Quantum measurement of photon distribution statistics for intra-cavity EM field monitored by dumping atom-pointer

We describe and theoretically study a process of photon distribution statistics measurement for intra-cavity mode of EM field monitored by indirect photo-detection scheme. In particular, we investigate photon number distribution and Mandel's parameter (normalized dispersion) of the mode using statistics of atomic state detector clicks. In our model, a two-level atom-pointer which passes through the cavity interacts with the mode and environment, distorting the measured statistical properties of the mode. To account for this, phase distortion (decoherece) and population relaxation are introduced in the model. In this paper, we use the super-operators approach to intra-cavity mode evolution conditioned by atomic state detector clicks.