Breaking strong symmetries in dissipative quantum systems: Bosonic atoms coupled to a cavity

In dissipative quantum systems, strong symmetries can lead to the existence of conservation laws and multiple steady states. In this Letter we investigate a strong symmetry for bosonic atoms coupled to an optical cavity, an experimentally relevant system, generalizing the adiabatic elimination techniques and using numerically exact matrix product state methods. We show that for ideal bosons coupled to the cavity multiple steady states exist and in each symmetry sector a dissipative phase transition occurs at a different critical point. This implies that phases of very different natures can coexist. We find that the introduction of a slight breaking of the strong symmetry by a small interaction term leads to a direct transition from multiple steady states to a unique steady state. We point out the phenomenon of dissipative freezing, the breaking of the conservation law at the level of individual realizations in the presence of strong symmetry. For a small breaking of the strong symmetry we see that the behavior of the individual trajectories still shows some signs of this dissipative freezing before it fades out for larger symmetry breaking terms.