Mediated nonreciprocal phase transitions in the open Dicke model with and without adiabatic elimination

Nonreciprocal phase transitions associated with spontaneous breaking of Z₂ parity-like symmetries have been observed in many classical systems and characterized theoretically (Fruchart et al 2021). The question arises whether or not similar nonreciprocal phase transitions can be observed in quantum mechanical systems, and how they might differ. Famously exhibiting the continuous superradiant phase transition, the Dicke model (Dicke 1954) and driven-dissipative analogues are well-established tools to study quantum coherence in a simplified fashion. Recently, the driven-dissipative Dicke model has been extended to a nonreciprocal (or non-standard) two-species model (Landini et al 2018) and shown to exhibit a nonreciprocal phase transition with spontaneous breaking of a Z₂ parity-like symmetry (Chiacchio et al 2023). In this work, we use the nonreciprocal Dicke model as a foundation to study the effect of mediation on nonreciprocity in open quantum systems and evaluate characteristically quantum mechanical behavior. We conclude with application to physical systems which could realize the model.