Phase diagram of the chiral Dicke model

We consider a collection of N two-level atoms coupled to a two-mode cavity, where each cavity mode appears only in co-rotating or counter-rotating terms with different coupling strengths. This model has a U(1) symmetry associated with the conservation of angular momentum. We dub this model the chiral Dicke model, in analogy with the recently proposed chiral Rabi model. We investigate the ground-state phase diagram and the associated quantum phase transition. We show that, while the U(1)-broken superradiant phase is destroyed over most of the phase diagram by the inclusion of cavity dissipation, it survives when both coupling constants are equal in strength.