Spontaneous polarized phase transitions and symmetry breaking in the imbalanced Dicke model

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Abstract
We investigated the ground-state properties and quantum phase transitions (QPTs) of an ensemble of N four-level atoms in an optical cavity, coupled to a single cavity mode and external laser fields. The system is described by an extended imbalanced Dicke model, in which the co-rotating and counter-rotating coupling terms are allowed to have different coupling strengths. We analytically identified several novel polarized phases characterized by the phase differences between the Raman laser and either the cavity field or the atomic spin excitation. Furthermore, the full phase diagram and QPTs were also revealed. Two sign-dependent coexisting phases were identified, in which the normal phase persists as a metastable state alongside the superradiant ground state. Finally, the breaking or restoration of the intrinsic symmetry in this system was addressed. It was found that, in addition to the continuous U ( 1 ) and discrete Z 2 symmetries, the system also exhibits two reflection symmetries σ v s and a central symmetry C 2 in the abstract position–momentum representation, as a discrete reflection parity–time ( PT ) symmetry and a parameter exchange symmetry T ex in the parameter space. These additional symmetries are governed by two Coxeter groups.

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