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Journal of Optics B Quantum and Semiclassical Optics

An analytic approach to a three-level atom interacting with a single-mode quantized field

Smail B. Bougouffa, Ali A. Kamli

Published Mar 1, 2004• 12 citations
Publisher

Abstract

An analytic approach is proposed for three-level systems, based on the Riccati nonlinear differential equation. We extract in a natural manner a set of conditions that permit an exact solution for a three-level atom interacting with a single-mode field. We obtain closed analytic exact solutions for the probability amplitudes and apply this approach to the Jaynes–Cummings model of three-level atoms.

DOI
10.1088/1464-4266/6/3/010

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An analytic approach is proposed for three-level systems, based on the Riccati nonlinear differential equation. We extract in a natural manner a set of conditions that permit an exact solution for a three-level atom interacting with a single-mode field. We obtain closed analytic exact solutions for the probability amplitudes and apply this approach to the Jaynes–Cummings model of three-level atoms.
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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.
In this article we present a simple and unified procedure to solve various nonlinear two-level Jaynes-Cummings models. By establishing their similarity to the model describing a spin- particle in a magnetic field, we obtain the standardized forms, appropriate uniformly for all Jaynes-Cummings models, of eigenvalues, eigenstates, evolution, and atomic inversion operators. In this way, we show that the analytical solution of any single-mode and two-mode nonlinear Jaynes-Cummings model can easily be obtained. We also apply this procedure to a three-mode Jaynes-Cummings model.