# Spontaneous symmetry breaking in a quadratically-driven nonlinear photonic lattice

## TL;DR

This paper explores phase transitions involving spontaneous symmetry breaking in a driven-dissipative Bose-Hubbard lattice with two-photon driving, revealing second- and first-order transitions depending on driving frequency.

## Contribution

It demonstrates the occurrence of spontaneous symmetry breaking and phase transitions in a quadratically-driven nonlinear photonic lattice, expanding understanding of non-equilibrium quantum phases.

## Key findings

- Second-order phase transition from symmetric to quasi-coherent state.
- Existence of a first-order transition at higher driving frequencies.
- Identification of a phase diagram with multiple stable phases.

## Abstract

We investigate the occurrence of a phase transition, characterized by the spontaneous breaking of a discrete symmetry, in a driven-dissipative Bose-Hubbard lattice in presence of two-photon coherent driving. The driving term does not lift the original $U(1)$ symmetry completely and a discrete $\mathbb{Z}_2$ symmetry is left. When driving the bottom of the Bose-Hubbard band, a mean-field analysis of the steady state reveals a second-order transition from a symmetric phase to a quasi-coherent state with a finite expectation value of the Bose field. For larger driving frequency, the phase diagram shows a third region, where both phases are stable and the transition becomes of first order.