Competition between two-photon driving, dissipation and interactions in bosonic lattice models: an exact solution

TL;DR

This paper provides an exact solution for steady states in driven-dissipative bosonic lattice models, revealing phenomena like phase transitions, mode competition, and symmetry breaking, especially where mean-field approaches fail.

Contribution

It introduces an exact, dimension-independent solution for complex quantum bosonic models with two-photon driving and interactions, uncovering novel dissipative phenomena.

Findings

Discovery of dissipative phase transitions

Observation of mode competition and symmetry breaking

Stabilization of many-body $SU(1,1)$ pair coherent states

Abstract

We present an exact solution in arbitrary dimensions for the steady states of a class of quantum driven-dissipative bosonic models, where a set of modes is subject to arbitrary two-photon driving, single-photon loss and a global Hubbard (or Kerr)-like interaction. Our solutions reveal a wealth of striking phenomena, including the emergence of dissipative phase transitions, nontrivial mode competition physics and symmetry breaking, and the stabilization of many-body $SU(1,1)$ pair coherent states. Our exact solutions enable the description of spatial correlations, and are fully valid in regimes where traditional mean-field and semiclassical approaches break down.