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Applied Mathematics & Information Sciences

Several Ways to Solve the Jaynes-Cummings Model

Raúl Juárez-Amaro, Arturo Zúñiga-Segundo, H. M. Moya-Cessa

Published Sep 8, 2014• 14 citations
Publisher
DOI
10.12785/amis/010136

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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.
This report presents an approach to the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without the rotating wave approximation (RWA). It is shown that there is a squeezing-operator unitary transformation for relating the J-C model without RWA and the one with RWA. Thus by using an appropriate squeezing unitary transformation, the time-dependent J-C model without RWA can be transformed into the one with RWA that has been exactly solved previously, and based on this one can readily obtain the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without RWA. The approach presented here also shows that we can treat these two kinds of time-dependent J-C models (both with and without RWA) in a unified way.