Quantum trajectory phase transitions in the micromaser

We study the dynamics of the single atom maser, or micromaser, by means of the recently introduced method of thermodynamics of quantum jump trajectories. We find that the dynamics of the micromaser displays multiple space-time phase transitions, i.e., phase transitions in ensembles of quantum jump trajectories. This rich dynamical phase structure becomes apparent when trajectories are classified by dynamical observables that quantify dynamical activity, such as the number of atoms that have changed state while traversing the cavity. The space-time transitions can be either first-order or continuous, and are controlled not just by standard parameters of the micromaser but also by non-equilibrium "counting" fields. We discuss how the dynamical phase behavior relates to the better known stationary state properties of the micromaser.