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Journal of Optics B Quantum and Semiclassical Optics

Time-interval distributions of a random point process in the detection of classical and nonclassical states of light

C. Bendjaballah

Published Jul 23, 2003• 5 citations
Publisher

Abstract

Time-interval distributions for nonstationary random point processes are calculated. Curves are presented to illustrate some examples encountered in the detection of classical and nonclassical states of light at low power levels.
DOI
10.1088/1464-4266/5/4/308

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The analysis of the statistical properties of the point process (PP) of photon detection times can be used to determine whether or not an optical field is classical, in the sense that its statistical description does not require the methods of quantum optics. This determination is, however, more difficult than ordinarily admitted and the first aim of this paper is to illustrate this point by using some results of the PP theory. For example, it is well known that the analysis of the photodetection of classical fields exhibits the so-called bunching effect. But this property alone cannot be used to decide the nature of a given optical field. Indeed, we have presented examples of point processes for which a bunching effect appears and yet they cannot be obtained from a classical field. These examples are illustrated by computer simulations. Similarly, it is often admitted that for fields with very low light intensity the bunching or antibunching can be described by using the statistical properties of the distance between successive events of the point process, which simplifies the experimental procedure. We have shown that, while this property is valid for classical PPs, it has no reason to be true for nonclassical PPs, and we have presented some examples of this situation also illustrated by computer simulations.
Wait-time distributions for the nthn\mathrm{th}nth photodetection at a detector illuminated by a stationary light beam are studied. Both unconditional measurements, initiated at an arbitrary instant, and conditional measurements, initiated upon a photodetection, are considered. Simple analytic expressions are presented for several classical and quantum sources of light and are used to quantify and compare photon sequences generated by them. These distributions can be measured in photon-counting experiments and are useful in characterizing and generating photon sequences with prescribed statistics. The effects of nonunit detection efficiency are also discussed, and curves are presented to illustrate the behavior.