Non-Equilibrium Phase Transitions in Cooperative Atomic Systems

We consider N two level atoms driven far from equilibrium by a coherent driving field. The atoms may decay by a cooperative (J2 preserving) mechanism or a non-cooperative (J2 non-conserving) mechanism where J is the atomic pseudo angular momentum. We adopt a mean field theory to study the J2 non-conserving interaction. This indicates that the system displays a first order phase transition in several observables, e.g., mean field, spectrum and photon statistics. The two stable branches of the hysteresis curve are shown to be regions of cooperative and non-cooperative behaviour respectively. In the case of cooperative atomic decays we find a solution to the Fokker-Planck equation in the atomic coherent state representation. This predicts a second order phase transition in atomic observables—a cooperative fluorescent critical point.