Phase transition to the spontaneous coherent state

The dynamics of the Dicke-maser model is considered when the phase transition to a spontaneous coherent state takes place. In the molecular field approximation an expression for the atomic correlation function is found which shows dynamic peculiarities of the spontaneous coherent state (SCS) in the form of a Goldstone mode and a temperature dependence of the resonance frequency of the system. Also the photon correlation function is obtained which consists of two parts in the SCS. The first part, which is coherent and proportional to the number of the atoms, has a pole Ω = 0. An ambiguity caused by this pole explains the SCS phase transition as the spontaneous appearance of the coherent state of the radiation field. The second uncoherent part is responsible for the dynamic properties of the radiation field into the resonance cavity. From a physical point of view the phase transition to the SCS is displayed by the spontaneous appearance of a constant transverse field with simultaneous transverse dipolar polarization of the atoms. By a simple decoupling of the equations of motion the existence of a soft mode is shown for T ⩾ Tinc