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Physical Review A

Stimulated versus spontaneous emission as a cause of photon correlations

N. B. Abraham, S. R. Smith

Published Jan 1, 1977• 22 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.15.421

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Stimulated emission and photon correlations

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Two-photon correlations in amplified laser light

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The authors have measured the two-photon correlation function in 632.8-nm single-mode He-Ne laser light which had been amplified by stimulated emission in a long He-Ne discharge tube. For laser light intensities which were comparable with the discharge-tube spontaneous-emission intensity into a single mode, the measured correlations agree well with those predicted for a simple mixture of laser and chaotic light. The results are consistent with the assumption that laser light linearly amplified by stimulated emission has the same statistical properties as unamplified laser light.

Physical Review A•May 1, 1979•15 citations
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.
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.
The well-known photon correlations of thermal light are now understood to result from the random superposition of independently emitted photons from spontaneous emission. Through random interference the number of photons evolves as a Bose-Einstein distribution rather than the Poisson distribution as one might expect for independent emissions of classical particles. By identifying terms in the density-matrix (\ensuremath{\rho}) equation for a linear amplifier, those terms giving rise to spontaneous emission were earlier distinguished from those causing amplification and absorption. We investigate the role of interference in the evolution of the photon statistics by further identifying terms in the equation for \ensuremath{\rho}${\ifmmode \dot{}\else \.{}\fi{}}_{n}$ solely responsible for quantum interference phenomena. The effects of this random interference on the photon factorial moments are quantified, even for those cases where the final field statistics are not Bose-Einstein. From our analysis we conclude that stimulated emission should be viewed as analogous to time-reversed absorption, rather than either a cascade process or pure constructive interference.
The authors have measured the two-photon correlation function in 632.8-nm single-mode He-Ne laser light which had been amplified by stimulated emission in a long He-Ne discharge tube. For laser light intensities which were comparable with the discharge-tube spontaneous-emission intensity into a single mode, the measured correlations agree well with those predicted for a simple mixture of laser and chaotic light. The results are consistent with the assumption that laser light linearly amplified by stimulated emission has the same statistical properties as unamplified laser light.