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.

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 propose an analog quantum simulator for the Holstein molecular-crystal model based on a superconducting circuit QED system in the dispersive regime. By varying the driving field on the superconducting resonators, one can access both the adiabatic and antiadiabatic regimes of this model, and the strong electron-phonon coupling required for small-polaron formation can be readily reached. We show that a small-polaron state of arbitrary quasimomentum can be generated by applying a microwave pulse to the resonators. We also show that significant squeezing in the resonator modes can be achieved in the polaron-crossover regime through a measurement-based scheme.

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 study the realization of a Toffoli gate with superconducting qubits in a circuit-quantum-electrodynamics 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 noncomputational 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. DOI: http://dx.doi.org/10.1103/PhysRevB.85.054504 ©2012 American Physical Society

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.