Dark Soliton Formation as a Dark-State Phase Transition in a Dissipative Superfluid Josephson Junction Chain

We identify and characterize a first-order dark-state phase transition between a discrete dark soliton and a uniform superfluid in a Bose-Hubbard chain with a single lossy site. Using classical-field (truncated-Wigner) simulations together with a Bogoliubov stability analysis, we show that the dark-state nature of the soliton suppresses fluctuations and shifts the critical point relative to the comparable phenomenon of optical bistability in driven-dissipative Kerr resonators. We then demonstrate that this mechanism quantitatively captures the bistability phase boundary observed in the experiment of R. Labouvie et al. [Phys. Rev. Lett. 116, 235302 (2016)], resolving substantial discrepancies in prior modeling efforts. Our results reveal how driving, dissipation and quantum coherence can interact to induce nonequilibrium phase transitions in ultra-cold atomic gases.