Dynamical and steady-state properties of a Bose-Hubbard chain with bond dissipation: A study based on matrix product operators

We study a dissipative Bose-Hubbard chain subject to an engineered bath using a superoperator approach based on matrix product operators. The dissipation is engineered to stabilize a Bose-Einstein condensate wave function in its steady state. We then characterize the steady state emerging from the interplay between incompatible Hamiltonian and dissipative dynamics. While it is expected that interactions lead to this competition, even the kinetic energy in an open boundary condition setup competes with the dissipation, leading to a nontrivial steady state. We also present results for the transient dynamics and probe the relaxation time revealing the closing of the dissipative gap in the thermodynamic limit.