**Florian Meier**

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Nature Physics

In the field of quantum information science, semiconductor quantum dots are of significant interest for their ability to confine a single electron for use as a qubit. However, to realize the potential offered by quantum information processing, it is necessary to couple two or more qubits. In contrast to coupling individual quantum dots, we demonstrate the integration of two coupled electronic states within a single quantum dot heterostructure. These chemically-synthesized nanocrystals, known as quantum dot quantum wells (QDQWs), are comprised of concentric layers of different semiconducting materials. We investigate carrier and spin dynamics in these structures using transient absorption and time-resolved Faraday rotation measurements. By tuning the excitation and probe energies, we find that we can selectively initialize and read out spins in different coupled states within the QDQW. These results open a pathway for engineering coupled qubits within a single nanostructure.

Phys. Rev. B

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.

Phys. Rev. B

Time-resolved Faraday rotation studies of CdS/CdSe/CdS quantum-dot quantum wells have recently shown that the Faraday rotation angle exhibits several well-defined resonances as a function of probe energy close to the absorption edge. Here, we calculate the Faraday rotation angle from the eigenstates of the quantum-dot quantum well obtained with k.p theory. We show that the large number of narrow resonances with comparable spectral weight observed in experiment is not reproduced by the level scheme of a quantum-dot quantum well with perfect spherical symmetry. A simple model for broken spherical symmetry yields results in better qualitative agreement with experiment.

Phys. Rev. B

We have characterized CdS/CdSe/CdS quantum-dot quantum wells using time-resolved Faraday rotation (TRFR). The spin dynamics show that the electron g-factor varies as a function of quantum well width and the transverse spin lifetime of several nano-seconds is robust up to room temperature. As a function of probe energy, the amplitude of the TRFR signal shows pronounced resonances, which allow one to identify individual exciton transitions. While the TRFR data are inconsistent with the conduction and valence band level scheme of spherical quantum-dot quantum wells, a model in which broken spherical symmetry is taken into account captures the essential features.

Phys. Rev. B

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.

Phys. Rev. B

A quantum dot interacting with two resonant cavity modes is described by a two-mode Jaynes-Cummings model. Depending on the quantum dot energy level scheme, the interaction of a singly doped quantum dot with a cavity photon generates entanglement of electron spin and cavity states or allows one to implement a SWAP gate for spin and photon states. An undoped quantum dot in the same structure generates pairs of polarization entangled photons from an initial photon product state. For realistic cavity loss rates, the fidelity of these operations is of order 80%.

Phys. Rev. B

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%.

Phys. Rev. B

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.

Phys. Rev. Lett.

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.

Phys. Rev. Lett.

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.

Physica B

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.

Monatshefte für Chemie

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.

Eur. Phys. J. B

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.

Phys. Rev. B

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.

Phys. Rev. Lett.

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.

Phys. Rev. A

Using a tunneling Hamiltonian description,
we calculate the Josephson, normal and interference currents between two
Bose-Einstein condensates described by the Bogoliubov theory. The dominant
Josephson term is of first order in the tunneling with a critical current
density proportional to the ground state pressure. In contrast to superconductors
the normal current remains finite at zero temperature. A functional integral
representation of the dynamics of the relative phase is derived and estimates
for an experimental realization of Josephson tunneling in cold atomic gases
are given.

Phys. Rev. A

We show that the condensate occupation
of a superfluid Bose liquid quite generally exhibits anomalously large
fluctuations at finite temperatures. In three dimensions, the variance
of the number N_{0} of particles in the condensate scales nonlinearly
with volume V like T^{2} V^{4/3} at low T, generalizing
the result obtained by Giorgini, Pitaevskii, and Stringari for a weakly
interacting Bose gas. In two dimensions there is only a quasicondensate
whose fluctuations are of the same order as the mean value.

Isaac Newton Institute workshop "Entanglement and Transfer of Quantum Information", Cambridge (UK), September 26 - 30, 2004.

3rd Swiss/US Nanoforum, Basel, October 13-14, 2003.

Seminar talk at the TU Braunschweig, November 21, 2002.

Presentation at the meeting of the MOLNANOMAG network, Manchester, 13.-15.12.2002.

A tutorial presentation at the workshop "Theoretical Concepts and Techniques for Spin Clusters and Single Molecule Magnets" of the MOLNANOMAG network, Florence, 16.-19.11.00.

Contributed talk SYBE 2.7 at the 1999 Annual Meeting of the German Physical Society.

NCCR Nanoscale Science: Scientific Advisory Board Site Visit, October 20, 2003.

Gordon Research Conference on Quantum Information Science, Ventura, CA, March 22-28, 2003.

Twannberg workshop on Nanoscience, October 16-19, 2001

International Conference on Molecule Based Magnets, Valencia, Spain, October 5-11, 2002

Hasliberg workshop on nanoscience 4, Hasliberg, October 16-20, 2000.