# Phase diagram of incoherently driven strongly correlated photonic lattices

## TL;DR

This paper theoretically investigates the nonequilibrium phases of a driven-dissipative photonic lattice, revealing a phase transition from a Mott-like state to a coherent phase driven by hopping rates and symmetry breaking.

## Contribution

It introduces a phase diagram for incoherently driven strongly correlated photonic lattices using a Gutzwiller approach and finite-size simulations, highlighting a novel nonequilibrium phase transition.

## Key findings

- Identifies a second-order phase transition with symmetry breaking.
- Shows the transition is driven by commensurability, not nonlinearity.
- Validates mean-field results with matrix product and corner-space methods.

## Abstract

We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator coupled to a two-level emitter, which is pumped incoherently. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of such a system. We find that, at a critical value of the inter-cavity photon hopping rate, a second-order nonequilibrium phase transition associated with the spontaneous breaking of the $U(1)$ symmetry occurs. The transition from an incompressible Mott-like photon fluid to a coherent delocalized phase is driven by commensurability effects and not by the competition between photon hopping and optical nonlinearity. The essence of the mean-field predictions is corroborated by finite-size simulations obtained with matrix product operators and corner-space renormalization methods.