Dynamics, correlations and phases of the micromaser

The micromaser possesses a variety of dynamical phase transitions parametrized by the flux of atoms and the time-of-flight of the atom within the cavity. We discuss how these phases may be revealed to an observer outside the cavity using the long-time correlation length in the atomic beam. Some of the phase transitions are not reflected in the average excitation level of the outgoing atom, which is the commonly used observable. The correlation length is directly related to the leading eigenvalue of the time evolution operator, which we study in order to elucidate the phase structure. We find that as a function of the time-of-flight the transition from the thermal to the maser phase is characterized by a sharp peak in the correlation length. For longer times-of-flight there is a transition to a phase where the correlation length grows exponentially with the flux. We present a detailed numerical and analytical treatment of the different phases and discuss the physics behind them.