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Physical Review A

Dynamical analysis of random, quantum interference of light

Edward B. Rockower

Published Jun 1, 1988• 1 citation

Abstract

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.

DOI: 10.1103/physreva.37.4319

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Journal de physique•Jan 1, 1984•8 citations

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.

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.

In this review the author discusses the major effects resulting from the modification of spontaneous emission by quantum interference. He begins in Section II by presenting elementary concepts and definitions of the first- and second-order correlation functions, which are frequently used in the analysis of the interference phenomena. Section III describes the master equation approach used for analyzing quantum interference effects in atomic and molecular systems. In Sections IV and V the author reviews the fundamental quentum interference effects in spontaneous emission and in coherently driven systems. He discusses different schemes for suppression of spontaneous emission and population trapping and gives an alternative explanation of these effects in the dressed-atom picture. Section VI deals with the problem of amplification on dark transitions, which are important for information processing without spontaneous emission. The effect of quantum interference on photon correlations is discussed in Section VII. Multilevel systems composed of two transitions with parallel dipole moments and methods for generating two transitions with nonorthogonal dipole moments are briefly discussed in Section VIII. The final section (Section IX) deals with the experimental demonstration of constructive and desctructive interference effects in a driven molecular system.

By performing an experiment on stimulated emission by two photons in the parametric amplification process and comparing it to a three-photon interference scheme, we present evidence in support of the idea that the underlying physics of stimulated emission is simply the constructive interference due to photon indistinguishability. So the observed signal enhancement upon the input of photons can be interpreted as a result of multiphoton interference of the input photons and the otherwise spontaneously emitted photon from the amplifier.