Cavity photon counting: ab-initio derivation of the quantum jump superoperators and comparison of the existing models

TL;DR

This paper derives the quantum jump superoperators for cavity photon counting from first principles and shows that the Srinivas and Davies model aligns with experimental results and quantum mechanics, unlike the Dodonov et al. model.

Contribution

It provides an ab-initio derivation of the SD model's superoperators using a non-perturbative approach, clarifying their validity over the E model.

Findings

SD model predictions match experimental results

The derived superoperators are consistent with quantum mechanics

E model predictions are inconsistent with quantum principles

Abstract

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.