Gaussian trajectory approach to dissipative phase transitions: the case of quadratically driven photonic lattices

TL;DR

This paper uses Gaussian trajectories to analyze dissipative phase transitions in large photonic lattices, revealing a second-order transition in the universality class of the thermal Ising model.

Contribution

It introduces a Gaussian trajectories method for studying critical behavior in large, dissipative photonic systems, enabling precise analysis of phase transitions.

Findings

Identification of a second-order dissipative phase transition

Transition belongs to the thermal Ising universality class

Crossover from quantum to thermal Ising behavior with increasing loss

Abstract

We apply the Gaussian trajectories approach to the study of the critical behavior of two-dimensional dissipative arrays of nonlinear photonic cavities, in presence of two-photon driving and in regimes of sizable loss rates. In spite of the highly mixed character of the density matrix of this system, the numerical approach is able to provide precise estimations of the steady-state expectation values, even for large lattices made of more than 100 sites. By performing a finite-size scaling of the relevant properties of the steady state, we extrapolate the behavior of the system in the thermodynamic limit and we show the emergence of a second-order dissipative phase transition, belonging to the universality class of thermal Ising model. This result indicates the occurrence of a crossover when the loss rate is increased from the weak-loss limit, in which the phase transition belongs to the universality class of the quantum Ising model