We explore the dissipative phase transition of the two-photon Dicke model, a topic that has garnered significant attention recently. Our analysis reveals that while single-photon loss does not stabilize the intrinsic instability in the model, the inclusion of two-photon loss restores stability, leading to the emergence of superradiant states, which coexist with the normal vacuum states. Using a second-order cumulant expansion for the photons, we derive an analytical description of the system in the thermodynamic limit, which agrees well with the exact calculation results. Additionally, we present the Wigner function for the system, shedding light on the breaking of the $Z_4$ symmetry inherent in the model. These findings offer valuable insights into stabilization mechanisms in open quantum systems and pave the way for exploring complex nonlinear dynamics in two-photon Dicke models.

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• Cavity quantum electrodynamics
• Hybrid quantum systems
• Non-gaussian quantum states
• Photon statistics
• Superradiance & subradiance