Phase probability density in subensembles of a quantum mode of a one-atom maser

The method of periodic trajectories is applied to the analysis of the phase states of a one-atom maser mode, information on which can be obtained from a series of consequent indirect phase-sensitive quantum measurements of atoms leaving the cavity. Such information allows one to study in detail the evolution of a maser mode in a stationary state. The evolution pattern is represented as a random sequence of subensembles in which the mode exists during different time intervals. An approximate stochastic recurrence relation is obtained, which allows us, using the Monte Carlo method, to generate a sequence of relative frequencies of detection of the states of a chosen basis in escaping atoms. Formulas for the phase probability density for subensembles of the mode are derived. These formulas are obtained using as initial data the average relative frequencies measured by an experimenter in a region of a stable trajectory.