Steady-state phases and tunneling-induced instabilities in the driven-dissipative Bose-Hubbard model

TL;DR

This paper investigates the steady-state phases of a driven-dissipative Bose-Hubbard model, revealing tunneling-induced phase transitions, quantum correlation differences from equilibrium, and modulational instabilities due to collective excitations.

Contribution

It introduces a mean-field master equation approach with exact quantum solutions to analyze phase transitions and instabilities in the driven-dissipative Bose-Hubbard model.

Findings

Identification of tunneling-induced monostable and bistable phases

Quantum correlations differ significantly from equilibrium cases

Discovery of collective excitations causing modulational instabilities

Abstract

We determine the steady-state phases of a driven-dissipative Bose-Hubbard model, describing, e.g., an array of coherently pumped nonlinear cavities with a finite photon lifetime. Within a mean-field master equation approach using exact quantum solutions for the one-site problem, we show that the system exhibits a tunneling-induced transition between monostable and bistable phases. We characterize the corresponding quantum correlations, highlighting the essential differences with respect to the equilibrium case. We also find collective excitations with a flat energy-momentum dispersion over the entire Brillouin zone that trigger modulational instabilities at specific wavevectors.