EPJ Quantum Technol. (2016) 3: 9
https://doi.org/10.1140/epjqt/s40507-016-0047-3

Research

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

¹ Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, Campinas, SP, 13083-970, Brazil
² Coordenação de Ciência da Computação, Universidade Estadual do Piauí (UESPI), Parnaíba, PI, 64202-220, Brazil
³ Department of Physics, Syracuse University, Syracuse, NY, 13244-1130, USA

^* e-mail: marcos@ifi.unicamp.br

Received: 16 December 2015
Accepted: 30 May 2016
Published online: 8 June 2016

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.