Abstract

A micromaser is pumped by a beam of excited Rydberg atoms,¹ the arrival times of the individual pump atoms at the microwave cavity being randomly distributed according to the pumping statistics. We suppose that all pump atoms are in the upper level of the maser transition and that the pumping statistics is represented by a stationary renewal process² that is completely characterized by the probability density distribution f^(t) for the waiting time between two successive pump atoms. To fix the time scale we assume that the first atom enters the cavity at t = 0. Neglecting the effect of cavity damping during the transit of a single atom we show that the field density operator ρ_c(τ) conditioned on the fact that another atom is injected at time t and referring to the time instant immediately before the injection of this other atom obeys the evolution equation with P₂(0, τ) being the two-time coincidence probability density of pump atoms and r denoting the injection rate. In the above equation ρ₀ stands for the density operator of the cavity field immediately after the transit of the first atom. The operator U(τ) is implicitly given by the relation where the operators M and exp(LT) describe the effect of the transit of a single atom and of cavity damping during an interval T, respectively, on the density operator of the cavity field. We obtain the steady-state condition.

© 1994 IEEE