Beyond mean-field bistability in driven-dissipative lattices: bunching-antibunching transition and quantum simulation

TL;DR

This paper investigates the limitations of mean-field theory in driven-dissipative lattices, revealing a bunching-antibunching transition and proposing a circuit QED quantum simulator for experimental study.

Contribution

It demonstrates that mean-field bistability is an artifact and introduces a quantum simulation approach to explore the true nonequilibrium behavior.

Findings

Mean-field predicts bistability, but correlations remove it.

A bunching-antibunching transition is observed when correlations are included.

A circuit QED setup is proposed for experimental validation.

Abstract

In the present work we investigate the existence of multiple nonequilibrium steady states in a coherently driven XY lattice of dissipative two-level systems. A commonly used mean-field ansatz, in which spatial correlations are neglected, predicts a bistable behavior with a sharp shift between low- and high-density states. In contrast one-dimensional matrix product methods reveal these effects to be artifacts of the mean-field approach, with both disappearing once correlations are taken fully into account. Instead, a bunching-antibunching transition emerges. This indicates that alternative approaches should be considered for higher spatial dimensions, where classical simulations are currently infeasible. Thus we propose a circuit QED quantum simulator implementable with current technology to enable an experimental investigation of the model considered.