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Optica Acta International Journal of Optics

A Non-markovian Model of Photodetection of Cavity Radiation

S. K. Srinivasan, Ramabhadra Vasudevan

Published Jul 1, 1985• 5 citations
Publisher

Abstract

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.

DOI
10.1080/713821793

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Journal of Physics A Mathematical and General•Jul 11, 1986•6 citations
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.
Some of the implications of non-Markov evolution of cavity radiation and its detection are examined. The cavity photons are modelled as members of a population governed by a Bellman-Harris process supported by immigration. Further it is assumed that there is a detector near the cavity and the photosensitive atoms of the detector absorb the photons with a uniform probability η per unit time. Explicit expressions for the first two moments of the equilibrium cavity distribution are provided. A general formula for the spectral profile is also given. The Markov model of Shepherd is recovered as a special case. A detailed analysis is provided for a special case in which the photon is assumed to go through two hypothetical phases before it gives rise to cavity absorption or stimulated emission. A noteworthy feature is the persistence of bunching, although the bunching is less than that of chaotic light.
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.
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.
The population model of cavity photons previously introduced is analysed by identifying the non-Markov evolution in terms of phases whose durations are themselves independent and exponentially distributed random variables. The resulting radiation is shown to have thermal characteristics for an appropriate choice of the population parameters. The detection process is explicitly introduced and its characteristics are obtained. The model is shown to be viable enough to produce intensity spectra of different shapes corresponding to the resulting radiation.
The problem of cavity radiation and its detection is reviewed and in particular the evolution equation of Scully and Lamb is studied with special reference to coarse-graining. It is shown that the resulting evolution equation corresponds to that of a Markov process representing the cavity population. The approximations corresponding to oscillations below and above threshold reduce the process to a branching process with immigration. The effect of the detector is also studied and the photocount statistics are shown to correspond to those of an emigration process superposed on the branching process. The identification of the evolution as a branching process is shown to result in considerable simplicity and ease in the determination of the statistical characteristics of the cavity population. In particular the Shepherd model is identified as a special case; a complex situation like the multi-mode oscillation is also identified and the corresponding statistical characteristics obtained.