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

TL;DR

This paper demonstrates how an array of nanoresonators can simulate quantum many-body effects like Anderson localization and thermalization, providing insights into disorder and temperature effects on phonon dynamics.

Contribution

It introduces a nanoresonator array as a quantum simulator for the Anderson model and studies the effects of disorder and thermalization on phonon localization.

Findings

Phonon localization persists at low temperatures for extended periods.

Increasing temperature leads to rapid thermalization and loss of localization.

Proposes an experimental setup using superconducting qubits for measurement.

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.