Quantum simulation of the Anderson Hamiltonian with an array of coupled nanoresonators: delocalization and thermalization effects

Abstract

The possibility of using nanoelectromechanical systems as a simulation tool for quantum many-body effects is explored. It is demonstrated that an array of electrostatically coupled nanoresonators can effectively simulate the Bose-Hubbard model without interactions, corresponding in the single-phonon regime to the Anderson tight-binding model. Employing a density matrix formalism for the system coupled to a bosonic thermal bath, we study the interplay between disorder and thermalization, focusing on the delocalization process. It is found that the phonon population remains localized for a long time at low enough temperatures; with increasing temperatures the localization is rapidly lost due to thermal pumping of excitations into the array, producing in the equilibrium a fully thermalized system. Finally, we consider a possible experimental design to measure the phonon population in the array by means of a superconducting transmon qubit coupled to individual nanoresonators. We also consider the possibility of using the proposed quantum simulator for realizing continuous-time quantum walks.

Measurements of nanoresonator-qubit interactions in a hybrid quantum electromechanical system

“…Indeed, with mechanical quantum systems now being engineered and studied, specific applications have begun to crystallize, such as quantum coherent optical-microwave converters [12][13][14], memory elements [15], and signal processing circuitry [16,17]. Moreover, these recent results have also stimulated new ideas for architectures to implement quantum simulators [18], quantum-state generation [19] and studies in quantum thermodynamics [20].…”

Staggered quantum walks with Hamiltonians

“…The generic form of the evolution operator of the SQW with Hamiltonians for 2-tessellable graphs is U = e iθ1H1 e iθ0H0 , where θ 0 and θ 1 are angles. This form is fitted for physical implementations in many physical systems, such as, cold atoms trapped in optical lattices [21,22] and arrays of electromechanical resonators [23].…”

“…Note that since the QW models considered here are single particles quantum walks, the corresponding picture in terms of Hamiltonians ( 12) and ( 13) implementation is to consider a single excitation in the encoding physical system. The joint Hamiltonian H 0 + H 1 describes a large number of physical systems, from cold atoms trapped in optical lattices [21,22] to a linear array of electromechanical resonators [23]. However the alternated action of the two local unitary operators in (7) requires that the Hamiltonians H 0 and H 1 be applied independently.…”

Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution

“…Introduction-The out-of-equilibrium behavior of dissipative many-body systems is of relevance to experimental platforms such as trapped ions [1], cold atoms [2], superconducting circuits [3][4][5], and nanoelectromechanical systems [6]. Theoretical activity has recently increased around developing numerical methods for determining the non-equilibrium steady states (NESS) of such dissipative lattices [7][8][9][10][11][12][13][14][15].…”