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Physical Review A

Quantum statistics of light after one-photon interaction with matter

Salvatore Carusotto

Published May 1, 1975• 41 citations
Publisher

Abstract

The time development of the normally ordered generating functional of a light beam interacting linearly with a collection of two-level atoms is determined exactly. Rigorous conclusions on changes of the statistical properties of the beam are drawn. It is shown that the field after the interaction appears to be the superposition of a thermal field and of a field statistically similar to the initial one.

DOI
10.1103/physreva.11.1629

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Physical Review A•Mar 1, 1978•37 citations
The time development of the normally ordered generating functional of a light beam interacting linearly with a collection of two-level atoms is determined exactly. Rigorous conclusions on changes of the statistical properties of the beam are drawn. It is shown that the field after the interaction appears to be the superposition of a thermal field and of a field statistically similar to the initial one.
Two-photon absorption and emission for a collection of two level atoms from a single mode beam of light are considered and the statistical proper- ties of the field after the interaction are investigated without placing any restriction of the population of the atomic levels . The dynamical behaviour of the field is described by assuming the atomic levels maintained with a nearly fixed popula- tion distribution . By applying iteration methods the time development for the density operator of the field is written and an expression for the coherent component is obtained . This component appears to be present only when there is a coherent component in the field before the interaction . The statistical properties of the field after the interaction, when the mean photon number is large initially, are then discussed and explicit calculations are carried out for some special cases of initial fields . Finally, it is shown that two-photon spontaneous emission field can be expressed as a superposition of chaotic fields .
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.