Collapse of superradiant phase and Dicke phase transition at finite temperature in a hybrid optical-mechanical system

Abstract

In this paper, we theoretically investigate Dicke phase transition at finite temperature in a hybrid optical-mechanical system. The thermodynamic equilibrium states are presented by means of the functional path-integral approach. We plot the mean photon number of the two cavities and the corresponding phase diagram showing the effects of the coupling strength between the two cavities, the nonlinear photon-phonon interaction strength, the finite temperature, the detuning of the two cavities. The coupling strength between the two cavities can make the phase boundary of the normal phase (NP) to the superradiant phase (SP) shift left with the increase of the atom-field coupling strength. The region of the SP is suppressed completely and the SP disappears completely with the increase of the coupling strength between the two cavities or the nonlinear photon-phonon interaction strength, finally just the NP and the dynamically unstable state (DUS) exist. The nonlinear photon-phonon coupling strength just affects the turning curve, but not the phase boundary. The unstable non-zero photon number state and the SP are coexistent, similar to the optical bistability.