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Laser Physics Letters

Jaynes–Cummings model with degenerate atomic levels and two polarization modes of the quantized field

Решетов Владимир Александрович

Published Mar 13, 2019• 4 citations
Publisher

Abstract

Abstract The Jaynes–Cummings model describing the interaction of two polarization modes of the quantized electromagnetic field with an isolated two-level atom with the levels degenerate in the projections of the angular momenta on the quantization axis is studied. The general expression for the evolution operator for such a model is obtained. The examples of low values of the level angular momenta or single photon in the cavity are discussed.

DOI
10.1088/1612-202x/ab0a5c

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Abstract The Jaynes–Cummings model describing the interaction of two polarization modes of the quantized electromagnetic field with an isolated two-level atom with the levels degenerate in the projections of the angular momenta on the quantization axis is studied. The general expression for the evolution operator for such a model is obtained. The examples of low values of the level angular momenta or single photon in the cavity are discussed.
The Jaynes-Cummings model describing the interaction of a single linearly- polarized mode of the quantized electromagnetic field with an isolated two- level atom is generalized to the case of atomic levels degenerate in the projections of the angular momenta on the quantization axis, which is a usual case in the experiments. This generalization, like the original model, obtains the explicit solution. The model is applied to calculate the dependence of the atomic level populations on the angle between the polarization of cavity field mode and that of the laser excitation pulse in the experiment with one-atom micromaser.
Abstract The master equation for the atom-field system with degenerate atomic levels and two polarization modes of the quantized field in a damped micro-cavity is obtained in the basis of eigenvectors of the interaction operator. The solution for the lossless cavity is obtained. The analytic expressions for the probability of emission of the photon in the cavity by an excited atom and of the photon polarization matrix are derived in the ‘strong coupling’ and ‘bad cavity’ approximations for arbitrary values of angular momenta of atomic levels. The dependence of the photon polarization on the polarization of the short excitation pulse is studied.
We take into account the two-photon process and generalize the Jaynes-Cummings (JC) model to the case of atomic level degenerate in the projections of the angular momenta and we establish two-photon degenerate JC models with and without the rotating-wave approximation (RWA) quantum theory. Comparing the atom population inversion of the generalized JC model with that of the original JC model, we found that the revival period of the degenerate JC model becomes longer and the maximum amplitude of atomic inversion decreases with RWA. Without RWA, the quantum chaos of the generalized JC model is much weaker than that of the original JC model.