  Time development of electromagnetic fields in closed cavities under
continuous detection of photons continues to be a subject of confusing
controversy. Recently Dodonov et al. [Phys. Rev. A, 75, 013806, 2007] argued
that their model of quantum superoperators (E model) invalidates some of the
predictions of the previously introduced photon counting model of Srinivas and
Davies [J. Mod. Optic. 28, 981, 1981] (SD model). Both the SD and the E models
are based on two postulated quantum jump superoperators: (1) the one-count
operator corresponding to the absorption of a single photon and (2) the
no-count operator. In this work we develop a stochastic difference equation
that describes the dissipative coupling of the cavity field and the detector.
The difference equation is based on non-perturbative treatment of the
cavity-detector coupling. In spite of being non-integrable due to the coupling
of the detector with an external reservoir it can be used to derive the exact
forms of the quantum jump superoperators. When applied to a particular photon
counting measurement our theory gives predictions identical with those of the
SD model which should be considered a non-perturbative and ab-initio result. It
is pointed out that available experimental results coincide with the results
given by the ab-initio SD model. We summarize some of the key characteristics
of cavity fields and photon counting processes to demonstrate that the results
given by the SD model are consistent with the principles of quantum mechanics
while those given by the E model are not.

Quantum Physics