We study the nonequilibrium steady state of the driven-dissipative
Bose-Hubbard model with Kerr nonlinearity. Employing a mean-field decoupling
for the intercavity hopping J, we find that the steep crossover between low
and high photon-density states inherited from the single cavity transforms into
a gas−liquid bistability at large cavity-coupling J. We formulate a van der
Waals like gas−liquid phenomenology for this nonequilibrium situation and
determine the relevant phase diagrams, including a new type of diagram where a
lobe-shaped boundary separates smooth crossovers from sharp, hysteretic
transitions. Calculating quantum trajectories for a one-dimensional system, we
provide insights into the microscopic origin of the bistability.Comment: 5 pages, 4 figures + Supplemental Material (2 pages, 2 figures
