0411235.

We show that electron recombination in spin light-emitting diodes provides an efficient method to transfer entanglement from electron spins onto pairs of polarization-entangled photons. Because of the interplay of quantum mechanical sel​ection rules and interference, maximally entangled electron pairs are converted into maximally entangled photon pairs with unity fidelity for a continuous set of observation directions. We describe the dynamics of the conversion process using a master-equation approach and show that the implementation of our scheme is feasible with current experimental techniques.

183.  Double Occupancy Errors in Quantum Computing Operations: Corrections to Adiabaticity
Ryan Requist (SUNY), John Schliemann, Alexander G. Abanov (SUNY), and Daniel Loss.
Phys. Rev. B 71, 115315 (2005); cond-mat/0409096.

We study the corrections to adiabatic dynamics of two coupled quantum dot spin-qubits, each dot singly occupied with an electron, in the context of a quantum computing operation. Tunneling can lead to a double occupancy at the conclusion of an operation and constitutes a processing error. Our model for the dynamics of an effective two-level system is integrable and possesses three independent parameters. We confirm the accuracy of Dykhne's formula, a nonperturbative estimate of transitions, and discuss physically intuitive conditions for its validity. Our semiclassical results are in excellent agreement with numerical simulations of the exact time evolution. A similar approach applies to two-level systems in different contexts.

184.  Spin Relaxation and Anticrossing in Quantum Dots: Rashba versus Dresselhaus Spin-Orbit Coupling
Denis V. Bulaev and Daniel Loss.
Phys. Rev. B 71, 205324 (2005); cond-mat/0409614.

The spin-orbit splitting of the electron levels in a two-dimensional quantum dot in a perpendicular magnetic field is studied. It is shown that at the point of an accidental degeneracy of the two lowest levels above the ground state the Rashba spin-orbit coupling leads to a level anticrossing and to mixing of spin-up and spin-down states, whereas there is no mixing of these levels due to the Dresselhaus term. We calculate the relaxation and decoherence times of the three lowest levels due to phonons. We find that the spin relaxation rate as a function of a magnetic field exhibits a cusp-like structure for Rashba but not for Dresselhaus spin-orbit interaction.

185.  Controlling Spin Qubits in Quantum Dots
Hans-Andreas Engel, L.P. Kouwenhoven (Delft), Daniel Loss, and C.M. Marcus (Harvard).; cond-mat/0409294.

We review progress on the spintronics proposal for quantum computing where the quantum bits (qubits) are implemented with electron spins. We calculate the exchange interaction of coupled quantum dots and present experiments, where the exchange coupling is measured via transport. Then, experiments on single spins on dots are described, where long spin relaxation times, on the order of a millisecond, are observed. We consider spin-orbit interaction as sources of spin decoherence and find theoretically that also long decoherence times are expected. Further, we describe the concept of spin filtering using quantum dots and show data of successful experiments. We also show an implementation of a read out scheme for spin qubits and define how qubits can be measured with high precision. Then, we propose new experiments, where the spin decoherence time and the Rabi oscillations of single electrons can be measured via charge transport through quantum dots. Finally, all these achievements have promising applications both in conventional and quantum information processing.

186.  Reduced Visibility of Rabi Oscillations in Superconducting Qubits
Florian Meier (UC Santa Barbara) and Daniel Loss.
Phys. Rev. B 71, 094519 (2005); cond-mat/0408594.

Coherent Rabi oscillations between quantum states of superconducting micro-circuits have been observed in a number of experiments, albeit with a visibility which is typically much smaller than unity. Here, we show that the coherent coupling to background charge fluctuators [R.W. Simmonds et al., Phys. Rev. Lett. 93, 077003 (2004)] leads to a significantly reduced visibility if the Rabi frequency is comparable to the coupling energy of micro-circuit and fluctuator. For larger Rabi frequencies, transitions to the second excited state of the superconducting micro-circuit become dominant in suppressing the Rabi oscillation visibility. We also calculate the probability for Bogoliubov quasi-particle excitations in typical Rabi oscillation experiments.

187.  Creation and detection of mobile and non-local spin-entangled electrons
Patrik Recher (Stanford), D.S. Saraga, and Daniel Loss.
pp. 179-202, in Fundamental Problems of Mesoscopic Physics, eds. I.V. Lerner et al., NATO Science Ser. II, Vol. 154 (Kluwer, Dordrecht, 2004); cond-mat/0408526.

We present electron spin entanglers--devices creating mobile spin-entangled electrons that are spatially separated--where the spin-entanglement in a superconductor present in form of Cooper pairs and in a single quantum dot with a spin singlet groundstate is transported to two spatially separated leads by means of a correlated two-particle tunneling event. The unwanted process of both electrons tunneling into the same lead is suppressed by strong Coulomb blockade effects caused by quantum dots, Luttinger liquid effects or by resistive outgoing leads. In this review we give a transparent description of the different setups, including discussions of the feasibility of the subsequent detection of spin-entanglement via charge noise measurements. Finally, we show that quantum dots in the spin filter regime can be used to perform Bell-type measurements that only require the measurement of zero frequency charge noise correlators.

188.  Probing Single-Electron Spin Decoherence in Quantum Dots using Charged Excitons
Oliver Gywat, Hans-Andreas Engel, and Daniel Loss.
Journal of Superconductivity 18 (2), 175 - 183 ( 2005);; cond-mat/0408451.

We propose to use optical detection of magnetic resonance (ODMR) to measure the decoherence time T2 of a single electron spin in a semiconductor quantum dot. The electron is in one of the spin 1/2 states and a circularly polarized laser can only create an optical excitation for one of the electron spin states due to Pauli blocking. An applied electron spin resonance (ESR) field leads to Rabi spin flips and thus to a modulation of the photoluminescence or, alternatively, of the photocurrent. This allows one to measure the ESR linewidth and the coherent Rabi oscillations, from which the electron spin decoherence can be determined. We study different possible schemes for such an ODMR setup, including cw or pulsed laser excitation.

189.  Coulomb scattering cross-section in a 2D electron gas and production of entangled electrons
D. S. Saraga, B. L. Altshuler (Princeton), Daniel Loss, and R. M. Westervelt (Harvard).
Phys. Rev. B 71, 045338 (2005); cond-mat/0408362.

We calculate the Coulomb scattering amplitude for two electrons injected with opposite momenta in an interacting 2DEG. We include the effect of the Fermi liquid background by solving the 2D Bethe-Salpeter equation for the two-particle Green function vertex, in the ladder and random phase approximations. This result is used to discuss the feasibility of producing spin EPR pairs in a 2DEG by collecting electrons emerging from collisions at a pi/2 scattering angle, where only the entangled spin-singlets avoid the destructive interference resulting from quantum indistinguishability. Furthermore, we study the effective 2D electron-electron interaction due to the exchange of virtual acoustic and optical phonons, and compare it to the Coulomb interaction. Finally, we show that the 2D Kohn-Luttinger pairing instability for the scattering electrons is negligible in a GaAs 2DEG.

190.  Spin susceptibilities, spin densities and their connection to spin-currents
Sigurdur I. Erlingsson, John Schliemann, and Daniel Loss.
Phys. Rev. B 71, 035319 (2005); cond-mat/0406531.

We calculate the frequency dependent spin susceptibilities for a two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit interaction. The resonances of the susceptibilities depends on the relative values of the Rashba and Dresselhaus spin-orbit constants, which could be manipulated by gate voltages. We derive exact continuity equations, with source terms, for the spin density and use those to connect the spin current to the spin density. In the free electron model the susceptibilities play a central role in the spin dynamics since both the spin density and the spin current are proportional to them.

191.  Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
W. A. Coish and Daniel Loss.
Phys. Rev. B 70, 195340 (2004); cond-mat/0405676.

We have performed a systematic calculation for the non-Markovian dynamics of a localized electron spin interacting with an environment of nuclear spins via the Fermi contact hyperfine interaction. This work applies to an electron in the s -type orbital ground state of a quantum dot or bound to a donor impurity, and is valid for arbitrary polarization p of the nuclear spin system, and arbitrary nuclear spin I in high magnetic fields. In the limit of p=1 and I=1/2, the Born approximation of our perturbative theory recovers the exact electron spin dynamics. We have found the form of the generalized master equation (GME) for the longitudinal and transverse components of the electron spin to all orders in the electron spin--nuclear spin flip-flop terms. Our perturbative expansion is regular, unlike standard time-dependent perturbation theory, and can be carried-out to higher orders. We show this explicitly with a fourth-order calculation of the longitudinal spin dynamics. In zero magnetic field, the fraction of the electron spin that decays is bounded by the smallness parameter \delta=1/p2N, where N is the number of nuclear spins within the extent of the electron wave function. However, the form of the decay can only be determined in a high magnetic field, much larger than the maximum Overhauser field. In general the electron spin shows rich dynamics, described by a sum of contributions with non-exponential decay, exponential decay, and undamped oscillations. There is an abrupt crossover in the electron spin asymptotics at a critical dimensionality and shape of the electron envelope wave function. We propose a scheme that could be used to measure the non-Markovian dynamics using a standard spin-echo technique, even when the fraction that undergoes non-Markovian dynamics is small.

192.  Rigorous Born Approximation and beyond for the Spin-Boson Model
D. P. DiVincenzo (IBM) and D. Loss.
The Mathematica file can be obtained directly here.
Phys. Rev. B 71, 035318 (2005); cond-mat/0405525.

Within the lowest-order Born approximation, we present an exact calculation of the time dynamics of the spin-boson model in the ohmic regime. We observe non-Markovian effects at zero temperature that scale with the system-bath coupling strength and cause qualitative changes in the evolution of coherence at intermediate times of order of the oscillation period. These changes could significantly affect the performance of these systems as qubits. In the biased case, we find a prompt loss of coherence at these intermediate times, whose decay rate is set by $\sqrt{\alpha}$, where $\alpha$ is the coupling strength to the environment. We also explore the calculation of the next order Born approximation: we show that, at the expense of very large computational complexity, interesting physical quantities can be rigorously computed at fourth order using computer algebra, presented completely in an accompanying Mathematica file. We compute the $O(\alpha)$ corrections to the long time behavior of the system density matrix; the result is identical to the reduced density matrix of the equilibrium state to the same order in $\alpha$. All these calculations indicate precision experimental tests that could confirm or refute the validity of the spin-boson model in a variety of systems.

193.  Spin-Hall transport of heavy holes in III-V semiconductor quantum wells
John Schliemann and Daniel Loss.
Phys. Rev. B 71, 085308 (2005); cond-mat/0405436.

We investigate spin transport of heavy holes in III-V semiconductor quantum wells in the presence of spin-orbit coupling of the Rashba type due to structure-inversion asymmetry. Similarly to the case of electrons, the longitudinal spin conductivity vanishes, whereas the off-diagonal elements of the spin-conductivity tensor are finite giving rise to an intrinsic spin-Hall effect. For a clean system we find a closed expression for the spin-Hall conductivity depending on the length scale of the Rashba coupling and the hole density. In this limit the spin-Hall conductivity is enhanced compared to its value for electron systems, and it vanishes with increasing strength of the impurity scattering. As an aside, we also derive explicit expressions for the Fermi momenta and the densities of holes in the different dispersion branches as a function of the spin-orbit coupling parameter and the total hole density. These results are of relevance for the interpretation of possible Shubnikov-de Haas measurements detecting the Rashba spin splitting.

194.  Coulomb scattering in a 2D interacting electron gas and production of EPR pairs
D.S. Saraga, B.L. Altshuler (Princeton), Daniel Loss, and R.M. Westervelt (Harvard).
Phys. Rev. Lett. 92, 246803 (2004); cond-mat/0310421.

We propose a setup to generate non-local spin-EPR pairs via pair collisions in a 2D interacting electron gas, based on constructive two-particle interference in the spin singlet channel at the pi/2 scattering angle. We calculate the scattering amplitude via the Bethe-Salpeter equation in the ladder approximation and small r_s limit, and find that the Fermi sea leads to a substantial renormalization of the bare scattering process. From the scattering length we estimate the current of spin-entangled electrons and show that it is within experimental reach.

195.  Molecular spintronics: Coherent spin transfer in coupled quantum dots
Florian Meier (UCSB), Veronica Cerletti, Oliver Gywat, Daniel Loss, and D. D. Awschalom (UCSB).
Phys. Rev. B 69, 195315 (2004); cond-mat/0401397.

Time-resolved Faraday rotation has recently demonstrated coherent transfer of electron spin between quantum dots coupled by conjugated molecules. Using a transfer Hamiltonian ansatz for the coupled quantum dots, we calculate the Faraday rotation signal as a function of the probe frequency in a pump-probe setup using neutral quantum dots. Additionally, we study the signal of one spin-polarized excess electron in the coupled dots. We show that, in both cases, the Faraday rotation angle is determined by the spin transfer probabilities and the Heisenberg spin exchange energy. By comparison of our results with experimental data, we find that the transfer matrix element for electrons in the conduction band is of order 0.08 eV and the spin transfer probabilities are of order 10%.

196.  Phonon-induced decay of the electron spin in quantum dots
Vitaly N. Golovach, Alexander Khaetskii, and Daniel Loss.
Phys. Rev. Lett. 93, 016601 (2004); cond-mat/0310655.

We study spin relaxation and decoherence in a
GaAs quantum dot due to spin-orbit interaction. We derive an effective Hamiltonian which couples the electron spin to phonons or any other fluctuation of the dot potential. We show that the spin decoherence time $T_2$ is as large as the spin relaxation time $T_1$, under realistic conditions. For the Dresselhaus and Rashba spin-orbit couplings, we find that, in leading order, the effective magnetic field can have only fluctuations transverse to the applied magnetic field. As a result, $T_2=2T_1$ for arbitrarily large Zeeman splittings, in contrast to the naively expected case
$T_2\ll T_1$. We show that the spin decay is drastically suppressed for certain magnetic field directions and values of the
Rashba coupling constant. Finally, for the spin coupling to acoustic phonons, we show that
$T_2=2T_1$ for all spin-orbit mechanisms in leading order in the electron-phonon interaction.

197.  Asymmetric Quantum Shot Noise in Quantum Dots
Hans-Andreas Engel and Daniel Loss.
Phys. Rev. Lett. 93, 136602 (2004); cond-mat/0312107.

We analyze the frequency-dependent noise of a current through a quantum dot which is coupled to Fermi leads and which is in the Coulomb blockade regime. We show that the asymmetric shot noise as function of frequency shows steps and becomes super-Poissonian. This provides experimental access to the quantum fluctuations of the current. We present an exact calculation for a single dot level and a perturbative evaluation of the noise in Born approximation (sequential tunneling regime but without Markov approximation) for the general case of many levels with charging interaction.

198.  Spin injection across magnetic/nonmagnetic interfaces with finite magnetic layers
Alexander Khaetskii, J. Carlos Egues, Daniel Loss, Charles Gould, Georg Schmidt, and Laurens W. Molenkamp (Wuerzburg).
Phys. Rev. B 71, 235327 (2005); cond-mat/0312705.

We have reconsidered the relevant problem of spin injection across ferromagnet/non-magnetic-semiconductor (FM/NMS) and dilute-magnetic-semiconductor/non-magnetic-semiconductor interfaces, for structures with \textit{finite} magnetic layers (FM or DMS). By using appropriate physical boundary conditions, we find new expressions for the resistances of these structures which are in general different from previous results in the literature. The results obtained can be important for the interpretation of the experimental data in the case of DMS/NMS structures.

199.  Towards Quantum Communication with Electron Spins
D.S. Saraga, G. Burkard, J.C. Egues, H.-A. Engel, P. Recher, and D. Loss.
Turk J Phys 27, 427 (2003) Proceedings of the Quantum Computation at the Atomic Scale Conference, (Istanbul, 1-11 June, 2003)

We review our recent work towards quantum communication in a solid-state environment with qubits carried by electron spins. We propose three schemes to produce spin-entangled electrons, where the required separation of the partner electrons is achieved via Coulomb interaction. The non-product spin-states originate either from the Cooper pairs found in a superconductor, or in the ground state of a quantum dot with an even number of electrons. In a second stage, we show how spin-entanglement carried by a singlet can be detected in a beam-splitter geometry by an increased (bunching) or decreased (antibunching) noise signal. We also discuss how a local spin-orbit interaction can be used to provide a continuous modulation of the noise as a signature of entanglement. Finally, we review how one can use a quantum dot as a spin- lter, a spin-memory read-out, a probe for single-spin decoherence and ultimately, a single-spin measurement apparatus.

200.  Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei
John Schliemann, Alexander Khaetskii, and Daniel Loss.
J. Phys.: Condens. Matter 15 (24 December 2003) R1809-R1833;; cond-mat/0311159.

We review and summarize recent theoretical and experimental work on electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with surrounding nuclear spins. This topic is of particular interest with respect to several proposals for quantum information processing in solid state systems. Specifically, we investigate the hyperfine interaction of an electron spin confined in a quantum dot in an s-type conduction band with the nuclear spins in the dot. This interaction is proportional to the square modulus of the electron wave function at the location of each nucleus leading to an inhomogeneous coupling, i.e. nuclei in different locations are coupled with different strength. In the case of an initially fully polarized nuclear spin system an exact analytical solution for the spin dynamics can be found. For not completely polarized nuclei, approximation-free results can only be obtained numerically in sufficiently small systems. We compare these exact results with findings from several approximation strategies.

201.  Transport through a double quantum dot in the sequential- and co- tunneling regimes
Vitaly N. Golovach and Daniel Loss.
Phys. Rev. B 69, 245327 (2004); cond-mat/0308241.

We study transport through a double quantum dot, both in the sequential tunneling and cotunneling regimes. Using a master equation approach, we find that, in the sequential tunneling regime, the differential conductance
$G$ as a function of the bias voltage $\Delta\mu$ has a number of satellite peaks with respect to the main peak of the Coulomb blockade diamond. The position of these peaks is related to the interdot tunnel splitting and the singlet-triplet splitting. We find satellite peaks with both {\em positive} and {\em negative} values of differential conductance for realistic parameter regimes. Relating our theory to a microscopic (Hund-Mulliken) model for the double dot, we find a temperature regime for which the Hubbard ratio (=tunnel coupling over on-site Coulomb repulsion) can be extracted from $G(\Delta\mu)$ in the cotunneling regime. In addition, we consider a combined effect of cotunneling and sequential tunneling, which leads to new peaks (dips) in $G(\Delta\mu)$ inside the Coulomb blockade diamond below some temperature scales, which we specify.

202.  Probing entanglement via Rashba-induced shot noise oscillations
J. Carlos Egues, Guido Burkard, and Daniel Loss.
J. Superconductivity, 16, 711 (2003); cond-mat/0207392.

We have recently calculated shot noise for entangled and spin-polarized electrons in novel beam-splitter geometries with a local Rashba s-o interaction in the incoming leads. This interaction allows for a gate-controlled rotation of the incoming electron spins. Here we present an alternate simpler route to the shot noise calculation in the above work and focus on only electron pairs. Shot noise for these shows continuous bunching and antibunching behaviors. In addition, entangled and unentangled triplets yield distinctive shot noise oscillations. Besides allowing for a direct way to identify triplet and singlet states, these oscillations can be used to extract s-o coupling constants through noise measurements. Incoming leads with spin-orbit interband mixing give rise an additional modulation of the current noise. This extra rotation allows the design of a spin transistor with enhanced spin control.

203.  Grover algorithm with large nuclear spins in semiconductors
Michael N. Leuenberger and Daniel Loss.
Phys. Rev. B 68, 165317 (2003); cond-mat/0304674.

We show a possible way to implement the Grover algorithm in large nuclear spins 1/2<I<9/2 in semiconductors. The Grover sequence is performed by means of multiphoton transitions that distribute the spin amplitude between the nuclear spin states. They are distinguishable due to the quadrupolar splitting, which makes the nuclear spin levels non-equidistant. We introduce a generalized rotating frame for an effective Hamiltonian that governs the non-perturbative time evolution of the nuclear spin states for arbitrary spin lengths I. The larger the quadrupolar splitting, the better the agreement between our approximative method using the generalized rotating frame and exact numerical calculations.

204.  Dissipation effects in spin-Hall transport of electrons and holes
John Schliemann and Daniel Loss.
Phys. Rev. B 69, 165315 (2004); cond-mat/0310108.

We investigate the spin-Hall effect of both electrons and holes in semiconductors using the Kubo formula in the correct zero-frequency limit taking into account the finite momentum relaxation time of carriers in real semiconductors. This approach allows to analyze the range of validity of recent theoretical findings. In particular, the spin-Hall conductivity vanishes for vanishing spin-orbit coupling if the correct zero-frequency limit is performed.

205.  Measurement efficiency and n-shot read out of spin qubits
Hans-Andreas Engel, Vitaly Golovach, Daniel Loss, L.M.K. Vandersypen (TU Delft), J.M. Elzerman (TU Delft), R. Hanson (TU Delft), and L.P. Kouwenhoven (TU Delft).
Phys. Rev. Lett. 93, 106804 (2004); cond-mat/0309023.

We consider electron spin qubits in quantum dots and define a measurement efficiency e to characterize reliable measurements via n-shot read outs. We propose various implementations based on a double dot and quantum point contact (QPC) and show that the associated efficiencies e vary between 50% and 100%, allowing single-shot read out in the latter case. We model the read out microscopically and derive its time dynamics in terms of a generalized master equation, calculate the QPC current and show that it allows spin read out under realistic conditions.

206.  Dynamical Coulomb blockade and spin-entangled electrons
Patrik Recher and Daniel Loss.
Phys. Rev. Lett. 91, 267003 (2003); cond-mat/0307444.

We consider the production of mobile and nonlocal pairwise spin-entangled electrons from tunneling of a BCS-superconductor (SC) to two normal Fermi liquid leads. The necessary mechanism to separate the two electrons coming from the same Cooper pair (spin-singlet) is achieved by coupling the SC to leads with a finite resistance. The resulting dynamical Coulomb blockade effect, which we describe phenomenologically in terms of an electromagnetic environment, is shown to be enhanced for tunneling of two spin-entangled electrons into the same lead compared to the process where the pair splits and each electron tunnels into a different lead. On the other hand in the pair-split process, the spatial correlation of a Cooper pair leads to a current suppression as a function of distance between the two tunnel junctions which is weaker for effectively lower dimensional SCs.

207.  Optical Detection of Single-Electron Spin Decoherence in a Quantum Dot
Oliver Gywat, Hans-Andreas Engel, Daniel Loss, R. J. Epstein, F. Mendoza, and D. D. Awschalom (UC Santa Barbara).
Phys. Rev. B 69, 205303 (2004); cond-mat/0307669.

We propose a method based on optically detected magnetic resonance (ODMR) to measure the decoherence time $T2$ of a single electron spin in a semiconductor quantum dot. The electron spin resonance (ESR) of a single excess electron on a quantum dot is probed by circularly polarized laser excitation. The photoluminescence is modulated due to the ESR which enables the measurement of electron spin decoherence. We study different possible schemes for such an ODMR setup.

208.  Anisotropic transport in the two-dimensional electron gas in the presence of spin-orbit coupling
John Schliemann and Daniel Loss.
Phys. Rev. B 68, 165311 (2003); cond-mat/0306528.

In a two-dimensional electron gas as realized by a semiconductor quantum well, the presence of spin-orbit coupling of both the Rashba and Dresselhaus type leads to anisotropic dispersion relations and Fermi contours. We study the effect of this anisotropy on the electrical conductivity in the presence of fixed impurity scatterers. The conductivity also shows in general an anisotropy which can be tuned by varying the Rashba coefficient. This effect provides a method of detecting and investigating spin-orbit coupling by measuring spin-unpolarized electrical currents in the diffusive regime. Our approach is based on an exact solution of the two-dimensional Boltzmann equation and provides also a natural framework for investigating other transport effects including the anomalous Hall effect.

209.  Hyperfine interactions and electron spin dynamics in a quantum dot
A. Khaetskii, D. Loss, and L. Glazman (Minnesota).
Journal of Superconductivity: Incorporating Novel Magnetism 16, 221 (2003)

We show that a wide range of spin clusters with antiferromagnetic intracluster exchange interaction allows one to define a qubit. For these spin cluster qubits, initialization, quantum gate operation, and readout are possible using the same techniques as for single spins. Quantum gate operation for the spin cluster qubit does not require control over the intracluster exchange interaction. Electric and magnetic fields necessary to effect quantum gates need only be controlled on the length scale of the spin cluster rather than the scale for a single spin. Here, we calculate the energy gap separating the logical qubit states from the next excited state and the matrix elements which determine quantum gate operation times. We discuss spin cluster qubits formed by one- and two-dimensional arrays of s=1/2 spins as well as clusters formed by spins s>1/2. We illustrate the advantages of spin cluster qubits for various suggested implementations of spin qubits and analyze the scaling of decoherence time with spin cluster size.

210.  Quantum computing with antiferromagnetic spin clusters
Florian Meier, Jeremy Levy (Pittsburgh), and Daniel Loss.
Phys. Rev. B 68, 134417 (2003); cond-mat/0304296.

We show that a wide range of spin clusters with antiferromagnetic intracluster exchange interaction allows one to define a qubit. For these spin cluster qubits, initialization, quantum gate operation, and readout are possible using the same techniques as for single spins. Quantum gate operation for the spin cluster qubit does not require control over the intracluster exchange interaction. Electric and magnetic fields necessary to effect quantum gates need only be controlled on the length scale of the spin cluster rather than the scale for a single spin. Here, we calculate the energy gap separating the logical qubit states from the next excited state and the matrix elements which determine quantum gate operation times. We discuss spin cluster qubits formed by one- and two-dimensional arrays of s = 1/2 spins as well as clusters formed by spins s > 1/2. We illustrate the advantages of spin cluster qubits for various suggested implementations of spin qubits and analyze the scaling of decoherence time with spin cluster size.

211.  Exact Born Approximation for the Spin-Boson Model
Daniel Loss and David P. DiVincenzo (IBM Yorktown).

Within the lowest-order Born approximation, we present an exact calculation of the time dynamics of the spin-boson model in the Ohmic regime. We observe non-Markovian effects at zero temperature that scale with the system-bath coupling strength and cause qualitative changes in the evolution of coherence at intermediate times of order of the oscillation period. These changes could significantly affect the performance of these systems as qubits. In the biased case, we find a prompt loss of coherence at these intermediate times, whose decay rate is set by $\sqrt{\alpha}$, where $\alpha$ is the coupling strength to the environment. These calculations indicate precision experimental tests that could confirm or refute the validity of the spin-boson model in a variety of systems.

212.  Shot noise for entangled and spin-polarized electrons
J. C. Egues, P. Recher, D. S. Saraga, V. N. Golovach, G. Burkard, E. V. Sukhorukov, and D. Loss.
Quantum Noise in Mesoscopic Physics, NATO ASI Series II, Vol. 97 (Kluwer, 2003), pp 241-274; Proceedings of the NATO Advanced Research Workshop (Delft, The Netherlands, 2-4 June 2002); cond-mat/0210498.

We review our recent contributions on shot noise for entangled electrons and spin-polarized currents in novel mesoscopic geometries. We first discuss some of our recent proposals for electron entanglers involving a superconductor coupled to a double dot in the Coulomb blockade regime, a superconductor tunnel-coupled to Luttinger-liquid leads, and a triple-dot setup coupled to Fermi leads. We calculate current and shot noise for spin-polarized currents and entangled/unentangled electron pairs in a beam-splitter geometry with a \textit{local} Rashba spin-orbit (s-o) interaction in the incoming leads. We find \textit{continuous} bunching and antibunching behaviors for the \textit{entangled} pairs -- triplet and singlet -- as a function of the Rashba rotation angle. In addition, we find that unentangled triplets and the entangled one exhibit distinct shot noise. Shot noise for spin-polarized currents shows sizable oscillations as a function of the Rashba phase. This happens only for electrons injected perpendicular to the Rashba rotation axis; spin-polarized carriers along the Rashba axis are noiseless. We find an additional spin rotation for electrons with energies near the crossing of the bands where s-o induced interband coupling is relevant. This gives rise to an additional modulation of the noise for both electron pairs and spin-polarized currents. Finally, we briefly discuss shot noise for a double dot near the Kondo regime.

213.  Spin-Orbit Coupling and Time-Reversal Symmetry in Quantum Gates
D. Stepanenko (Florida State), N. E. Bonesteel (Florida State), D.P. DiVincenzo (IBM Yorktown), G. Burkard (IBM Yorktown), and D. Loss.
Phys. Rev. B 68, 115306 (2003); cond-mat/0303474.

We study the effect of spin-orbit coupling on quantum gates produced by pulsing the exchange interaction between two single electron quantum dots. Spin-orbit coupling enters as a small spin precession when electrons tunnel between dots. For adiabatic pulses the resulting gate is described by a unitary operator acting on the four-dimensional Hilbert space of two qubits. If the precession axis is fixed, time-symmetric pulsing constrains the set of possible gates to those which, when combined with single qubit rotations, can be used in a simple CNOT construction. Deviations from time-symmetric pulsing spoil this construction. The effect of time asymmetry is studied by numerically integrating the Schr\"odinger equation using parameters appropriate for GaAs quantum dots. Deviations of the implemented gate from the desired form are shown to be proportional to dimensionless measures of both spin-orbit coupling and time asymmetry of the pulse.

214.  Semiconductor Spintronics and Quantum Computation
eds. D.D. Awschalom, D. Loss, and N. Samarth.

The manipulation of electric charge in bulk semiconductors and their heterostructures forms the basis of virtually all contemporary electronic and optoelectronic devices. Recent studies of spin-dependent phenomena in semiconductors have now opened the door to technological possibilities that harness the spin of the electron in semiconductor devices. In addition to providing spin-dependent analogies that extend existing electronic devices into the realm of semiconductor "spintronics" the spin degree of freedom also offers prospects for fundamentally new functionality within the quantum domain, ranging from storage to computation. It is anticipated that the spin degree of freedom in semiconductors will play a crucial role in the development of information technologies in the 21st century. This book brings together a team of experts to provide an overview of emerging concepts in this rapidly developing field. The topics range from spin transport and injection in semiconductors and their heterostructures to coherent processes and quantum computation in semiconductor quantum structures and microcavities.

215.  Noise of Spin-Polarized Currents at a Beam Splitter with Local Spin-Orbit Interaction
G. Burkard, J. C. Egues (Sao Paulo), and D. Loss.
J. Supercond. 16, 237 (2003)

An electronic beam splitter with a local Rashba spin-orbit coupling can serve as a detector for spin-polarized currents. The spin-orbit coupling plays the role of a tunable spin rotator and can be controlled via a gate electrode on top of the conductor. We use spin-resolved scattering theory to calculate the zero-temperature current fluctuations (shot noise) for such a four-terminal device and show that the shot noise is proportional to the spin polarization of the source. Moreover, we analyze the effect of spin-orbit-induced intersubband coupling, leading to an additional spin rotation.

216.  Lower bound for electron spin entanglement from beamsplitter current correlations
Guido Burkard (IBM Yorktown Heights) and Daniel Loss.
Phys. Rev. Lett. 91, 087903 (2003); cond-mat/0303209.

We determine a lower bound for the entanglement of pairs of electron spins injected into a mesoscopic conductor. The bound can be expressed in terms of experimentally accessible quantities, the zero-frequency current correlators (shot noise power or cross-correlators) after transmission through an electronic beam splitter. The effect of spin relaxation (T_1 processes) and decoherence (T_2 processes) during the ballistic coherent transmission of the carriers in the wires is taken into account within Bloch theory. The presence of a variable inhomogeneous magnetic field allows the determination of a useful lower bound for the entanglement of arbitrary entangled states. The decrease in entanglement due to thermally mixed states is studied. Both the entanglement of the output of a source (entangler) and the relaxation (T_1) and decoherence (T_2) times can be determined.

217.  Shot Noise of Cotunneling Current
Eugene Sukhorukov (Geneva), Guido Burkard (IBM Yorktown), and Daniel Loss.
in "Quantum Noise in Mesoscopic Physics", ed. Y.V. Nazarov, pp 149-172, Kluwer, 2003, The Netherlands; cond-mat/0211024.

We study the noise of the cotunneling current through one or several tunnel-coupled quantum dots in the Coulomb blockade regime. The various regimes of weak and strong, elastic and inelastic cotunneling are analyzed for quantum-dot systems (QDS) with few-level, nearly-degenerate, and continuous electronic spectra. In the case of weak cotunneling we prove a non-equilibrium fluctuation-dissipation theorem, which leads to a universal expression for the noise-to-current ratio (Fano factor). The noise of strong inelastic cotunneling can be super-Poissonian due to switching between QDS states carrying currents of different strengths. The transport through a double-dot (DD) system shows an Aharonov-Bohm effect both in noise and current. In the case of cotunneling through a QDS with a continuous energy spectrum the Fano factor is very close to one.

218.  Dynamics of entanglement between quantum dot spin-qubits
John Schliemann and Daniel Loss.

We briefly review the physics of gate operations between quantum dot spin-qubits and analyze the dynamics of quantum entanglement in such processes. The indistinguishable character of the electrons whose spins realize the qubits gives rise to further entanglement-like quantum correlations that go beyond simple antisymmetrization effects. We also summarize further recent results concerning this type of quantum correlations of indistinguishable particles. Finally we discuss decoherence properties of spin-qubits when coupled to surrounding nuclear spins in a semiconductor nanostructure

219.  Discrete Fourier Transform in Nanostructures using Scattering
Michael N. Leuenberger (Iowa), Michael E. Flatte (Iowa), and D. D. Awschalom (UCSB).
J. Appl. Phys. 95, 8167 (2004); cond-mat/0302279.

In this paper we show that the discrete Fourier transform can be performed by scattering a coherent particle or laser beam off a two-dimensional potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant.

220.  Electron spin evolution induced by interaction with nuclei in a quantum dot
Alexander Khaetskii, Daniel Loss, and Leonid Glazman (Minnesota).
Phys. Rev. B 67, 195329 (2003); cond-mat/0211678.

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei for times smaller than the nuclear spin relaxation time. The decay is caused by the spatial variation of the electron envelope wave function within the dot, leading to a non-uniform hyperfine coupling $A$. We show that the usual treatment of the problem based on the Markovian approximation is impossible because the correlation time for the nuclear magnetic field seen by the electron spin is itself determined by the flip-flop processes.
The decay of the electron spin correlation function is not exponential but rather power (inverse logarithm) law-like. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by $\hbar N/A$, where $N$ is the number of nuclei inside the dot. The amplitude of precession, reached as a result of the decay, is finite. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.

221.  Coherent spin quantum dynamics in antiferromagnetic molecular rings
Florian Meier and Daniel Loss.
Physica B 329, 1140 (2003)

Molecular magnetic clusters with antiferromagnetic exchange interaction and easy axis anisotropy belong to the most promising candidate systems for the observation of coherent spin quantum tunneling on the mesoscopic scale. We point out that both nuclear magnetic resonance and electron spin resonance on doped rings are adequate experimental techniques for the detection of coherent spin quantum tunneling in antiferromagnetic molecular rings. Although challenging, the experiments are feasible with present day techniques.

222.  Non-ballistic spin field-effect transistor
John Schliemann, J. Carlos Egues, and Daniel Loss.
Phys. Rev. Lett. 90, 146801 (2003); cond-mat/0211603.

We propose a spin field-effect transistor based on spin-orbit (s-o) coupling of both the Rashba and the Dresselhaus types. Differently from earlier proposals, spin transport through our device is tolerant against spin-independent scattering processes. Hence the requirement of strictly ballistic transport can be relaxed. This follows from a unique interplay between the Dresselhaus and the (gate-controlled) Rashba interactions; these can be tuned to have equal strengths thus yielding k-independent eigenspinors even in two dimensions. We discuss implementations with two-dimensional devices and quantum wires. In the latter, our setup presents strictly parabolic dispersions which avoids complications arising from anticrossings of different bands.

223.  Spin qubits in solid-state structures
G. Burkard and D. Loss.
Europhysics News 33 5 (2002) 166-170; 10.1051/epn:2002503

It is remarkable that today's computers, after the tremendous development during the last 50 years, are still essentially described by the mathematical model formulated by Alan Turing in the 1930's. Turing's model describes computers which operate according to the laws of classical physics. What would happen if a computer was operating according to the quantum laws? Physicists and computer scientists have been interested in this question since the early 1980's, but research in quantum computation really started to flourish after 1994 when Peter Shor discovered a quantum algorithm to find prime factors of large integers efficiently, a problem which is intrinsically hard for any classical computer (see [1] for an introduction into quantum computation). The lack of an algorithm for efficient factoring on a classical machine is actually the basis of the widely used RSA encryption scheme. Phase coherence needs to be maintained for a sufficiently long time in the memory of a quantum computer. This may sound like a harmless requirement, but in fact it is the main reason why the physical implementation of quantum computation is so difficult. Usually, a quantum memory is thought of as a set of two-level systems, named quantum bits, or qubits for short. In analogy to the classical bit, two orthogonal computational basis states |0> and |1> are defined. The textbook example of a quantum two-level system is the spin 1/2 of, say, an electron, where one can identify the "spin up" state with |0> and the "spin down" state with |1>. While several other two-level systems have been proposed for quantum computing, we will devote the majority of our discussion to the potential use of electron spins in nanostructures (such as quantum dots) as qubits.

224.  Magnetization transport and quantized spin conductance
Florian Meier and Daniel Loss.
Phys. Rev. Lett. 90, 167204 (2003); cond-mat/0209521.

We analyze transport of magnetization in insulating systems described by a spin Hamiltonian. The magnetization current through a quasi one-dimensional magnetic wire of finite length suspended between two bulk magnets is determined by the spin conductance which remains finite in the ballistic limit due to contact resistance. For ferromagnetic systems, magnetization transport can be viewed as transmission of magnons and the spin conductance depends on the temperature T. For antiferromagnetic isotropic spin-1/2 chains, the spin conductance is quantized in units of order $(g \mu_B)^2/h$ at T=0. Magnetization currents produce an electric field and hence can be measured directly. For magnetization transport in electric fields phenomena analogous to the Hall effect emerge.

225.  A Datta-Das transistor with enhanced spin control
J. Carlos Egues, Guido Burkard, and Daniel Loss.
Appl. Phys. Lett. 82, 2658 (2003); cond-mat/0209682.

We consider a two-channel spin transistor with weak spin-orbit induced interband coupling. We show that the coherent transfer of carriers between the coupled channels gives rise to an \textit{additional} spin rotation. We calculate the corresponding spin-resolved current in a Datta-Das geometry and show that a weak interband mixing leads to enhanced spin control.

226.  Variational study of the nu=1 quantum Hall ferromagnet in the presence of spin-orbit interaction
John Schliemann, J. Carlos Egues, and Daniel Loss.
Phys. Rev. B 67, 085302 (2003); cond-mat/0209185.

We investigate the nu=1 quantum Hall ferromagnet in the presence of spin-orbit coupling of the Rashba or Dresselhaus type by means of Hartree-Fock-typed variational states. In the presence of Rashba (Dresselhaus) spin-orbit coupling the fully spin-polarized quantum Hall state is always unstable resulting in a reduction of the spin polarization if the product of the particle charge $q$ and the effective $g$-factor is positive (negative). In all other cases an alternative variational state with O(2) symmetry and finite in-plane spin components is lower in energy than the fully spin-polarized state for large enough spin-orbit interaction. The phase diagram resulting from these considerations differs qualitatively from earlier studies.

227.  Spin decay and quantum parallelism
John Schliemann, Alexander V. Khaetskii, and Daniel Loss.
Phys. Rev. B 66, 245303 (2002); cond-mat/0207195.

We study the time evolution of a single spin coupled inhomogeneously to a spin environment. Such a system is realized by a single electron spin bound in a semiconductor nanostructure and interacting with surrounding nuclear spins. We find striking dependencies on the type of the initial state of the nuclear spin system. Simple product states show a profoundly different behavior than randomly correlated states whose time evolution provides an illustrative example of quantum parallelism and entanglement in a decoherence phenomenon.

228.  Quantum computing with spin cluster qubits
Florian Meier, Jeremy Levy (Pittsburgh), and Daniel Loss.
Phys. Rev. Lett. 90, 047901 (2003); cond-mat/0206310.

We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) exchange interaction with uniform and non-uniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and inter-cluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decoherence times and short gate operation times of single spins. Control of single spins is hence not necessary for the realization of universal quantum gates.

229.  Quantum Spin Dynamics in Molecular Magnets
Michael N. Leuenberger, Florian Meier, and Daniel Loss.
Monatshefte für Chem. 134, 217(2003); cond-mat/0205457.

The detailed theoretical understanding of quantum spin dynamics in various molecular magnets is an important step on the roadway to technological applications of these systems. Quantum effects in both ferromagnetic and antiferromagnetic molecular clusters are, by now, theoretically well understood. Ferromagnetic molecular clusters allow one to study the interplay of incoherent quantum tunneling and thermally activated transitions between states with different spin orientation. The Berry phase oscillations found in Fe_8 are signatures of the quantum mechanical interference of different tunneling paths. Antiferromagnetic molecular clusters are promising candidates for the observation of coherent quantum tunneling on the mesoscopic scale. Although challenging, applications of molecular magnetic clusters for data storage and quantum data processing are within experimental reach already with present day technology.

230.  Spin-entangled currents created by a triple quantum dot
Daniel S. Saraga and Daniel Loss.
Phys. Rev. Lett. 90, 166803 (2003); cond-mat/0205553.

We propose a simple setup of three coupled quantum dots in the Coulomb blockade regime as a source for spatially separated currents of spin-entangled electrons. The entanglement originates from the singlet ground state of a quantum dot with an even number of electrons. To preserve the entanglement of the electron pair during its extraction to the drain leads, the electrons are transported through secondary dots. This prevents one-electron transport by energy mismatch, while joint transport is resonantly enhanced by conservation of the total two-electron energy.

231.  Rashba spin-orbit interaction and shot noise for spin-polarized and entangled electrons
J. Carlos Egues, Guido Burkard, and Daniel Loss.
Phys. Rev. Lett. 89, 176401 (2002); cond-mat/0204639.

We study shot noise for spin-polarized currents and entangled electron pairs in a four-probe (beam splitter) geometry with a local Rashba spin-orbit (s-o) interaction in the incoming leads. Within the scattering formalism we find that shot noise exhibits Rashba-induced oscillations with continuous bunching and antibunching. We show that entangled states as well as triplet states can be identified via their Rashba phase in noise measurements. For two-channel leads we find an additional spin rotation due to s-o induced interband coupling which provides additional spin control. We show that the s-o interaction determines the Fano factor which provides a direct way to measure the Rashba coupling constant via noise.

232.  Quantum information processing with large nuclear spins in GaAs semiconductors
Michael N. Leuenberger, Daniel Loss, Martino Poggio (UCSB), and David D. Awschalom (UCSB).
Phys. Rev. Lett. 89, 207601 (2002); cond-mat/0204355.

We propose an implementation for quantum information processing based on coherent manipulations of nuclear spins I=3/2 in GaAs semiconductors. We describe theoretically an NMR method which involves multiphoton transitions and which exploits the non-equidistance of nuclear spin levels due to quadrupolar splittings. Starting from known spin anisotropies we derive effective Hamiltonians in a generalized rotating frame, valid for arbitrary I, which allow us to describe the non-perturbative time evolution of spin states generated by magnetic rf fields. We identify an experimentally accessible regime where multiphoton Rabi oscillations are observable. In the nonlinear regime, we find Berry phase interference effects.

233.  Superconductor coupled to two Luttinger liquids as an entangler for electron spins
Patrik Recher and Daniel Loss.
Phys. Rev. B 65, 165327 (2002); cond-mat/0112298.

We consider an s-wave superconductor (SC) which is tunnel-coupled to two spatially separated Luttinger liquid (LL) leads. We demonstrate that such a setup acts as an entangler, i.e. it creates spin-singlets of two electrons which are spatially separated, thereby providing a source of electronic Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage, which is smaller than the energy gap in the SC, a stationary current of spin-entangled electrons can flow from the SC to the LL leads due to Andreev tunneling events. We discuss two competing transport channels for Cooper pairs to tunnel from the SC into the LL leads. On the one hand, the coherent tunneling of two electrons into the same LL lead is shown to be suppressed by strong LL correlations compared to single-electron tunneling into a LL. On the other hand, the tunneling of two spin-entangled electrons into different leads is suppressed by the initial spatial separation of the two electrons coming from the same Cooper pair. We show that the latter suppression depends crucially on the effective dimensionality of the SC. We identify a regime of experimental interest in which the separation of two spin-entangled electrons is favored. We determine the decay of the singlet state of two electrons injected into different leads caused by the LL correlations. Although the electron is not a proper quasiparticle of the LL, the spin information can still be transported via the spin density fluctuations produced by the injected spin-entangled electrons.

234.  Electron spin decoherence in quantum dots due to interaction with nuclei
Alexander Khaetskii, Daniel Loss, and Leonid Glazman (Univ. of Minnesota).
Phys. Rev. Lett. 88, 186802 (2002); cond-mat/0201303.

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei for times smaller than the nuclear spin relaxation time. The decay is caused by the spatial variation of the electron envelope wave function within the dot, leading to a non-uniform hyperfine coupling.
We evaluate the spin correlation function with and without magnetic fields and find that the decay of the spin precession amplitude is not exponential but rather power (inverse logarithm) law-like. For fully polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field.
The corresponding decay time is given by $\hbar N/A$, where $A$ is a hyperfine interaction constant and $N$ the number of nuclei inside the dot. The amplitude of precession, reached as a result of the decay, is finite. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.

235.  Creation of Nonlocal Spin-Entangled Electrons via Andreev Tunneling, Coulomb Blockade, and Resonant Transport
Patrik Recher and Daniel Loss.
Journal of Superconductivity: Incorporating Novel Magnetism 15 (1): 49-65, February 2002

We discuss several scenarios for the creation of nonlocal spin-entangled electrons which provide a source of electronic Einstein-Podolsky-Rosen (EPR) pairs. Such EPR pairs can be used to test nonlocality of electrons in solid state systems, and they form the basic resources for quantum information processing. The central idea is to exploit the spin correlations naturally present in superconductors in form of Cooper pairs possessing spin-singlet wavefunctions. We show that nonlocal spin-entanglement in form of an effective Heisenberg spin interaction is induced between electron spins residing on two quantum dots with no direct coupling between them, but each of them being tunnel-coupled to the same superconductor. We then discuss a nonequilibrium setup with an applied bias where mobile and nonlocal spin-entanglement can be created by coherent injection of two electrons, in a pair (Andreev) tunneling process, into two spatially separated quantum dots and subsequently into two Fermi liquid leads. The current for injecting two spin-entangled electrons into different leads shows a resonance and allows the injection of electrons at the same orbital energy, which is a crucial requirement for the detection of spin-entanglement via the current noise. On the other hand, tunneling via the same dot into the same lead is suppressed by the Coulomb blockade effect of the quantum dots. We discuss Aharonov-Bohm oscillations in the current and show that they contain h/e and h/2e periods, which provides an experimental means to test the nonlocality of the entangled pair. Finally, we discuss a structure consisting of a superconductor weakly coupled to two separate one-dimensional leads with Luttinger liquid properties. We show that strong correlations again suppress the coherent subsequent tunneling of two electrons into the same lead, thus generating again nonlocal spin-entangled electrons in the Luttinger liquid leads.

236.  Electron Spins in Artificial Atoms and Molecules for Quantum Computing
Vitaly N. Golovach and Daniel Loss.
Semicond. Sci. Technol. 17, 355- 366 (2002); cond-mat/0201437.

Achieving control over the electron spin in quantum dots (artificial atoms) or real atoms promises access to new technologies in conventional and in quantum information processing. Here we review our proposal for quantum computing with spins of electrons confined to quantum dots. We discuss the basic requirements for implementing spin-qubits, and describe a complete set of quantum gates for single- and two-qubit operations. We show how a quantum dot attached to leads can be used for spin filtering and spin read-out, and as a spin-memory device. Finally, we focus on the experimental characterization of the quantum dot systems, and discuss transport properties of a double-dot and show how Kondo correlations can be used to measure the Heisenberg exchange interaction between the spins of two dots.

237.  Entanglement and Quantum Gate Operations with Spin-Qubits in Quantum Dots
John Schliemann and Daniel Loss.
``Future Trends in Microelectronics: The Nano Millenium", eds. S. Luryi, J. Xu, and A. Zaslavsky, Wiley, 2002, pp. 319-334; cond-mat/0110150.

We give an elementary introduction to the notion of quantum entanglement between distinguishable parties and review a recent proposal about solid state quantum computation with spin-qubits in quantum dots. The indistinguishable character of the electrons whose spins realize the qubits gives rise to further entanglement-like quantum correlations. We summarize recent results concerning this type of quantum correlations of indistinguishable particles.

238.  Single Spin Dynamics and Decoherence in a Quantum Dot via Charge Transport
Hans-Andreas Engel and Daniel Loss.
Phys. Rev. B 65, 195321-1 (2002); cond-mat/0109470.

We investigate the spin dynamics of a quantum dot with a spin-1/2 ground state in the Coulomb blockade regime and in the presence of a magnetic rf field leading to electron spin resonances (ESR). We show that by coupling the dot to leads, spin properties on the dot can be accessed via the charge current in the stationary and non-stationary limit. We present a microscopic derivation of the current and the master equation of the dot using superoperators, including contributions to decoherence and energy shifts due to the tunnel coupling. We give a detailed analysis of sequential and co-tunneling currents, for linearly and circularly oscillating ESR fields, applied in cw and pulsed mode. We show that the sequential tunneling current exhibits a spin satellite peak whose linewidth gives a lower bound on the decoherence time T_2 of the dot-spin. Similarly, the spin decoherence can be accessed also in the cotunneling regime via ESR induced spin flips. We show that the conductance ratio of the spin satellite peak and the conventional peak due to sequential tunneling saturates at the universal conductance ratio of 0.71 for strong ESR fields. We describe a double-dot setup which generates spin dependent tunneling and acts as a current pump (at zero bias), and as a spin inverter which inverts the spin-polarization of the current. We show that Rabi oscillations of the dot-spin induce coherent oscillations in the time-dependent current. These oscillations are observable in the time-averaged current as function of ESR pulse-duration, and they allow one to access the spin coherence directly in the time domain. We analyze the measurement and read-out process of the dot-spin via currents in spin-polarized leads and identify measurement time and efficiency by calculating the counting statistics, noise, and the Fano factor.

239.  Biexcitons in Coupled Quantum Dots as a Source for Entangled Photons
Oliver Gywat, Guido Burkard, and Daniel Loss.
Phys. Rev. B 65, 205329 (2002); cond-mat/0109223.

We study biexcitonic states in two tunnel-coupled semiconductor quantum dots and show that they provide a source for entangled photons which are spatially separated at production. We distinguish between the various spin configurations and calculate the low-energy biexciton spectrum using the Heitler-London approximation as a function of magnetic and electric fields. We calculate the oscillator strengths for the biexciton recombination involving the sequential emission of two photons with entangled polarizations corresponding to the spin configuration in the biexciton states.

240.  Quantum coherent dynamics in molecular magnetic rings
A. Honecker, F. Meier, Daniel Loss, and B. Normand.
Eur. Phys. J. B 27, 487 (2002); cond-mat/0109201.

We present detailed calculations of low-energy spin dynamics in the ``ferric wheel'' systems Na:Fe_6 and Cs:Fe_8 in a magnetic field. We compute by exact diagonalization the low-energy spectra and matrix elements for total-spin and N'eel-vector components, and thus the time-dependent correlation functions of these operators. We compare our results with semiclassical tunneling descriptions, and discuss their implications for mesoscopic quantum coherence, as well as for the experimental techniques to observe it, in molecular magnetic rings.

241.  Kondo effect and singlet-triplet splitting in coupled quantum dots in a magnetic field
Vitaly N. Golovach and Daniel Loss.
Europhys. Lett. 62, 83 (2003); cond-mat/0109155.

We study two tunnel-coupled quantum dots each with a spin 1/2 and attached to leads in the Coulomb blockade regime. We study the interplay between Kondo correlations and the singlet-triplet exchange splitting $K$ between the two spins. We calculate the cotunneling current with elastic and inelastic contributions and its renormalization due to Kondo correlations, away and at the degeneracy point K=0. We show that these Kondo correlations induce pronounced peaks in the conductance as function of magnetic field $B$, inter-dot coupling $t_0$, and temperature. Moreover, the long-range part of the Coulomb interaction becomes visibile due to Kondo correlations resulting in an additional peak in the conductance vs $t_0$ with a strong $B$-field dependence. These conductance peaks thus provide direct experimental access to $K$, and thus to a crucial control parameter for spin-based qubits and entanglement.

242.  Cancellation of spin-orbit effects in quantum gates based on the exchange coupling
Guido Burkard and Daniel Loss.
Phys. Rev. Lett. 88, 047903 (2002); cond-mat/0108101.

We study the effect of the spin-orbit interaction on quantum gate operations based on the spin exchange coupling where the qubit is represented by the electron spin in a quantum dot or a similar nanostructure. Our main result is the exact cancellation of the spin-orbit effects in the sequence producing the quantum XOR gate for the ideal case where the pulse shapes of the exchange and spin-orbit interactions are identical. For the non-ideal case, we show that the two pulse shapes can be made almost identical and that the gate error is strongly suppressed by two small parameters, the spin-orbit interaction constant and the smallness of the deviation of the two pulse shapes. Similarly, we show that the dipole-dipole interaction leads only to very small errors in the XOR gate.

243.  Electron and Nuclear Spin Dynamics in Ferric Wheels
Florian Meier and Daniel Loss.
Phys. Rev. Lett. 86, 5373 (2001); cond-mat/0101073.

We study theoretically the spin dynamics of the ferric wheel, an antiferromagnetic molecular ring. For a single nuclear or impurity spin coupled to one of the electron spins of the ring, we calculate nuclear and electronic spin correlation functions and show that nuclear magnetic resonance (NMR) and electron spin resonance (ESR) techniques can be used to detect coherent tunneling of the Neel vector in these rings. The location of the NMR/ESR resonances gives the tunnel splitting and its linewidth an upper bound on the decoherence rate of the electron spin dynamics. We illustrate the experimental feasibility of our proposal with estimates for Fe_10 molecules.

244.  Thermodynamics and Spin Tunneling Dynamics in Ferric Wheels with Excess Spin
Florian Meier and Daniel Loss.
Phys. Rev. B 64, 224411 (2001); cond-mat/0107025.

We study theoretically the thermodynamic properties and spin dynamics of a class of magnetic rings closely related to ferric wheels, antiferromagnetic ring systems, in which one of the Fe (III) ions has been replaced by a dopant ion to create an excess spin. Using a coherent-state spin path integral formalism, we derive an effective action for the system in the presence of a magnetic field. We calculate the functional dependence of the magnetization and tunnel splitting on the magnetic field and show that the parameters of the spin Hamiltonian can be inferred from the magnetization curve. We study the spin dynamics in these systems and show that quantum tunneling of the Neel vector also results in tunneling of the total magnetization. Hence, the spin correlation function shows a signature of Neel vector tunneling, and electron spin resonance (ESR) techniques or AC susceptibility measurements can be used to measure both the tunneling and the decoherence rate. We compare our results with exact diagonalization studies on small ring systems. Our results can be easily generalized to a wide class of nanomagnets, such as ferritin.

245.  Quantum Correlations in Two-Fermion Systems
John Schliemann (Univ. of Texas), J. I. Cirac (Univ. of Innsbruck), M. Kus (Polish Academy of Science, Warsaw), M. Lewenstein (Univ. of Hannover), and Daniel Loss.
Phys. Rev. A 64, 022303-9 (2001); quant-ph/0012094.

We characterize and classify quantum correlations in two-fermion systems having 2K single-particle states. For pure states we introduce the Slater decomposition and rank (in analogy to Schmidt decomposition and rank), i.e. we decompose the state into a combination of elementary Slater determinants formed by mutually orthogonal single-particle states. Mixed states can be characterized by their Slater number which is the minimal Slater rank required to generate them. For K=2 we give a necessary and sufficient condition for a state to have a Slater number of 1. We introduce a correlation measure for mixed states which can be evaluated analytically for K=2. For higher K, we provide a method of constructing and optimizing Slater number witnesses, i.e. operators that detect Slater number for some states.

246.  Quantum Computing in Molecular Magnets
Michael N. Leuenberger and Daniel Loss.
Nature 410, 789 (2001); cond-mat/0011415.

We propose the implementation of Grover's algorithm with molecular magnets with spin s>>1 in a unary representation. Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers[1] and in searching a database[2] by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system[3], the superposition of single-particle quantum states is sufficient for Grover's algorithm[4]. Recently, the latter has been successfully implemented[5] using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses molecular magnets[6,7,8,9,10], which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theoretically that molecular magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 105, with access times as short as 10-10 seconds. We show that our proposal should be feasible using the molecular magnets Fe8 and Mn12.

247.  Detection of Single Spin Decoherence in a Quantum Dot via Charge Currents
Hans-Andreas Engel and Daniel Loss.
Phys. Rev. Lett. 86, 4648 (2001); cond-mat/0011193.

We consider a quantum dot attached to leads in the Coulomb blockade regime which has a spin 1/2 ground state. We show that by applying an ESR field to the dot-spin the stationary current in the sequential tunneling regime exhibits a resonance whose line width is determined by the single-spin decoherence time T_2. The Rabi oscillations of the dot-spin are shown to induce coherent current oscillations from which T_2 can be deduced in the time domain. We describe a spin-inverter which can be used to pump current through a double-dot via spin flips generated by ESR.

248.  Magnetization in Molecular Iron Rings
B. Normand, X. Wang, X. Zotos, and Daniel Loss.
Phys. Rev. B 63, 184409 (2001); cond-mat/0011403.

The organometallic ring molecules Fe_6 and Fe_10 are leading examples of a class of nanoscopic molecular magnets, which have been of intense recent interest both for their intrinsic magnetic properties and as candidates for the observation of macroscopic quantum coherent phenomena. Torque magnetometry experiments have been performed to measure the magnetization in single crystals of both systems. We provide a detailed interpretation of these results, with a view to full characterization of the material parameters. We present both the most accurate numerical simulations performed to date for ring molecules, using Exact Diagonalization and Density Matrix Renormalization Group techniques, and a semiclassical description for purposes of comparison. The results permit quantitative analysis of the variation of critical fields with angle, of the nature and height of magnetization and torque steps, and of the width and rounding of the plateau regions in both quantities.

249.  Noise of a Quantum-Dot System in the Cotunneling Regime
Eugene V. Sukhorukov, Guido Burkard, and Daniel Loss.
Phys. Rev. B 63, 125315 (2001); cond-mat/0010458.

We study the noise of the cotunneling current through one or several tunnel-coupled quantum dots in the Coulomb blockade regime. The various regimes of weak and strong, elastic and inelastic cotunneling are analyzed for quantum-dot systems (QDS) with few-level, nearly-degenerate, and continuous electronic spectra. We find that in contrast to sequential tunneling where the noise is either Poissonian (due to uncorrelated tunneling events) or sub-Poissonian (suppressed by charge conservation on the QDS), the noise in inelastic cotunneling can be super-Poissonian due to switching between QDS states carrying currents of different strengths. In the case of weak cotunneling we prove a non-equilibrium fluctuation-dissipation theorem which leads to a universal expression for the noise-to-current ratio (Fano factor). In order to investigate strong cotunneling we develop a microscopic theory of cotunneling based on the density-operator formalism and using the projection operator technique. The master equation for the QDS and the expressions for current and noise in cotunneling in terms of the stationary state of the QDS are derived and applied to QDS with a nearly degenerate and continuous spectrum.

250.  Andreev-Tunneling, Coulomb Blockade, and Resonant Transport of Non-Local Spin-Entangled Electrons
Patrik Recher, Eugene V. Sukhorukov, and Daniel Loss.
Phys. Rev. B 63, 165314 (2001); cond-mat/0009452.

We propose and analyze a spin-entangler for electrons based on an s-wave superconductor coupled to two quantum dots each of which is tunnel-coupled to normal Fermi leads. We show that in the presence of a voltage bias and in the Coulomb blockade regime two correlated electrons provided by the Andreev process can coherently tunnel from the superconductor via different dots into different leads. The spin-singlet coming from the Cooper pair remains preserved in this process, and the setup provides a source of mobile and nonlocal spin-entangled electrons. The transport current is calculated and shown to be dominated by a two-particle Breit-Wigner resonance which allows the injection of two spin-entangled electrons into different leads at exactly the same orbital energy, which is a crucial requirement for the detection of spin entanglement via noise measurements. The coherent tunneling of both electrons into the same lead is suppressed by the on-site Coulomb repulsion and/or the superconducting gap, while the tunneling into different leads is suppressed through the initial separation of the tunneling electrons. In the regime of interest the particle-hole excitations of the leads are shown to be negligible. The Aharonov-Bohm oscillations in the current are shown to contain single- and two-electron periods with amplitudes that both vanish with increasing Coulomb repulsion albeit differently fast.

251.  Spintronics and Quantum Computing: Switching Mechanisms for Qubits
Michael N. Leuenberger and Daniel Loss.
Physica E 10 452-457 (2001); cond-mat/0010434.

Quantum computing and quantum communication are remarkable examples of new information processing technologies that arise from the coherent manipulation of spins in nanostructures. We review our theoretical proposal for using electron spins in quantum-confined nanostructures as qubits. We present single- and two-qubit gate mechanisms in laterally as well as vertically coupled quantum dots and discuss the possibility to couple spins in quantum dots via exchange or superexchange. In addition, we propose a new stationary wave switch, which allows to perform quantum operations with quantum dots or spin-1/2 molecules placed on a 1D or 2D lattice.

252.  Double-Occupancy Errors, Adiabaticity, and Entanglement of Spin-Qubits in Quantum Dots
John Schliemann (University of Texas, USA), Daniel Loss, and A.H. MacDonald (University of Texas, USA).
Phys. Rev. B 63, 085311 (2001); cond-mat/0009083.

Quantum gates that temporarily increase singlet-triplet splitting in order to swap electronic spins in coupled quantum dots, lead inevitably to a finite double-occupancy probability for both dots. By solving the time-dependent Schröodinger equation for a coupled dot model, we demonstrate that this does not necessarily lead to quantum computation errors. Instead, the coupled dot ground state evolves quasi-adiabatically for typical system parameters so that the double-occupancy probability at the completion of swapping is negligibly small. We introduce a measure of entanglement which explicitly takes into account the possibilty of double occupancies and provides a necessary and sufficient criterion for entangled states.

253.  Quantum Dot as Spin Filter and Spin Memory
Patrik Recher, Eugene V. Sukhorukov, and Daniel Loss.
Phys. Rev. Lett. 85, 1962 (2000); cond-mat/0003089].

We consider a quantum dot in the Coulomb blockade regime weakly coupled to current leads and show that in the presence of a magnetic field the dot acts as an efficient spin-filter (at the single-spin level) which produces a spin-polarized current. Conversely, if the leads are fully spin-polarized the up or down state of the spin on the dot results in a large sequential or small cotunneling current, and thus, together with ESR techniques, the setup can be operated as a single-spin memory.

254.  Spintronics and Quantum Computing with Quantum Dots
Patrik Recher, Daniel Loss, and Jeremy Levy (University of Pittsburgh, USA).
p.293-306, in Macroscopic Quantum Coherence and Quantum Computing", eds. D.V. Averin, B. Ruggiero, and P. Silvestrini, Kluwer Academic/Plenum Publishers, New York, 2001; cond-mat/0009270.

The creation, coherent manipulation, and measurement of spins in nanostructures open up completely new possibilities for electronics and information processing, among them quantum computing and quantum communication. We review our theoretical proposal for using electron spins in quantum dots as quantum bits. We present single- and two qubit gate mechanisms in laterally as well as vertically coupled quantum dots and discuss the possibility to couple spins in quantum dots via superexchange. We further present the recently proposed schemes for using a single quantum dot as spin-filter and spin read-out/memory device. 

255.  Spin tunneling and topological sel​ection rules for integer spins
Michael N. Leuenberger and Daniel Loss.
Phys. Rev. B 63, 054414 (2001); cond-mat/0006075.

We present new topological interference effects for the tunneling of a single large spin, which are caused by the symmetry of a general class of magnetic anisotropies. The interference results from spin Berry phases associated with different tunneling paths exposed to the same dynamics. Introducing a generalized path integral for coherent spin states we evaluate transition amplitudes between ground as well as low-lying excited states. We show that these interference effects lead to topological sel​ection rules and spin parity effects for integer spins which agree with quantum sel​ection rules and which thus provide a generalization of the Kramers degeneracy to integer spins.

256.  Coulomb Blockade in the Fractional Quantum Hall Effect Regime
Michael R. Geller (Athens, Georgia, USA) and Daniel Loss.
Phys. Rev. B 62, 16298 (2000) (Rapid Communication); cond-mat/0003318.

We use chiral Luttinger liquid theory to study transport through a quantum dot in the fractional quantum Hall effect regime and find rich non-Fermi-liquid tunneling characteristics. In particular, we predict a remarkable Coulomb-blockade-type energy gap that is quantized in units of the noninteracting level spacing, new power-law tunneling exponents for voltages beyond threshold, and a line shape as a function of gate voltage that is dramatically different than that for a Fermi liquid. We propose experiments to use these unique spectral properties as a new probe of the fractional quantum Hall effect.

257.  Spin-Dependent Josephson Current through Double Quantum Dots and Measurement of Entangled Electron States
Mahn-Soo Choi, C. Bruder, and Daniel Loss.
Phys. Rev. B 62, 13569 (2000)

We study a double quantum dot each dot of which is tunnel-coupled to superconducting leads. In the Coulomb blockade regime, a spin-dependent Josephson coupling between two superconductors is induced, as well as an antiferromagnetic Heisenberg exchange coupling between the spins on the double dot which can be tuned by the superconducting phase difference. We show that the correlated spin states-singlet or triplets-on the double dot can be probed via the Josephson current in a dc-SQUID setup.

258.  Spintronics and Quantum Dots for Quantum Computing and Quantum Communication
Guido Burkard, Hans-Andreas Engel, and Daniel Loss.
Fortschr. Phys. 48, 9-11, pp 965-986 (2000); special issue on Experimental Proposals for Quantum Computation, eds. H.-K. Lo and S. Braunstrein; cond-mat/0004182.

Control over electron-spin states, such as coherent manipulation, filtering and measurement promises access to new technologies in conventional as well as in quantum computation and quantum communication. We review our proposal of using electron spins in quantum confined structures as qubits and discuss the requirements for implementing a quantum computer. We describe several realizations of one- and two-qubit gates and of the read-in and read-out tasks. We discuss recently proposed schemes for using a single quantum dot as spin-filter and spin-memory device. Considering electronic EPR pairs needed for quantum communication we show that their spin entanglement can be detected in mesoscopic transport measurements using metallic as well as superconducting leads attached to the dots.

259.  Conductance fluctuations in diffusive rings: Berry phase effects and criteria for adiabaticity
Hans-Andreas Engel and Daniel Loss.
Phys. Rev. B 62, 10238-10254 (2000); cond-mat/0002396.

We study Berry phase effects on conductance properties of diffusive mesoscopic conductors, which are caused by an electron spin moving through an orientationally inhomogeneous magnetic field. Extending previous work, we start with an exact, i.e. not assuming adiabaticity, calculation of the universal conductance fluctuations in a diffusive ring within the weak localization regime, based on a differential equation which we derive for the diffuson in the presence of Zeeman coupling to a magnetic field texture. We calculate the field strength required for adiabaticity and show that this strength is reduced by the diffusive motion. We demonstrate that not only the phases but also the amplitudes of the h/2e Aharonov-Bohm oscillations are strongly affected by the Berry phase. In particular, we show that these amplitudes are completely suppressed at certain magic tilt angles of the external fields, and thereby provide a useful criterion for experimental searches. We also discuss Berry phase-like effects resulting from spin-orbit interaction in diffusive conductors and derive exact formulas for both magnetoconductance and conductance fluctuations. We discuss the power spectra of the magnetoconductance and the conductance fluctuations for inhomogeneous magnetic fields and for spin-orbit interaction.

260.  Quantum Computers and Quantum Coherence
David P. DiVincenzo (IBM Yorktown Heights, NY, USA) and Daniel Loss.
J. of Magnetism and Magnetic Matls. 200, 202 (1999); cond-mat/9901137.

If the states of spins in solids can be created, manipulated, and measured at the single-quantum level, an entirely new form of information processing, quantum computing, will be possible. We first give an overview of quantum information processing, showing that the famous Shor speedup of integer factoring is just one of a host of important applications for qubits, including cryptography, counterfeit protection, channel capacity enhancement, distributed computing, and others. We review our proposed spin-quantum dot architecture for a quantum computer, and we indicate a variety of first generation materials, optical, and electrical measurements which should be considered. We analyze the efficiency of a two-dot device as a transmitter of quantum information via the propagation of qubit carriers (i.e. electrons) in a Fermi sea.

261.  Transport and Noise of Entangled Electrons
Eugene V. Sukhorukov, Daniel Loss, and Guido Burkard.

We consider a scattering set-up with an entangler and beam splitter where the current noise exhibits bunching behavior for electronic singlet states and antibunching behavior for triplet states. We show that the entanglement of two electrons in the double-dot can be detected in mesoscopic transport measurements. In the cotunneling regime the singlet and triplet states lead to phase-coherent current contributions of opposite signs and to Aharonov-Bohm and Berry phase oscillations in response to magnetic fields. We analyze the Fermi liquid effects in the transport of entangled electrons.

262.  Electron Spins in Quantum Dots as Quantum Bits
Daniel Loss, Guido Burkard, and David P. DiVincenzo.
JNR 2, 401-411 (2000)

The creation, coherent manipulation, and measurement of spins in nanostructures open up completely new possibilities for electronics and information processing, among them quantum computing and quantum communication. We review our theoretical proposal for using electron spins in quantum dots as quantum bits, explaining why this scheme satisfies all the essential requirements for quantum computing. We include a discussion of the recent measurements of surprisingly long spin coherence times in semiconductors. Quantum gate mechanisms in laterally and vertically tunnel-coupled quantum dots and methods for single-spin measurements are introduced. We discuss detection and transport of electronic EPR pairs in normal and superconducting systems.

263.  Spin interactions and switching in vertically tunnel-coupled quantum dots
Guido Burkard, Georg Seelig, and Daniel Loss.
Phys. Rev. B 62, 2581 (2000); cond-mat/9910105.

We determine the spin exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting of the triplet, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization, occurring at in-plane fields of a few Tesla, and perpendicular fields of the order of 10 Tesla for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken technique, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states and therefore for a microscopic spin measurement. In the case where quantum dots of different size are coupled, we present a simple method to switch on and off the spin coupling with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.

264.  Probing Entanglement and Non-locality of Electrons in a Double-Dot via Transport and Noise
Daniel Loss and Eugene V. Sukhorukov.
Phys. Rev. Lett. 84 1035-1038 (2000); cond-mat/9907129.

Addressing the feasibilty of quantum communication with electrons we consider entangled spin states of electrons in a double-dot which is weakly coupled to in--and outgoing leads. We show that the entanglement of two electrons in the double-dot can be detected in mesoscopic transport and noise measurements. In the Coulomb blockade and cotunneling regime the singlet and triplet states lead to phase-coherent current and noise contributions of opposite signs and to Aharonov-Bohm and Berry phase oscillations in response to magnetic fields. These oscillations are a genuine two-particle effect and provide a direct measure of non-locality in entangled states. We show that the ratio of zero-frequency noise to current (Fano factor) is universal and equal to the electron charge.

265.  Quantum Computation and Spin Electronics
D. P. DiVincenzo, G. Burkard, D. Loss, and E. Sukhorukov.
in Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics,
eds. I. O. Kulik and R. Ellialtoglu (NATO ASI), p. 399-428, 2000, Kluwer, Netherlands

In this chapter we explore the connection between mesoscopic physics and quantum computing.  After giving a bibliography providing a general introduction to the subject of quantum information processing, we review the various approaches that are being considered for the experimental implementation of quantum computing and quantum communication in atomic physics, quantum optics, nuclear magnetic resonance, superconductivity, and, especially, normal-electron solid state physics.  We discuss five criteria for the realization of a quantum computer and consider the implications that these criteria have for quantum computation using the spin states of single-electron quantum dots.  Finally, we consider the transport of quantum information via the motion of individual electrons in mesoscopic structures; specific transport and noise measurements in coupled quantum dot geometries for detecting and characterizing electron-state entanglement are analyzed.

266.  Spin tunneling and phonon-assisted relaxation in Mn12-acetate
Michael Leuenberger and Daniel Loss.
cond-mat/9810156; Phys. Rev. B 61, 1286 (2000); cond-mat/9907154; cond-mat/0006149.

We present a comprehensive theory of the magnetization relaxation in a Mn12-acetate crystal in the high temperature regime (T>1K), which is based on phonon-assisted spin tunneling induced by quartic magnetic anisotropy and weak transverse magnetic fields. The overall relaxation rate as function of the longitudinal magnetic field is calculated and shown to agree well with experimental data including all resonance peaks measured so far. The Lorentzian shape of the resonances, which we obtain via a generalized master equation that includes spin tunneling, is also in good agreement with recent data. We derive a general formula for the tunnel splitting energy of these resonances. We show that fourth-order diagonal terms in the Hamiltonian lead to satellite peaks. A derivation of the effective linewidth of a resonance peak is given and shown to agree well with experimental data. In addition, previously unknown spin-phonon coupling constants are calculated explicitly. The values obtained for these constants and for the sound velocity are also in good agreement with recent data. We show that the spin relaxation in Mn12-acetate takes place via several transition paths of comparable weight. These transition paths are expressed in terms of intermediate relaxation times, which are calculated and which can be tested experimentally.

267.  Nonlinear sigma Model Treatment of Quantum Antiferromagnets in a Magnetic Field
Bruce Normand (Univ. of Augsburg), Jordan Kyriakidis, and Daniel Loss.

We present a theoretical analysis of the properties of low-dimensional quantum antiferromagnets in applied magnetic fields. In a nonlinear sigma model description, we use a spin stiffness analysis, a 1/N expansion, and a renormalization group approach to describe the broken-symmetry regimes of finite magnetization, and, in cases of most interest, a low-field regime where symmetry is restored by quantum fluctuations. We compute the magnetization, critical fields, spin correlation functions, and decay exponents accessible by nuclear magnetic resonance experiments. The model is relevant to many systems exhibiting Haldane physics, and provides good agreement with data for the two-chain spin ladder compound CuHpCl. 

268.  Noise of Entangled Electrons: Bunching and Antibunching
Guido Burkard, Daniel Loss, and Eugene V. Sukhorukov.
Phys. Rev. B 61, R16303 (2000); cond-mat/9906071].

Addressing the feasibility of quantum communication with entangled electrons in an interacting many-body environment, we propose an interference experiment using a scattering set-up with an entangler and a beam splitter. It is shown that, due to electron-electron interaction, the delity of the entangled singlet and triplet states is reduced by z_F^2 in a conductor described by Fermi liquid theory. We calculate the quasiparticle weight factor z_F for a two-dimensional electron system. The current noise for electronic singlet states turns out to be enhanced (bunching behavior), while it is reduced for triplet states (antibunching). Within standard scattering theory, we nd that the Fano factor (noise-to-current ratio) for singlets is twice as large as for independent classical particles and is reduced to zero for triplets.

269.  Quantum Dynamics of Pseudospin Solitons in Double-Layer Quantum Hall, Systems
J. Kyriakidis, D. Loss, and A. MacDonald (Bloomington, IN, USA).
Phys. Rev. Lett. 83, 1411-1414 (1999); cond-mat/9904185.

Pseudospin solitons in double-layer quantum Hall systems can be introduced by a magnetic field component coplanar with the electrons and can be pinned by applying voltages to external gates. We estimate the temperature below which depinning occurs predominantly via tunneling and calculate low-temperature depinning rates for realistic geometries.  We discuss the local changes in charge and current densities and in spectral functions that can be used to detect solitons and observe their temporal evolution. 

270.  Observing the Berry phase in diffusive conductors: Necessary conditions for adiabaticity
D. Loss, H. Schoeller (Karlsruhe, D), and P.M. Goldbart (Urbana, IL, USA).
Phys. Rev. B 59 (1999) 13328-13337

We investigate Berry phase effects in the magnetoconductance of diffusive systems and determine the precise criterion for adiabaticity within the weak localization formalism. We show that  the exact solution of the Cooperon propagator for the special case of a cylindrically symmetric texture agrees with the adiabatic approximation in the adiabatic limit characterized by $\tau \gg {1\over d} {l2\over L2}$.  We point out that orientational inhomogeneities in the magnetic field induce dephasing effects that can mask the Berry phase (and any other phase coherent phenomena) for certain parameter values of system and field. 

271.  Incoherent Zener tunneling and its application to molecular magnets
Michael Leuenberger and Daniel Loss.
Phys. Rev. B 61, 12200 (2000); cond-mat/9911065.

We generalize the Landau-Zener theory of coherent tunneling transitions by taking thermal relaxation into account. The evaluation of a new generalized master equation containing a dynamic tunneling rate that includes the interaction between the relevant system and its environment leads to an incoherent Zener transition probability with an exponent that is twice as large as the one of the coherent Zener probability in the limit T->0. We apply our results to molecular clusters, in particular to recent measurements of the tunneling transition of spins in Fe8 crystals performed by Wernsdorfer and Sessoli  [Science 284, 133 (1999)].

272.  Excess Spin and the Dynamics of Antiferromagnetic Ferritin
J.G.E. Harris (UC Santa Barbara, CA, USA), J.E. Grimaldi (UCSB), D.D. Awschalom (UCSB), A. Chiolero, and D. Loss.
Phys. Rev. B 60, 3453-3456 (1999); cond-mat/9904051.

Temperature-dependent magnetization measurements on a series of synthetic ferritin proteins containing from 100 to 3000 Fe(III) ions are used to determine the uncompensated moment of these antiferromagnetic particles. The results are compared with recent theories of macroscopic quantum coherence which explicitly include the effect of this excess moment. The scaling of the excess moment with protein size is consistent with a simple model of finite size effects and sublattice noncompensation. 

273.  Physical Optimization of Quantum Error Correction Circuits
Guido Burkard, Daniel Loss, David P. DiVincenzo (IBM Yorktown Heights, NY, USA), and John A. Smolin (IBM).
Phys. Rev. B 60, 11404 (1999); cond-mat/9905230.

Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes. First, we discuss an optimal quantum circuit implementation of the smallest error-correcting code (the three bit code). Quantum circuits are physically implemented by serial pulses, i.e. by switching on and off external parameters in the Hamiltonian one after another. In contrast to this, we introduce a new parallel switching method which allows faster gate operation by switching all external parameters simultaneously, and which has potential applications for arbitrary quantum computer architectures. We apply both serial and parallel switching to electron spins in coupled quantum dots subject to a Heisenberg coupling $H=J(t) S1· S2$. We provide a list of steps that can be implemented experimentally and used as a test for the functionality of quantum error correction. 

274.  Quantum information processing using electron spins and cavity-QED
A. Imamoglu (UC Santa Barbara, CA, USA), D. D. Awschalom (UCSB), G. Burkard, D. P. DiVincenzo (IBM Yorktown), D. Loss, M. Sherwin (UC Santa Barbara), and A. Small (UC Santa Barbara).
Phys. Rev. Lett. 83, 4204 (1999); quant-ph/9904096.

The electronic spin degrees of freedom in semiconductors typically have decoherence times that are several orders of magnitude longer than other relevant timescales. A solid-state quantum computer based on localized electron spins as qubits is therefore of potential interest. Here, a scheme that realizes controlled interactions between two distant quantum dot spins is proposed. The effective long-range interaction is mediated by the vacuum field of a high finesse microcavity. By using conduction-band-hole Raman transitions induced by classical laser fields and the cavity-mode, arbitrary single qubit rotations and controlled-not operations can be realized. Optical techniques can also be used to measure the spin-state of each quantum dot. 

275.  Coupled quantum dots as quantum gates
G. Burkard, D. Loss, and D.P. DiVincenzo (IBM Yorktown Heights, NY, USA).
Phys. Rev. B 59, 2070 (1999); cond-mat/9808026.

We consider a new quantum gate mechanism based on electron spins in coupled semiconductor quantum dots.  Such gates provide a general source of spin entanglement and can be used for quantum computers.  We determine the exchange coupling $J$ in the effective Heisenberg model as a function of magnetic ($B$) and electric fields, and of the inter-dot distance $a$ within the Heitler-London approximation of molecular physics. This result is refined by using sp-hybridization, and by the Hund-Mulliken molecular-orbit approach which leads to an extended Hubbard description for the two-dot system that shows a remarkable dependence on $B$ and $a$ due to the long-range Coulomb interaction. We find that the exchange $J$ changes sign at a finite field (leading to a pronounced jump in the magnetization) and then decays exponentially.  The magnetization and the spin susceptibilities of the coupled dots are calculated.  We show that the dephasing due to nuclear spins in GaAs can be strongly suppressed by dynamical nuclear spin polarization and/or by magnetic fields. 

276.  Noise in Multiterminal Diffusive Conductors: Universality, Nonlocality and Exchange Effects
Eugene V. Sukhorukov and Daniel Loss.
Phys. Rev. Lett. 80, 4959 (1998); cond-mat/9802050; Phys. Rev. B 59, 13054-13066 (1999); cond-mat/9809239.

We study noise and transport in multiterminal diffusive conductors. Using a Boltzmann-Langevin equation approach we reduce the calculation of shot-noise correlators to the solution of diffusion equations. Within this approach we prove the universality of shot noise in multiterminal diffusive conductors of arbitrary shape and dimension for purely elastic scattering as well as for hot electrons. We show that shot noise in multiterminal conductors is a non-local quantity and that exchange effects can occur in the absence of quantum phase coherence even at zero electron temperature. It is also shown that the exchange effect measured in one contact is always negative -- in agreement with the Pauli principle. We discuss a new phenomenon in which current noise is induced by thermal transport. We propose a possible experiment to measure locally the effective noise temperature. Concrete numbers for shot noise are given that can be tested experimentally. 

277.  Quantum computation with quantum dots
D. Loss and D.P. DiVincenzo (IBM Yorktown Heights, NY, USA).
Phys. Rev. A 57 120-126 (1998); cond-mat/9701055.

We propose a new implementation of a universal set of one- and two-qubit gates for quantum computation using the spin states of coupled single-electron quantum dots.  Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a newly derived spin master equation incorporating decoherence caused by a prototypical magnetic environment.  Dot-array experiments which would provide an initial demonstration of the desired non-equilibrium spin dynamics are proposed. 

278.  Quantum dynamics in mesoscopic magnetism
D. Loss, in Dynamical Properties of, and Unconventional Magnetic Systems.
A.T. Skjeltorp and D. Sherrington (eds.), NATO ASI Series E: Applied Sciences,
Vol. 349, 1998 Kluwer Academic Publishers, p. 29-75

A review of quantum coherence effects in mesoscopic  spin systems is presented. We  begin with a general introduction to the topic of mesoscopic effects in magnetism and give some specific examples of current interest. We review then theoretical results in single domain magnetism of superparamagnetic type and mention  recent measurements on antiferromagnetic  grains (ferritin) and their interpretation in terms of macroscopic quantum coherence. Introducing the effects originating from  spin parity in the context of ferromagnetic grains, we discuss antiferromagnetic particles with excess spins and  molecular magnets such as the ferric wheel. It is shown that tunneling in such magnets can be tuned by external magnetic fields and is directly observable via the magnetization and the Schottky anomaly in the specific heat. The main part of the review  will be devoted to non-uniform magnets and specifically to the   quantum dynamics of domain walls or magnetic solitons.  In a semiclassical analysis based on coherent spin-state path-integrals an effective model for the  domain wall dynamics is derived which includes the effects of spin-wave dissipation and of quantum spin phases (Berry phases). In the presence of a Peierls potential (e.g. due to the discrete lattice)  the soliton center can tunnel coherently between the lattice sites and form a Bloch band. Integer and half-odd integer spins have different energy dispersions resulting from interference between soliton states of opposite chirality--the internal rotation sense of the soliton. These effects occur in ferro- and antiferromagnets due to the presence of a topological spin phase. For antiferromagnetic chains, this spin phase occurs in addition to the Pontryagin-index phase.We will discuss  experimental consequences of this Bloch band structure and  show that ---in analogy to Bloch oscillations of crystal electrons--- static magnetic fields induce large oscillations in the sample magnetization. We will also discuss the extreme quantum limit of spin-1/2 chains in the Ising regime, and show that, quite remarkably, the semiclassical analysis  is valid even in this regime. In particular, for antiferromagnetic Ising chains the low-energy excitations are solitons (Villain modes) which have  been observed in neutron scattering experiments on CsCoCl3. We show that the prediction of chirality effects could be tested via the measurement of the off-diagonal components of the dynamical structure factor. The concept of chirality is shown to be of universal character in a variety of magnetic systems, a notable example being the motion of a hole in a 2D antiferromagnetic background. A common thread in the discussion of quantum dynamics in magnets is provided by the Berry phases and their associated interference effects which can lead to surprising spin parity effects. 

279.  Macroscopic quantum coherence in molecular magnets
A. Chiolero and D. Loss.
Phys. Rev. Lett. 80, 169-172 (1998)

We study macroscopic quantum coherence in antiferromagnetic molecular magnets in the presence of magnetic fields. Such fields generate artificial tunnel barriers with externally tunable strength.  We give detailed semi-classical predictions for the tunnel splitting in various regimes for low and high magnetic fields. We show that the tunneling dynamics of the N\'eel vector can be directly measured via the static magnetization and the specific heat.  We also report on a new quantum phase arising from fluctuations. The analytic results are complemented by numerical simulations. 

280.  Bloch oscillations of magnetic solitons in anisotropic spin-1/2 chains
Jordan Kyriakidis and Daniel Loss.
Phys. Rev. B 58 5568-5583 (1998); cond-mat/9803156.

We study the quantum dynamics of soliton-like domain walls in anisotropic spin-1/2 chains in the presence of magnetic fields. In the absence of fields, domain walls form a Bloch band of delocalized quantum states while a static field applied along the easy axis localizes them into Wannier wave packets and causes them to execute Bloch oscillations, i.e.\ the domain walls oscillate along the chain with a finite Bloch frequency and amplitude.  In the presence of the field, the Bloch band, with a continuum of extended states, breaks up into the Wannier-Zeeman ladder---a discrete set of equally spaced energy levels.  We calculate the dynamical structure factor $Szz (q,\omega)$ in the one-soliton sector at finite frequency, wave vector, and temperature, and find sharp peaks at frequencies which are integer multiples of the Bloch frequency.  We further calculate the uniform magnetic susceptibility and find that it too exhibits peaks at the Bloch frequency.  We identify several candidate materials where these Bloch oscillations should be observable, for example, via neutron scattering measurements. For the particular compound ${\rm CoCl2 \!  · \!  2H2O}$ we estimate the Bloch amplitude to be on the order of a few lattice constants, and the Bloch frequency on the order of 100\,GHz for magnetic fields in the Tesla range and at temperatures of about 18\,Kelvin. 

281.  Macroscopic quantum coherence in ferrimagnets
A. Chiolero and D. Loss.
Phys. Rev. B 56, 738 (1997)

We study macroscopic quantum coherence (MQC) in small magnetic particles where the magnetization (in ferromagnets) or the N\'eel vector (in antiferromagnets) can tunnel between energy minima.  We consider here the more general case of MQC in ferrimagnets by studying a model for a mesoscopic antiferromagnet with an uncompensated magnetic moment.  Through semi-classical calculations we show that even a small moment has a drastic effect on MQC. In particular, there is a rapid crossover to a regime where the MQC tunnel splitting is equal to that obtained for a ferromagnet, even though the system is still an antiferromagnet for all other aspects.  We calculate this tunnel splitting via instanton methods and compare it with numerical evaluations. As an application we re-examine the experimental evidence for MQC in ferritin and show that even though the  uncompensated  moment of ferritin is small it greatly modifies the MQC behavior. The excess spin allows us to extract values for experimental parameters without making any assumption about the classical attempt frequency, in contrast to previous fits. Finally, we also discuss the implications of our results for MQC in molecular magnets. 

282.  Aharonov-Bohm effect in the chiral Luttinger liquid
M. R. Geller (Athens, Georgia, USA) and D. Loss.
Phys. Rev. B 56 9692-9706 (1997)

Edge states of the quantum Hall fluid provide an almost unparalled opportunity to study mesoscopic effects in a highly correlated electron system. In this paper we develop a bosonization formalism for the finite-size edge state, as described by chiral Luttinger liquid theory, and use it to study the Aharonov-Bohm effect. We study tunneling through an edge state formed around an antidot in the fractional quantum Hall regime using Wen's chiral Luttinger liquid theory extended to include mesoscopic effects. We identify a new regime where the Aharonov-Bohm oscillation amplitude exhibits a distinctive crossover from Luttinger liquid power-law behavior to Fermi-liquid-like behavior as the temperature is increased. Near the crossover temperature the amplitude has a pronounced maximum. This non-monotonic behavior and  novel high-temperature nonlinear phenomena that we also predict provide new ways to distinguish experimentally between Luttinger and Fermi liquids. Finally, we predict new mesoscopic edge-current oscillations, which are similar to the persistent currentoscillations in a mesoscopic ring, except that they are not reduced in amplitude by weak disorder. In the fractional quantum Hall regime, these ``chiral persistent currents'' have a universal non-Fermi-liquid temperature dependence and may be another ideal system to observe a chiral Luttinger liquid. 

283.  Chirality correlation of spin solitons: Bloch walls, spin-1/2 solitons and holes in a 2d antiferromagnetic background
Hans-Benjamin Braun and Daniel Loss.
Int. J. Mod. Phys. 10, 21 (1996)

We consider the quantum dynamics of spin solitons in a variety of low-dimensional magnetic systems in the semiclassical and the extreme quantum limit. Introducing the concept of chirality of the soliton we derive the dispersion of spin solitons moving through a periodic pinning potential and show that for half-odd integer spin the topological part of the Berry phase induces a halving of the Brillouin zone as well as chirality correlations between subsequent band minima. We demonstrate that these chirality and spin parity effects are universal by considering quasi-one-dimensional ferromagnets and antiferromagnets with local anisotropies and large spins, as well as spin-½ ferromagnetic and antiferromagnetic Heisenberg chains in the Ising limit. For large spin systems, the tunneling rate between states of opposite chiralities is derived and shown to provide a novel scenario for macroscopic quantum phenomena. The results are extended to solitons moving as holes in a two-dimensional antiferromagnetic background, leading to a hole spectrum which is in remarkable agreement with recent ARPES measurements on high-Tc compounds.

284.  Macroscopic quantum tunneling of ferromagnetic domain walls
H.-B. Braun (Paul Scherrer Institut, CH), J. Kyriakidis, and D. Loss.
Phys. Rev. B 56, 8129-8137 (1997); cond-mat/9710064.

Quantum tunneling of domain walls out of an impurity potential in a mesoscopic ferromagnetic sample is investigated.  Using improved expressions for the domain wall mass and for the pinning potential, we find that the cross-over temperature between thermal activation and quantum tunneling is of a different functional form than found previously. In materials like Ni or YIG, the crossover temperatures are around 5 mK. We also find that the WKB exponent is typically two orders of magnitude larger than current estimates. The sources for these discrepancies are discussed, and precise estimates for the transition from three-dimensional to one-dimensional magnetic behavior of a wire are given. The cross-over temperatures from thermal to quantum transitions and tunneling rates are calculated for various materials and sample sizes.

285.  Mesoscopic Effects in the Fractional Quantum Hall Regime: Chiral Luttinger versus Fermi Liquid
Michael R. Geller, Daniel Loss, and George Kirczenow.
Phys. Rev. Lett. 77, 5110-5113(1996); cond-mat/9606070.

We study tunneling through an edge state formed around an antidot in the fractional quantum Hall regime using Wen's chiral Luttinger liquid theory extended to include mesoscopic effects. We identify a new regime where the Aharonov-Bohm oscillation amplitude exhibits a distinctive crossover from Luttinger liquid power-law behavior to Fermi-liquid-like behavior as the temperature is increased. Near the crossover temperature the amplitude has a pronounced maximum. This non-monotonic behavior and novel high-temperature nonlinear phenomena that we also predict provide new ways to distinguish experimentally between Luttinger and Fermi liquids.

286.  Berry's phase and quantum dynamics of ferromagnetic solitons
Hans-Benjamin Braun and Daniel Loss.
Phys. Rev. B 53, 3237 (1996)

We study spin parity effects and the quantum propagation of solitons "Bloch walls" in quasi-one-dimensional ferromagnets. Within a coherent state path integral approach we derive a quantum field theory for nonuniform spin configurations. The effective action for the soliton position is shown to contain a gauge potential due to the Berry phase and a damping term caused by the interaction between soliton and spin waves. For tempera- tures below the anisotropy gap this dissipation reduces to a pure soliton mass renormalization. The quantum dynamics of the soliton in a periodic lattice or pinning potential reveals remarkable consequences of the Berry phase. For half-integer spin, destructive interference between opposite chiralities suppresses nearest-neighbor hopping. Thus the Brillouin zone is halved, and for small mixing of the chiralities the dispersion reveals a surprising dynamical correlation: Two subsequent band minima belong to different chirality states of the soliton. For integer spin the Berry phase is inoperative and a simple tight-binding dispersion is obtained. Finally it is shown that external fields can be used to interpolate continuously between the Bloch wall disper- sions for half-integer and integer spin.

287.  Absence of spontaneous persistent current for interacting fermions in a one-dimensional mesoscopic ring
Daniel Loss and Thierry Martin.
Phys. Rev. B 47, 4619 (1993)

We address the issue of whether a system of interacting electrons confined to a one-dimensional ring can sustain a spontaneous persistent current in the absence of an externally applied flux. The current-current coupling between electrons, describing radiative back-action effects, is exactly treated in the formalism of quantum electrodynamics, where the electrons interact via the exchange of virtual photons. In addition, the instantaneous screened Coulomb potential is taken into account using the Luttinger liquid model including finite-size parity effects. The partition function is calculated exactly, with the result that the system does not possess a spontaneous persistent current. We show that, in the presence of an external flux, the amplitude of the (conventional) persistent current is reduced by quantum fluctuations of the internal transverse electromagnetic field. These corrections can be expressed in terms of the self-induction of the ring and are shown to be of first and higher order in the small dimensionless parameter αvF*/c, where α is the fine-structure constant and vF* the Fermi velocity renormalized through Coulomb interactions.

288.  Suppression of tunneling due to interference in spin sytems
Daniel Loss, David P. DiVincenzo (IBM Watson, NY), and Goeffrey Grinstein (IBM Watson, NY).
Phys. Rev. Lett. 69, 3232 (1992)

Within a wide class of ferromagnetic and antiferromagnetic systems, quantum tunneling of magnetization direction is spin-parity dependent: it vanishes for magnetic particles with half-integer spin, but is allowed for integer spin. A coherent-state path-integral calculation shows that this topological effect results from interference between tunneling paths.

289.  Macroscopic Quantum Tunneling in Magnetic Proteins
D. D. Awschalom, J. F. Smyth, G. Grinstein, D. P. DiVincenzo, and D. Loss.
Phys. Rev. Lett. 68, 3092 (1992); Phys. Rev. Lett. 71, 4279 (1993); Phys. Rev. Lett. 70, 2199 (1993).

We report low-temperature measurements of the frequency-dependent magnetic noise and magnetic susceptibility of nanometer-scale antiferromagnetic horse-spleen ferritin particles, using an integrated dc SQUID microsusceptometer. A sharply defined resonance near 1 MHz develops below T∼0.2 K. The behavior of this resonance as a function of temperature, applied magnetic field, and particle concentration indicates that it results from macroscopic quantum tunneling of the Néel vector of the antiferromagnets.

290.  Josephson current and proximity effect in Luttinger liquids
D. L. Maslov, M. Stone, P. M. Goldbart, and D. Loss.
Phys. Rev. B53, 1548 (1996)

A theory describing a one-dimensional Luttinger liquid in contact with a superconductor is developed. Boundary conditions for the fermion fields describing Andreev reflection at the contacts are derived and used to construct a bosonic representation of the fermions. The Josephson current through a superconductor/Luttinger liquid/superconductor junction is considered for both perfectly and poorly transmitting interfaces. In the former case, the Josephson current at low temperatures is found to be essentially unaffected by electron-electron interactions. In the latter case, significant renormalization of the Josephson current occurs. The profile of the (induced) condensate wave function in a semi-infinite Luttinger liquid in contact with a superconductor is shown to decay as a power law, the exponent depending on the sign and strength of the interactions. In the case of repulsive (attractive) interactions the decay is faster (slower) than in their absence. An equivalent method of calculating the Josephson current through a Luttinger liquid, which employs the bosonization of the system as a whole (i.e., superconductor, as well as Luttinger liquid) is developed and shown to give the results equivalent to those obtained via boundary condition describing Andreev reflection.

291.  Onset of superconducting fluctuations for interacting fermions coupled to acoustic phonons in one dimension
Thierry Martin (Marseille) and Daniel Loss.
Int. J. Mod. Phys. B 9, 495 (1995)

We consider a one-dimensional system consisting of electrons with short-ranged repulsive interactions and coupled to small-momentum transfer acoustic phonons. The interacting electrons are bosonized and described in terms of a Luttinger liquid which allows us to calculate exactly the one- and two-electron Green function. For non-interacting electrons, the coupling to phonons alone induces a singularity at the Fermi surface which is analogous to that encountered for electrons with an instantaneous attractive interaction. The exponents which determine the presence of singlet/triplet superconducting pairing fluctuations, and spin/charge density wave fluctuations are strongly affected by the presence of the Wentzel-Bardeen singularity, resulting in the favoring of superconducting fluctuations. For the Hubbard model the equivalent of a phase diagram is established, as a function of: the electron-phonon coupling, the electron filling factor, and the on-site repulsion between electrons. The Wentzel-Bardeen singularity can be reached for arbitrary values of the electron-phonon coupling constant by varying the filling factor. This provides an effective mechanism to push the system from the antiferromagnetic into the metallic phase, and finally into the superconducting phase as the electron filling factor is increased towards half-filling.

292.  Wentzel-Bardeen singularity and phase diagram for interacting electrons coupled to acoustic phonons in one dimension
Daniel Loss and Thierry Martin (Marseille).
Phys. Rev. B 50, 12160 (1994)

We consider strongly correlated electrons coupled to low-energy acoustic phonons in one dimension. Using a Luttinger liquid description we calculate the exponents of various response functions and discuss their remarkable sensitivity to the Wentzel-Bardeen singularity induced by the presence of phonons. For the Hubbard model plus phonons the equivalent of a phase diagram is established. By increasing the filling factor towards half filling the Wentzel-Bardeen singularity is approached. This in turn triggers a simple and efficient mechanism to suppress antiferromagnetic fluctuations and to drive the system via a normal metallic state towards a superconducting phase.

293.  Parity effects in a Luttinger liquid: Diamagnetic and paramagnetic ground states
Daniel Loss
Phys. Rev. Lett. 69, 343 (1992)

The concept of a Luttinger liquid in 1D is extended to include twisted boundary conditions on a ring and mesoscopic parity effects due to evenness and oddness of the particle number N0. Using Haldane’s notion of topological excitations, a proof of Leggett’s conjecture is presented, stating that the ground state of interacting 1D quantum systems is diamagnetic or paramagnetic depending on the parity of N0. The persistent currents produced by an Aharonov-Bohm flux are calculated and shown to have period and amplitude that are in agreement with recent experiments.

294.  Experimental consequences of persistent currents due to the Berry phase
Daniel Loss and Paul Goldbart.
Phys. Lett. A 215, 197 (1996)

It has recently been proposed that a mesoscopic ring of normal metal or semiconductor should exhibit equilibrium persistent currents of charge and spin, when embedded in an inhomogeneous magnetic field. The origin of these phenomena lies in the coupling between spin and orbital motion due to the Zeeman interaction, and the resulting geometric phase acquired during orbital motion. We present expressions for the ground state charge and spin currents for systems of many spin-l /2 fermions moving in a one-dimensional ring, and give numerical estimates of the magnitudes of the currents, and also ol‘ the electric field which results from the spin current.

295.  Period and amplitude halving in mesoscopic rings with spin
Daniel Loss and Paul Goldbart.
Phys. Rev. B 43, 13762 (1991)

We consider the flux dependence of persistent currents in mesoscopic rings threaded by magnetic flux, and extend well-known arguments to include particles of spin 1/2. We find several interesting consequences of spin, such as period and amplitude halving in a single ring, without including electron-electron interactions, transverse channels, or disorder. These consequences depend sensitively on the fixed number (modulo 4) of particles on a given ring, and lead to strong fluctuations between samples containing a small number of rings.

296.  Persistent currents from Berry's phase in mesoscopic systems
Daniel Loss and Paul M. Goldbart (Urbana-Champaign).
Phys. Rev. B 45, 13544 (1992)

The quantum orbital motion of electrons in mesoscopic normal-metal rings threaded by a magnetic flux produces striking interference phenomena such as persistent currents due to the Aharonov-Bohm effect. Similarly, when a quantum spin adiabatically follows a magnetic field that rotates slowly in time, the phase of its state vector acquires an additional contribution known as the Berry phase. We explore the combination of these two quantum phenomena by examining the interplay between orbital and spin degrees of freedom for a charged spin-1/2 particle moving in a mesoscopic ring embedded in a classical, static inhomogeneous magnetic field, i.e, a texture. As a consequence of its orbital motion through the texture, the spin experiences, via the Zeeman interaction, a varying magnetic field. This results in a Berry—or geometric—phase, leading to persistent (i.e., equilibrium) currents of charge and spin. These mesoscopic phenomena are related to (but should be distinguished from) the conventional persistent currents that result from magnetic flux through a ring. We develop a path-integral approach to decouple the orbital and spin motion and, by using an adiabatic approximation, we compute the equilibrium expectation values of the persistent charge and spin currents and the magnetization. We find that the persistent currents depend on the texture in a striking manner through a geometric phase (related to a surface area characterizing the texture) and a geometric vector (related to the projections of this area). In the special case of a cylindrically symmetric texture we use a spectrum obtained by Kuratsuji and Iida to obtain exact results that confirm, independently, the validity of the path-integral approach in the adiabatic limit. We discuss the connection between the geometric vector and quantum-mechanical correlations, and examine quantum fluctuations and the zero-point energy.

297.  Weak-localization effects and conductance fluctuations: Implications of inhomogeneous magnetic fields
Paul M. Goldbart, Herbert Schoeller, and Daniel Loss.
Phys. Rev. B 48, 15218–15236 (1993)

Low-temperature transport in disordered conductors exhibits a variety of fascinating quantum-mechanical interference effects associated with the phenomenon of weak localization. Such effects are typically isolated and probed by virtue of their sensitivity to applied homogeneous magnetic fields, which introduce Aharonov-Bohm phase factors into quantum-mechanical amplitudes. Analogous interference effects have been proposed in the context of the quantum transport of (possibly electrically neutral) particles with spin in the presence of inhomogeneous magnetic fields, which have the effect of introducing Berry phases. Thus, the possibility is raised of isolating and probing quantum interference effects through their sensitivity to the inhomogeneity of applied magnetic fields. In this appear we develop an approach to the study of quantum transport in disordered conductors in the presence of almost arbitrarily inhomogeneous magnetic fields, which is based on diagrammatic and semiclassical path-integral techniques and a subsequent adiabatic approximation. We illustrate these ideas with applications to three examples: anomalous weak-field magnetoconductance, conductance oscillations in mesoscopic multiply connected structures, and sample-dependent mesoscopic conductance fluctuations. Among other things, we find that while in the context of the disorder-averaged conductance it is accurate to regard systems as being composed of two independent subsystems (having spins aligned or antialigned with the local external magnetic field) a more interesting and refined structure emerges in the context of conductance fluctuations.

298.  Berry's phase and persistent charge and spin currents in textured mesoscopic rings
Daniel Loss, Paul Goldbart (Urbana-Champaign), and A. V. Balatsky (Los Alamos).
Phys. Rev. Lett. 65, 1655 (1990)

We consider the motion of electrons through a mesoscopic ring in the presence of a classical, static, inhomogeneous, magnetic field. Zeeman interaction between the electron spin and this texture couples spin and orbital motion, and results in a Berry phase. As a consequence, the system supports persistent equilibrium spin and charge currents, even in the absence of conventional electromagnetic flux through the ring. We mention the possibility of analogous persistent mass and spin currents in normal 3He.