First order phase transition in a dissipative Bose-Hubbard chain

Atomic condensates are attractive simulators to study quantum systems at equilibrium thanks to their highly controllable nature. In recent years, they have also become more prominent in studies on non-equilibrium physics. One way to achieve out-of-equilibrium ultracold gases is by introducing dissipation, which can be done in a controllable way. In this talk we theoretically address a Bose-Hubbard chain with losses at one site in the centre, using the Truncated Wigner approximation. We observe bimodality and critical behaviour in the non-equilibrium steady states of the dissipative site, qualitatively corresponding to experimental observations. This indicates the presence of a first order phase transition. Further, we investigate the ability of a more compact, effective description to reproduce this steady-state physics. We find that the suggested model approaches the steady states remarkably well with small deviations in its dynamical properties like the effective Liouvillian gap. The dark soliton state, observed in simulations of the dissipative Bose-Hubbard model, can also be reproduced with this effective description.