Nonequilibrium Phase Diagram of a Driven-Dissipative Many-Body System

TL;DR

This paper explores the nonequilibrium phase diagram of a driven-dissipative bosonic lattice system, revealing phase transitions, instabilities, and the role of collective variables through a mean-field approach.

Contribution

It introduces a generalized Gutzwiller mean field method to analyze the steady states and phase transitions in a driven-dissipative many-body bosonic system.

Findings

Identification of a phase transition into a non-long-range order state.

Discovery of a domain with spontaneously broken translational symmetry.

Analytical description of the system's evolution during instability at low densities.

Abstract

We study the nonequilibrium dynamics of a many-body bosonic system on a lattice, subject to driving and dissipation. The time-evolution is described by a master equation, which we treat within a generalized Gutzwiller mean field approximation for density matrices. The dissipative processes are engineered such that the system, in the absence of interaction between the bosons, is driven into a homogeneous steady state with off-diagonal long range order. We investigate how the coherent interaction affects qualitatively the properties of the steady state of the system and derive a nonequilibrium phase diagram featuring a phase transition into a steady state without long range order. The phase diagram exhibits also an extended domain where an instability of the homogeneous steady state gives rise to a persistent density pattern with spontaneously broken translational symmetry. In the limit of small particle density, we provide a precise analytical description of the time-evolution during the instability. Moreover, we investigate the transient following a quantum quench of the dissipative processes and we elucidate the prominent role played by collective topological variables in this regime.