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Dissipative Dicke model with nonlinear atom–photon interaction

We study a generalized Dicke model, as recently realized in an atomic quantum gas experiment, describing the collective interaction of N two-level atoms with a single cavity mode. The model takes account of dissipation of the cavity field, and includes a nonlinear atom–photon coupling, not present in the conventional Dicke model. We extend previous theoretical investigations of a semiclassical model by including all quantum effects and considering finite atom number N. Our results show good agreement between quantum expectation values and the semiclassical model as N is increased, but also show exotic behaviour for the corresponding quantum state as the nonlinear atom–photon coupling is varied. We consider the cavity-field Wigner function, the atomic Q-function for the collective spin, and the entanglement between the cavity mode and the spin.