Dissipation-induced dynamical phases in a three-level Dicke trimer

Abstract

We investigate the dynamical phases of a dissipative bosonic trimer model, which describes the thermodynamic limit of a three-level generalization of an open Dicke trimer. The model showcases different types of spatial ordering, namely the symmetric (SSR) and the frustrated antisymmetric (fASR) superradiant states. Furthermore, for a certain range  of dissipation strength, there are  occurrences of symmetric (SLC) and antisymmetric (ALC) limit cycles. We also find hybrid static-dynamical phases, wherein some of the sites are in the static superradiant phase while the others exhibit limit cycles. We classify these hybrid phases depending on the number of sites in the limit cycle phase and their symmetry as one-site symmetric (SLC₁) and one-site antisymmetric (ALC₁) limit cycles; and, two-site symmetric (SLC₂) and two-site antisymmetric (ALC₂) limit cycles.  We demonstrate that dissipation plays a crucial role in the existence of these various states in the three-level generalization of an open Dicke trimer close to the thermodynamic limit.