On the origin of divergences in the coincidence probabilities in cavity photodetection experiments

The theory of photon correlation is an established part of quantum electronics. However, recently reported divergences in the theory of time correlated detection of photons show that important details of cavity photon statistics are still incompletely understood. The quantum jump superoperators of the SD photon counting model given by Srinivas and Davies (1981 J. Mod. Opt. 28 981-96 ) do not fulfil the assumption of the bounded interaction rate. This has raised doubts about the consistency of the SD photon counting model and especially about the existence of coincidence probability density (CPD) functions (Dodonov et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 99-108). In this work, we start from the first principles of the quantum trajectory theory and show how the different coincidence probability densities and coincidence probabilities (CPs) have to be calculated. CPDs derived by us are well defined, and CPs are finite and correctly normalized for all fields with finite photon number expectation value. Furthermore, we show that the SD model reproduces photon bunching and antibunching phenomena when consistent derivation for the second-order coherence degree is used.