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Physical Review A

Stimulated emission and photon correlations

L. Mandeļ

Published Dec 1, 1976• 15 citations
Publisher

Abstract

It is pointed out that photoelectric counting correlations in an electromagnetic field that are associated with induced and spontaneous emission at the source, and the so-called Hanbury Brown-Twiss effect, are indistinguishable effects. It is shown by examples that interference effects involving the stimulated emission may be regarded as a source of the counting correlations. The results reported in a recent experiment of Scarl and Smith are therefore readily understandable.

DOI
10.1103/physreva.14.2351

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Proceedings of the Physical Society•Sep 1, 1964•254 citations
It is pointed out that photoelectric counting correlations in an electromagnetic field that are associated with induced and spontaneous emission at the source, and the so-called Hanbury Brown-Twiss effect, are indistinguishable effects. It is shown by examples that interference effects involving the stimulated emission may be regarded as a source of the counting correlations. The results reported in a recent experiment of Scarl and Smith are therefore readily understandable.
We have measured antinormally ordered Hanbury Brown-Twiss correlations for coherent states of the electromagnetic field by using a stimulated parametric down-conversion process. Photons were detected by stimulated emission, rather than by absorption, so that the detection responded not only to actual photons but also to zero-point fluctuations via spontaneous emission. The observed correlations were distinct from normally ordered ones as they showed excess positive correlations, i.e., photon bunching effects, which arose from the thermal nature of zero-point fluctuations.
Recently, the question of the origin of correlations in thermal light has again been debated. The alternative viewpoints suggest that (i) stimulated emission causes the correlations implied by Bose-Einstein statistics and exemplified by the Hanbury Brown-Twiss effect, or (ii) stimulated emission coherently amplifies any initial field, with no change in the nature of photon statistics, apart from the addition of, and interference with, spontaneous-emission noise. It is shown that two essentially different physical models have been considered previously, with many results being only approximate. For these models we obtain the evolution of the photon statistics by deriving exactly the generating function for the diagonal elements of the field density matrix and the quantum characteristic function. The source of Bose-Einstein correlations is seen to be merely the interference in the superposition of random independent fields from a chaotic source, spontaneous emission being one example. Extending the investigation to a nonlinear model, we show that, although there is no longer coherent amplification, it is still not correct to infer that this interaction, which produces the amplification, also leads to Bose-Einstein statistics.
Assertions that stimulated emission may cause photon correlations (or, properly, photocount correlations) are discussed. A particular association of terms in the density matrix rate equation for first order, linear, interactions is urged, following the literature of maser amplifiers. With this association of terms, a consistent picture results in which stimulated emission amplifies without altering the statistical character of an incident field. Spontaneous emission generates excess correlations, through its interference with the incident field. Objections to Webb's thermodynamic argument for an association between stimulated emission and the occurrence of photon correlations are also discussed.
The basic formulae governing the fluctuations of counts registered by photoelectric detectors in an optical field are derived. The treatment, which has its origin in Purcell's explanation of the Hanbury Brown-Twiss effect, is shown to apply to any quasi-monochromatic light, whether stationary or not, and whether of thermal origin or not. The representation of the classical wave amplitude, of the light by Gabor's complex analytic signal appears naturally in this treatment. It is shown that the correlation of counts registered by N separate photodetectors at N points in space is determined by a 2 N th order correlation function of the complex classical field. The variance of the individual counts is shown to be expressible as the sum of terms representing the effects of classical particles and classical waves, in analogy to a well-known result of Einstein relating to black-body radiation. Since the theory applies to correlation effects obtained with any type of light it applies, in particular, to the output of an optical maser, although, for a maser operating on one mode, correlation effects are likely to be very small.