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Physical Review A

Effect of cooperative atomic interactions on photon statistics in a two-photon laser

M. P. Sharma, Luiz Marco Brescansin

Published Apr 1, 1981• 7 citations
Publisher

Abstract

The effects of cooperative atomic interactions on photon statistics in a single mode as well as two-mode two-photon lasers are studied using the equation of motion for the reduced-density operator for the field. The steady-state solution of this equation of motion is used to determine the photon number distribution. The importance of the cooperative effects is discussed.

DOI
10.1103/physreva.23.1893

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Acta Optica Sinica•Jan 1, 1988•0 citations
The effects of cooperative atomic interactions on photon statistics in a single mode as well as two-mode two-photon lasers are studied using the equation of motion for the reduced-density operator for the field. The steady-state solution of this equation of motion is used to determine the photon number distribution. The importance of the cooperative effects is discussed.
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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.
A theory of a quantum amplifier based on two-photon transitions is presented. The model consists of an assemblage of atoms interacting with a single mode of the light field via two-photon absorption and emission. The treatment is quantum mechanical, and the emphasis is on the photon-statistical aspects of the problem. Difference-differential equations for the density matrix of the field mode are derived. The equations are solved for a special case. Differential equations for the expectation vaues of the number of photons and of the field amplitudes, and for their higher statistical moments, are also obtained. Approximate solutions for the average number of photons are found, and the effect of the amplification process on the statistical fluctuations of the number of photons and the field amplitudes is discussed. The results of this study suggest that such an amplifier does not have the coherence properties of a laser amplifier because it tends to increase the statistical fluctuations of the field.
Starting from the master equation for density operator of the atoms and the field mode and applying the operator method of adiabatic elimination of the atomio variables developed by Haake and Lewenstein, we derived the Fokker-Planck Equation for Wigner function of the lightfield and its steady-state solution. With a Gaussian approximation to the solution, analytical and numerical results on the photon statistics for various pumping strengths are obtained. Comparisons with previous works are made.