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.

Replaced with new improved version. To appear in EPJ QT

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Cited by in corpus (8)

• Measurements of nanoresonator-qubit interactions in a hybrid quantum electromechanical system
• Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution
• Staggered Quantum Walks with Hamiltonians
• Staggered quantum walks with superconducting microwave resonators
• Two component quantum walk in one-dimensional lattice with hopping imbalance
• Decoherence in the three-state quantum walk
• Absorption-based qubit estimation in discrete-time quantum walks
• Inverse determination of light-matter coupling in disordered systems from transmittance spectra