The quantum transverse-field Ising chain in circuit QED: effects of disorder on the nonequilibrium dynamics

TL;DR

This paper investigates how disorder affects the nonequilibrium dynamics of a quantum transverse-field Ising chain implemented in circuit QED, highlighting the robustness of certain phenomena and the transition to Anderson localization with increasing disorder.

Contribution

It provides a numerical analysis of disorder effects on the quantum Ising chain in circuit QED, including estimates of mean free path and the transition to localization.

Findings

Small disorder does not prevent observing predicted phenomena.

Disorder impacts the system's dynamics quantitatively.

Transition to Anderson localization occurs with strong disorder.

Abstract

We study several dynamical properties of a recently proposed implementation of the quantum transverse-field Ising chain in the framework of circuit QED. Particular emphasis is placed on the effects of disorder on the nonequilibrium behavior of the system. We show that small amounts of fabrication-induced disorder in the system parameters do not jeopardize the observation of previously-predicted phenomena. Based on a numerical extraction of the mean free path of the system, we also provide a simple quantitative estimate for certain disorder effects on the nonequilibrium dynamics of the circuit QED quantum simulator. We discuss the transition from weak to strong disorder, characterized by the onset of Anderson localization of the system's wave functions, and the qualitatively different dynamics it leads to.