Spatial correlations in driven-dissipative photonic lattices

TL;DR

This paper develops a self-consistent expansion method to analyze the nonequilibrium steady states of interacting photons in driven-dissipative lattices, revealing complex phase transitions and correlations beyond mean-field approximations.

Contribution

It introduces a novel inverse coordination number expansion to solve Lindblad equations, surpassing mean-field limitations, and benchmarks this approach with exact numerical methods.

Findings

Large density fluctuations at the gas-liquid transition.

Photon antibunching-bunching transition explained.

Insights into phase behavior beyond mean-field approximations.

Abstract

We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose-Hubbard and spin-$1/2$ XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array ($\sim 1/z$) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) We show that the gas--liquid transition in the driven-dissipative Bose-Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching--bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-$1/2$ XY model and provide a simple explanation of this phenomenon.