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Optica Acta International Journal of Optics

A Model for Photodetection of Single-mode Cavity Radiation

Terence J. Shepherd

Published Apr 1, 1981• 42 citations
Publisher

Abstract

A model for photodetection is presented which permits evolution of the detected field during the detection process. The integrated univariate and bivariate statistics of the photocount are obtained exactly for detection of single-mode thermal, coherent and free-field cavity radiation. The scheme encompasses the results of three hitherto disparate photocounting models, and demonstrates explicitly the relation between the univariate photon counting statistics and the photon statistics of the field. First-order photocount correlation functions are derived and compared with the corresponding cavity photon population correlations. Photocount antibunching is examined and found to be possible in this model.

DOI
10.1080/713820581

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Journal of Modern Optics•Feb 1, 1987•3 citations
A model for photodetection is presented which permits evolution of the detected field during the detection process. The integrated univariate and bivariate statistics of the photocount are obtained exactly for detection of single-mode thermal, coherent and free-field cavity radiation. The scheme encompasses the results of three hitherto disparate photocounting models, and demonstrates explicitly the relation between the univariate photon counting statistics and the photon statistics of the field. First-order photocount correlation functions are derived and compared with the corresponding cavity photon population correlations. Photocount antibunching is examined and found to be possible in this model.
One can attempt to derive some information of the field from the measured random properties of the photoelectron process: this is the object of photodetection theory developed first for classical fields. This chapter presents a review of photodetection theory, quantum theory and population monitoring model. It discusses two interesting applications to photostatistics. The photodetection equation is used to classify quantum and classical fields. The chapter presents an example of collective antibunching of photons. The double random character of the photodetection process prevents a simple correspondence between the statistical properties of the intensity and the statistics of the photocounts. However it is more instructive to connect the photoelectron process with the quantum nature of the electromagnetic field. Although the problem of photodetection appears to be satisfactorily solved for free fields interacting only with the detector, a heuristic model permits evolution of the detected field during the detection process.
The semiclassical formalism for integrated statistics in photoelectron counting is compared with a method of population monitoring for a single-mode cavity field evolving according to an arbitrary Markov process. Equations governing the exact integrated statistics in the two approaches are shown to be identical up to a single-photon loss process associated with the photodetection. Specific examples are provided, illustrating the relation of these methods to explicitly second-quantized formulations.
A non-markovian model of the detection of cavity photons is proposed. The cavity photons interact with the atoms of the detector in a two-stage process, while the evolution of the cavity photons is modelled, as usual, as a population process with constant rate parameters. The joint distribution of the cavity photons and the number of detected photoelectrons is studied. The results corresponding to the markovian model proposed by Shepherd are recovered by an appropriate limiting procedure. Some simple characteristics of the twofold counting statistics are also obtained. In particular, the memory effects of two-stage detection are shown to result in a depletion of bunching; the shape of the spectrum (in the time domain), while similar to that obtained using the Shepherd model, is depressed pointwise by a memory-dependent factor.
A simple model is introduced to simulate the detection of cavity radiation with the detector placed outside the cavity. Explicit expressions, in terms of initial photon-number distribution, for the time-dependent distributions of photoelectron number and conditional as well as unconditional waiting times are derived. The effect of photodetection on the quantum state of the radiation in the present arrangement is found to be unchanged from that with the detector placed inside the cavity. The well-known Q parameter introduced by Mondel [Opt. Lett. 4, 205 (1979)] is found to be exactly equal to the change in the expectation value of photon number due to the detection of a photon. Photon bunching or antibunching, reflecting classical or nonclassical radiation, is determined by whether conditional waiting time is less or greater than unconditional waiting time. When this criterion is applied to three specific examples, namely, coherent, thermal, and number states, the results are as expected.
The conventional model of the photodetection process and the short-time approximation are used to obtain the factorial moment generating function for the NNN-fold detection of mixed thermal and coherent radiation. This generating function is then used to obtain the photocount distribution for twofold joint photodetection. The photocount distribution is expressed as a threefold summation over Laguerre polynomials. The distribution is examined for the limiting cases of purely thermal radiation and uncorrelated fields.
A detailed analysis is provided of a non-Markov model of cavity population in which each emission gives rise to a random dead-time during which no further emissions can take place. Differential equations are derived for the generating functions governing the cavity population size. The moment structure of the population size is examined and explicit expressions for the first two moments are provided. The photon population statistics are shown to be antibunched for a wide choice of the population parameters. The detection process is analysed and an explicit expression is provided for the Hanbury Brown-Twiss type of correlation. It is further shown that an appropriate choice of the population parameters can produce a thermal stream with Lorentzian profile.