Quantum photodetection distributions with 'nonlinear' quantum jump superoperators

We address the issue of the detection and counting of photons. We assume an electromagnetic field enclosed in an ideal cavity, which together with the detector constitute a closed system, so no photon is lost to the environment. Basing ourselves on a microscopic model consisting of a set of two-level atoms (the detector) interacting with the field, we derive a 'nonlinear' jump superoperator. We compare the count statistics calculated within our model with those obtained from previous models, such as the coincidence probability density, two-count conditional probability density, waiting times and the second order correlation function, for several field states