Vladimir M. Stojanovi&#263, Dr.

We propose an analog quantum simulator for the Holstein molecular-crystal model based on a dispersive superconducting circuit QED system composed of transmon qubits and microwave resonators. By varying the circuit parameters, one can readily access both the adiabatic and the anti-adiabatic regimes of this model, and realize the coupling strengths required for small-polaron formation. We present a pumping scheme for preparing small-polaron states of arbitrary quasimomentum within time scales much shorter than the qubit decoherence time. The ground state of the system is characterized by anomalous amplitude fluctuation and measurement-based momentum squeezing in the resonator modes.

We present a method for implementing stabilizer-based codes with encoding schemes of the operator quantum error correction paradigm, e.g., the "standard" five-qubit and CSS codes, on solid-state qubits with Ising or XY-type interactions. Using pulse sequences, we show how to induce the effective dynamics of the stabilizer Hamiltonian, the sum of an appropriate set of stabilizer operators for a given code. Within this approach, the encoded states (ground states of the stabilizer Hamiltonian) can be prepared without measurements and preserved against both the time evolution governed by the original qubit Hamiltonian, and energy-nonconserving errors caused by the environment.

We propose an analog quantum simulation of small-polaron physics using a one-dimensional system of trapped ions acted upon by off-resonant standing waves. This system, envisioned as an array of microtraps, in the single-excitation case allows the realization of the antiadiabatic regime of the Holstein model. We show that the strong excitation-phonon coupling regime, characterized by the formation of small polarons, can be reached using realistic values of the relevant system parameters. Finally, we propose measurements of the quasiparticle residue and the average number of phonons in the ground state, experimental probes validating the polaronic character of the phonon-dressed excitation.

We study two-species Bose-Einstein condensates in quasi two-dimensional optical lattices of varying geometry and potential depth. Based on the numerically exact Bloch and Wannier functions obtained using the plane-wave expansion method, we quantify the drag (entrainment coupling) between the condensate components. This drag originates from the (short range) inter-species interaction and increases with the kinetic energy. As a result of the interplay between interaction and kinetic energy effects, the superfluid-drag coefficient shows a non-monotonic dependence on the lattice depth. To make contact with future experiments, we quantitatively investigate the drag for mass ratios corresponding to relevant atomic species.

The common spin Hamiltonians such as the Ising, XY, or Heisenberg model do not have ground states that are the graph states needed in measurement-based quantum computation. Various highly-entangled many-body states have been suggested as a universal resource for this type of computation, however, it is not easy to preserve these states in solid-state systems due to their short coherence times. Here we propose a scheme for generating a Hamiltonian that has a cluster state as ground state. Our approach employs a series of pulse sequences inspired by established NMR techniques and holds promise for applications in many areas of quantum information processing.

We consider electron(hole)-phonon coupling in crystalline organic semiconductors, using naphthalene for our case study. Employing a first-principles approach, we compute the changes in the self-consistent Kohn-Sham potential corresponding to different phonon modes and go on to obtain the carrier-phonon coupling matrix elements (vertex functions). We then evaluate perturbatively the quasiparticle spectral residues for electrons at the bottom of the lowest-unoccupied- (LUMO) and holes at the top of the highest-occupied (HOMO) band, respectively obtaining $Z_{\textrm{e}}\approx 0.74$ and $Z_{\textrm{h}}\approx 0.78$. Along with the widely accepted notion that the carrier-phonon coupling strengths in polyacenes decrease with increasing molecular size, our results provide a strong microscopic evidence for the previously conjectured non-polaronic nature of band-like carriers in these systems.

We study the realization of a Toffoli gate with superconducting qubits in a circuit-QED setup using quantum-control methods. Starting with optimized piecewise-constant control fields acting on all qubits and typical strengths of XY-type coupling between the qubits, we demonstrate that the optimal gate fidelities are affected only slightly by a "low-pass" filtering of these fields with the typical cutoff frequencies of microwave driving. Restricting ourselves to the range of control-field amplitudes for which the leakage to the non-computational states of a physical qubit is heavily suppressed, we theoretically predict that in the absence of decoherence and leakage, within 75 ns a Toffoli gate can be realized with intrinsic fidelities higher than 90%, while fidelities above 99% can be reached in about 140 ns.

We investigate anisotropic $XXZ$ Heisenberg spin-1/2 chains with control fields acting on one of the end spins, with the aim of exploring local quantum control in arrays of interacting qubits. In this work, which uses a recent Lie-algebraic result on the local controllability of spin chains with "always-on" interactions, we determine piecewise-constant control pulses corresponding to optimal fidelities for quantum gates such as spin-flip (NOT), controlled-NOT (CNOT), and square-root-of-SWAP ($\sqrt{\textrm{SWAP}}$). We find the minimal times for realizing different gates depending on the anisotropy parameter $\Delta$ of the model, showing that the shortest among these gate times are achieved for particular values of $\Delta$ larger than unity. To study the influence of possible imperfections in anticipated experimental realizations of qubit arrays, we analyze the robustness of the obtained results for the gate fidelities to random variations in the control-field amplitudes and finite rise time of the pulses. Finally, we discuss the implications of our study for superconducting charge-qubit arrays.

Motivated by some recent results of quantum control theory, we discuss the feasibility of local operator control in arrays of interacting qubits modeled as isotropic Heisenberg spin chains. Acting on one of the end spins, we aim at finding piecewise-constant control pulses that lead to optimal fidelities for a chosen set of quantum gates. We analyze the robustness of the obtained results for the gate fidelities to random errors in the control fields, finding that with faster switching between piecewise-constant controls the system is less susceptible to these errors. The observed behavior falls into a generic class of physical phenomena that are related to a competition between resonance- and relaxation-type behavior, exemplified by motional narrowing in NMR experiments. Finally, we discuss how the obtained optimal gate fidelities are altered when the corresponding rapidly-varying piecewise-constant control fields are smoothened through spectral filtering.

We explore the consequences of electron-phonon (e-ph) coupling in graphene antidot lattices (graphene nanomeshes), i.e., triangular superlattices of circular holes (antidots) in a graphene sheet. They display a direct band gap whose magnitude can be controlled via the antidot size and density. The relevant coupling mechanism in these semiconducting counterparts of graphene is the modulation of the nearest-neighbor electronic hopping integrals due to lattice distortions (Peierls-type e-ph coupling). We compute the full momentum dependence of the e-ph vertex functions for a number of representative antidot lattices. Based on the latter, we discuss the origins of the previously found large conduction-band quasiparticle spectral weight due to e-ph coupling. In addition, we study the nonzero-momentum quasiparticle properties with the aid of the self-consistent Born approximation, yielding results that can be compared with future angle-resolved photoemission spectroscopy measurements. Our principal finding is a significant e-ph mass enhancement, an indication of polaronic behavior. This can be ascribed to the peculiar momentum dependence of the e-ph interaction in these narrow-band systems, which favors small phonon momentum scattering. We also discuss implications of our study for recently fabricated large-period graphene antidot lattices.

We study graphene antidot lattices -- superlattices of perforations (antidots) in a graphene sheet -- using a model that accounts for the phonon-modulation of the π-electron hopping integrals. We calculate the phonon spectra of selected antidot lattices using two different semi-empirical interatomic potentials. Based on the adopted model and the obtained phonon modes, we quantify the nature of charge-carriers in the system by computing the quasiparticle spectral weight due to the electron-phonon interaction for an excess electron in the conduction band. We show that the phonon-induced renormalization is much stronger than in graphene, with the effective electron masses exhibiting an interesting nonmonotonic dependence on the superlattice period for a given antidot diameter. Our study provides an indication of polaronic behavior and points to the necessity of taking into account the inelastic degrees of freedom in future studies of electronic transport in graphene antidot lattices.

Graphene antidot lattices have recently been proposed as a new breed of graphene-based superlattice structures. We study electronic properties of triangular antidot lattices, with emphasis on the occurrence of dispersionless (flat) bands and the ensuing electron localization. Apart from strictly flat bands at zero energy (Fermi level), whose existence is closely related to the bipartite lattice structure, we also find quasiflat bands at low energies. We predict the real-space electron density profiles due to these localized states for a number of representative antidot lattices. We point out that the studied low-energy localized states compete with states induced by the superlattice-scale defects in this system, which have been proposed as hosts for electron-spin qubits. Furthermore, we suggest that local moments formed in these midgap zero-energy states may be at the origin of a surprising saturation of the electron dephasing length observed in recent weak localization measurements in graphene antidot lattices.

We describe quantum entanglement inherent to the polaron ground states of coupled electron-phonon (or, more generally, particle-phonon) systems based on a model comprising both local (Holstein-type) and nonlocal (Peierls-type) couplings. We study this model using a variational method supplemented by the exact numerical diagonalization on a system of finite size. By way of subsequent numerical diagonalization of the reduced density matrix, we determine the particle-phonon entanglement as given by the von Neumann and linear entropies. Our results are strongly indicative of the intimate relationship between the particle localization/delocalization and the particle-phonon entanglement. In particular, we find a compelling evidence for the existence of a nonanalyticity in the entanglement entropies with respect to the Peierls-coupling strength. The occurrence of such nonanalyticity - not accompanied by an actual quantum phase transition - reinforces analogous conclusion drawn in several recent studies of entanglement in the realm of quantum-dissipative systems. In addition, we demonstrate that the entanglement entropies saturate inside the self-trapped region where the small-polaron states are nearly maximally mixed.

We study bosons in the first excited Bloch band of a double-well optical lattice, recently realized at NIST. By calculating the relevant parameters from a realistic nonseparable lattice potential, we find that in the most favorable cases, the boson lifetime in the first excited band can be several orders of magnitude longer than the typical nearest-neighbor tunneling time scales, in contrast with that of a simple single-well lattice. In addition, for sufficiently small lattice depths, the excited band has minima at nonzero momenta incommensurate with the lattice period, which opens a possibility to realize an exotic superfluid state that spontaneously breaks the time-reversal, rotational, and translational symmetries. We discuss possible experimental signatures of this novel state.

Recently, a homogeneous superfluid state with a single gapless Fermi surface was predicted to be the ground state of an ultracold Fermi gas with spin population imbalance in the regime of molecular Bose-Einstein condensation. We study vortices in this novel state using a symmetry-based effective field theory, which captures the low-energy physics of gapless fermions and superfluid phase fluctuations. This theory is applicable to all spin-imbalanced ultracold Fermi gases in the superfluid regime, regardless of whether the original fermion-pairing interaction is weak or strong. We find a remarkable, unconventional form of the interaction between vortices. The presence of gapless fermions gives rise to a spatially oscillating potential, akin to the RKKY indirect-exchange interaction in non-magnetic metals. We compare the parameters of the effective theory to the experimentally measurable quantities and further discuss the conditions for the verification of the predicted new feature. Our study opens up an interesting question as to the nature of the vortex lattice resulting from the competition between the usual repulsive logarithmic (2D Coulomb) and predominantly attractive fermion-induced interactions.

We develop a variational approach to an extended Holstein model, comprising both local and nonlocal electron-phonon coupling. The approach is based on the minimization of a Bogoliubov bound to the Helmholtz free energy. The ambivalent character of nonlocal coupling, which both promotes and hinders transport, is clearly observed. Furthermore, a salient feature of our results is that the local and nonlocal couplings can compensate each other, leading to a reduction of polaronic effects and a quasi-free character of the excitation. Our findings have implications for organic crystals of π-conjugated molecules, where this electron-phonon coupling mechanism plays an important role.

We present a theoretical description of polaron bandwidth narrowing in organic molecular crystals. Based on a solution of a Holstein-Peierls model for tightly bound electrons interacting with phonons, an explicit expression for the temperature dependence of the electronic bandwidths is found. This formula generalizes the result of Holstein polaron theory by treating local and nonlocal electron-phonon coupling on equal footing. The usefulness of the method is demonstrated by model studies for oligo-acene crystals from which microscopic insight into the relevance of the different coupling mechanisms is obtained.

We present a theoretical description of polaron band narrowing in oligo-acene crystals due to electron-lattice interaction. The analysis is based on a model which takes both local and nonlocal contributions to the electron-phonon coupling into account. Different approximation schemes are discussed and compared. The theory is supplemented by quantitative ab-initio calculations of the temperature dependence of polaron bandwidths in oligo-acene crystals which show the important role of in-plane nonlocal electron-phonon coupling.