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Physical Review A

Analytical approach to the photon statistics in the thermal Jaynes-Cummings model with an initially unexcited atom

S. M. Chumakov, M. Kozierowski, J. J. Sánchez-Mondragón

Published Dec 1, 1993• 17 citations
Publisher

Abstract

Simple analytical expressions for the time evolution of the mean photon number and its normally ordered variance for the case of an initially thermal cavity field coupled to an initially unexcited two-level atom are proposed. The possibility of appearance of sub-Poissonian field statistics is discussed.
DOI
10.1103/physreva.48.4594

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The Jaynes-Cummings model describes the interaction between a two-level atom and a single mode of the radiation field. This system has a conservation law which restricts its dynamics. On the basis of this conservation law alone one can make useful statements about the photon statistics of the fields which arise in the model. Two cases are considered. In the first the field is initially in a coherent state. Here it is found that the field statistics become less sub-Poissonian as the amplitude of the initial state increases. The case of an initial thermal state is also considered. In that situation, if the average number of photons present in the initial state is greater than 2.55, then the field statistics can never become sub-Poissonian.
Photon statistics in some fully quantized models of the interaction of a two-level atom with a single-mode radiation field have been studied using the operator equations of motion. Expressions for the photon number distribution and the mean photon number are presented for various initial conditions. It is found that the mean photon number may show decays and revivals of coherence similar to those of the atomic inversion in the coherent-state Jaynes-Cummings model. Application of these models to the study of multiphoton laser, absorption, and emission processes is also discussed.