Collective dynamics of the unbalanced three-level Dicke model

We study a three-level Dicke model in V-configuration under both closed and open conditions. With independently tunable co- and counter-rotating coupling strength of the interaction Hamiltonian, this model is a generalization of the standard Dicke model that features multiple distinct parameter regimes. Based on a mean-field approach and third quantization analysis, it is found that the system exhibits rich quantum phase behaviours, including distinct superradiant fixed points, multi-phase coexistence and limit cycle oscillation. In particular, the cavity dissipation stabilizes a family of inverted spin coherent steady states, whose stability region can be enlarged or reduced by properly tuning the imbalance between the co- and counter-rotating interactions. This property provide a conceptually new scenario to prepare coherent atomic state with high fidelity.