Decay-dephasing-induced steady states in bosonic Rydberg-excited quantum gases in an optical lattice

We investigate the possibility of realizing supersolid quantum phases in bosonic Rydberg-excited quantum lattice gases in the presence of nonunitary processes, by simulating the dynamical evolution starting from initial preparation in nondissipative equilibrium states. Within Gutzwiller theory, we first analyze the many-body ground state of a bosonic Rydberg-excited quantum gas in a two-dimensional optical lattice for variable atomic hopping rates and Rabi detunings. Furthermore, we perform time evolution of different supersolid phases using the Lindblad-master equation. With the inclusion of two different nonunitary processes, namely, spontaneous decay from a Rydberg state to the ground state and dephasing of the addressed Rydberg state, we study the effect of nonunitary processes on those quantum phases and observe long-lived states in the presence of decay and dephasing. We find that long-lived supersolid quantum phases are observable within a range of realistic decay and dephasing rates, while high rates cause any initial configuration to homogenize quickly, preventing possible supersolid formation.