Extending the concept of the classical addition of wave packets to that of a random ensemble, a hypothesis has been proposed that treats the classical field as such an ensemble. Computations of the resulting field envelope and short-term counting statistics were also made. As a consequence, a test was proposed that would essentially measure the “shot noise” inherent in such a model and differentiate it from the discreteness resulting from the photodetection process. In this paper the test is examined in terms of the resources and environment necessary to perform it.
Extending the concept of the classical addition of wave packets to that of a random ensemble, a hypothesis has been proposed that treats the classical field as such an ensemble. Computations of the resulting field envelope and short-term counting statistics were also made. As a consequence, a test was proposed that would essentially measure the “shot noise” inherent in such a model and differentiate it from the discreteness resulting from the photodetection process. In this paper the test is examined in terms of the resources and environment necessary to perform it.
In recent articles by this author, [ S. Karp , Statistical properties of ensembles of classical wave packets, J. Opt. Soc. Am.65, 421 ( 1975); S. Karp , Test for the nonexistence of photons, J. Opt. Soc. Am.66, 1421 ( 1976)], a radiation model was proposed that could lead to the identification of certain classical properties of the field, based upon photoelectric counting experiments. Mandel [ L. Mandel , Photoelectric counting measurements as a test for the existence of photons, J. Opt. Soc. Am.67, 1101 ( 1977)] responded by asserting that “It follows that for any field for which a classical wave description exists, in the sense that the phase-space density ϕ({ν}), and therefore P(u), are non-negative it is impossible to distinguish between photons and light waves in photoelectric counting experiments.” This statement is based upon the derivation of similar photoelectron counting equations using quantum and classical techniques. It is the mathematically loose associations and subsequent rigid physical interpretation implied in relating the two equations that is under contention. It seems to us that the model-computation-effect approach to physics is still solvent. In particular, if we can model an effect as small as the radiation from an individual electron and produce a predictable effect, then the physics underlying the model must be seriously considered.
Over the past two decades there has been a renewed interest in the properties of light and its interactions with matter. In particular, the phenomenon of mixing on the surface of a quantum detector, first performed by Forrester and Gudmundsen, has had significant impact on the treatment of the interaction of light with matter. Mandel and Wolf have interpreted optical mixing of two fields in terms of wave-packet interactions. The wave packets of the fields were allowed to add in a classical manner, without any interaction between photons. In this paper, we consider the extension to an ensemble of statistical wave packets. This is accomplished by considering the wave-packet ensemble as a generalized shot-noise process, and generating statistical properties of the ensemble. The first-order probability density is obtained for the envelope of an ensemble in which each member has uniform and independently distributed phase. This is then used to compute the resulting photoelectron-counting distribution. The results can be shown to be somewhat different than would arise from a gaussian field, and a statistical test is derived to compare the two.
It is pointed out that it is impossible to distinguish between photons and classical wave packets by measurement of photoelectric counting statistics for any state of a light beam for which a classical description exists. Therefore, an experiment with a thermal light source recently proposed by Karp as a test for the existence of photons can yield no information on this question, even if it should be able to distinguish between two different statistical models of a light beam. The quantum nature of the optical field can, however, be inferred from other photoelectric measurements, some of which are briefly discussed.
In semiclassical theory, light is a classical electromagnetic wave and the fundamental source of photodetection noise is the shot effect arising from the discreteness of the electron charge. In quantum theory, light is a quantum-mechanical entity and the fundamental source of photodetection noise comes from measuring the photon-flux operator. The Glauber coherent states are Gaussian quantum states which represent classical electromagnetic radiation. Quantum photodetection of these states yields statistics that are indistinguishable from the corresponding Poisson point-process results of semiclassical photodetection. Optical parametric interactions, however, can be used to produce other Gaussian quantum states, states whose photodetection behavior cannot be characterized semiclassically. A unified analytical framework is presented for Gaussian-state photodetection that includes the full panoply of nonclassical effects that have been produced via parametric interactions.
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.
We examine the coherence properties and photon statistics of stationary light obtained by the superposition of nonstationary emissions occurring at random times, in accordance with a homogeneous Poisson point process. The individual emissions are assumed to be in a coherent, chaotic, or n state. The statistical nature of the emission times results in fluctuations of the relative contributions of different emissions at a given time. This is manifested by an additional positive term, exhibiting particlelike properties, in the normalized second-order correlation function. Thus, the photon-counting variance is increased. For coherent emissions, interference between the randomly delayed emissions produces additional wavelike noise. In the limit when the emissions overlap strongly, the field exhibits the correlation properties of chaotic light, regardless of the statistics of the individual emissions. In the opposite limit, when emissions seldom overlap, the light intensity is describable by a shot-noise stochastic process, and the detected photocounts show an enhanced particlelike noise, which has its largest value when the counting time is long. In that limit, the photocounts obey the Neyman type-A and generalized Polya-Aeppli distributions, when the individual emissions are coherent and chaotic, respectively. When the individual emissions correspond to the n state, the Poisson emission times result in bunching which reduces or eliminates the inherent antibunching associated with the n state.