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Journal de physique

Correlations in single photon amplification : stimulated versus spontaneous processes

A. Heidmann, Serge Reynaud

Published Jan 1, 1984• 8 citations
Publisher

Abstract

We study temporal correlations between photons going out an optical amplifier (stimulated emission amplification) when the input consists of a single photon. It is shown that this amplifier thus appears not at all as a « photon cloner » but rather as a noise source statistically independent from the input field (spontaneous emission noise).

DOI
10.1051/jphys:01984004505087300

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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.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 7, 2006•0 citations
We study temporal correlations between photons going out an optical amplifier (stimulated emission amplification) when the input consists of a single photon. It is shown that this amplifier thus appears not at all as a « photon cloner » but rather as a noise source statistically independent from the input field (spontaneous emission noise).
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.
Introduction Most of the lightwave transmission systems operating today benefit fully from extensive deployment of optical amplifiers (OA). These components perform the amplification of optical intensity directly in the optical domain, without resorting to any electrical-domain regeneration. Optical amplifiers increase the average number of output photons per unit time by several orders of magnitude compared with the incoming signal intensity. However, as with every amplifying process, optical amplification cannot be achieved without paying back for the unavoidable noise power added to the signal intensity. As we will see in detail in Chapter 6, the optical amplification process comes with optical noise generated by spontaneous emission inside the active medium. The intensity of the optical signal is represented by the flux of the signal photon population. Conversely, the photons generated by the spontaneous emission process inside the optical cavity represent the noise photon population. The fundamental phenomenon supporting optical amplification is stimulated emission. The basic property of stimulated emission, making the great difference from spontaneous emission and enabling optical amplification, is the coherent nature of the photon generation process. Accordingly, both signal and noise photons go through the same multiplication process by means of stimulated emission. Unless the optical cavity where the stimulated emission takes place (the active cavity) presents selective features for enhancing the signal photon population relative to the spontaneous one, there is no way to avoid noise photons going through stimulated emission, filling most of the cavity population. As a consequence, both photon populations increase, leading respectively to amplified signal intensity and to amplified spontaneous emission intensity. It should be apparent that every noise photon can create a new identical noise photon as a result of stimulated emission, effectively increasing the noise intensity in the active optical cavity. This is the well-known mechanism of amplified spontaneous emission (ASE) noise in optical amplification. Any improvement in the optical amplifier structure devoted to increasing stimulated over spontaneous emission will probably increase the optical signal-to-noise ratio (OSNR) at the cavity output. The spectrum of gain characteristic of the optical active medium is usually wide enough to support an efficient amplification of the broadband spontaneous emission spectrum, leading to the broadband ASE noise power spectral density.