ONE-ATOM MASER - STATISTICS OF DETECTOR CLICKS

We present a general theory for the calculation of various characteris tic properties of the beam of atoms emerging from a resonator in one-a tom-maser experiments. The beam is described in terms of the statistic s of the detector clicks. The evolution of the state of the maser phot ons between clicks is governed by a nonlinear master equation. The non linearity originates in the necessity to account for the atoms that es cape detection. Despite the permanent reductions of the photon state, resulting from the detections, the steady state of the conventional li near master equation determines the statistics of the detector clicks. The whole process is ergodic, in the sense that a single run of the e xperiment contains all reproducible statistical data, provided the dur ation of the run is much longer than all relevant correlation times. T he nonlinear master equation is used to calculate the distribution of waiting times between detector clicks. Other statistical properties of the clicks that are derived include correlation functions and varianc es of the counting statistics. The formalism is applied to standard on e-atom-maser experiments and to parity measurements on both unpumped a nd pumped cavities. We find that, for the standard one-atom-maser oper ation, none of the said statistical properties is a simple immediate i ndicator for a sub-Poissonian variance of the photon number. For examp le, the detector clicks may be antibunched although the photon distrib ution has a super-Poissonian variance.