Transition between vacuum and finite-density states in the infinite-dimensional Bose–Hubbard model with spatially inhomogeneous dissipation

Abstract

Abstract We analyze the dynamics of the infinite-dimensional Bose–Hubbard model with spatially inhomogeneous dissipation in the hardcore boson limit by solving the Lindblad master equation with use of the Gutzwiller variational method. We consider dissipation processes that correspond to inelastic light scattering in the case of Bose gases in optical lattices. We assume that the dissipation is applied to half of the lattice sites in a spatially alternating manner. We focus on steady states at which the system arrives after long time evolution. We find that when the average particle density is varied, the steady state exhibits a transition between a state in which the sites without dissipation are vacuum and one containing a finite number of particles at those sites. We associate the transition with the notion that the sites with dissipation tend towards a local state at infinite temperature.