One-atom maser: Phase-sensitive measurements

We reconsider a variant of the one-atom-maser setup in which the emerging atoms are probed for coherent superpositions of the two Rydberg states of the maser transition. The statistical properties of the corresponding detector clicks contain information about the temporal evolution of the phase of the quantized electromagnetic field inside the resonator. We derive analytical expressions for certain statistical quantities, such as the mean number of successive clicks of the same kind, or the atom-atom and the photon-photon correlation functions. The latter are closely related if the photon-number distribution in steady state is dominated by a single narrow peak.