Dark-state phase transition to a dark soliton in a dissipative Bose-Hubbard chain

We show that a Bose-Hubbard model with local loss exhibits a first-order dark-state phase transition between a dark soliton and a uniform superfluid. Semiclassical simulations and stability analysis reveal that the soliton acts as a many-body dark state, whose suppressed fluctuations modify the transition relative to the comparable phenomenon of optical bistability in Kerr resonators. This mechanism quantitatively captures the bistable phase boundary observed in the experiment of Labouvie [], resolving long-standing discrepancies in previous theoretical modeling. Our results identify a general route by which spatial coherence and engineered loss can generate nonequilibrium phase transitions in ultracold gases.