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Annual Meeting Optical Society of America

Exact periodic solution in the semiclassical Jaynes-Cummings model

Adam Kujawski

Published Jan 1, 1987• 0 citations
Publisher

Abstract

In the semiclassical version of the Jaynes-Cummings1 model without the rotating-wave approximation, an exact periodic solution has been obtained and studied for some specific values of the coupling constant and the detuning. It is shown that when the atomic frequency is equal to three times the cavity frequency and the coupling constant is arbitrary, the oscillation amplitudes are maximal. The Fourier spectrum of the inversion is discrete. As is known (see, for example, Ref. 2) chaos has been found for the semiclassical Jaynes-Cummings model.

DOI
10.1364/oam.1987.tht4

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Europhysics Letters (EPL)•Sep 15, 1990•2 citations
In the semiclassical version of the Jaynes-Cummings1 model without the rotating-wave approximation, an exact periodic solution has been obtained and studied for some specific values of the coupling constant and the detuning. It is shown that when the atomic frequency is equal to three times the cavity frequency and the coupling constant is arbitrary, the oscillation amplitudes are maximal. The Fourier spectrum of the inversion is discrete. As is known (see, for example, Ref. 2) chaos has been found for the semiclassical Jaynes-Cummings model.
The values of the characteristic frequencies in the Fourier spectrum for the semiclassical Jaynes-Cummings model in the case of a weak-coupling constant are found analytically and are also confirmed numerically. The rotating-wave approximation is not assumed. The sidebands of atomic and cavity modes occur at the characteristic frequencies and play an essential role in characterizing the Fourier spectra of chaotic behavior. The question of transition from nonchaotic to chaotic behavior is also studied.