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Journal of the Optical Society of America B

Extended Jaynes–Cummings model in a damped cavity

JOSIP SEKE

Published Oct 1, 1985• 14 citations
Publisher

Abstract

By using a new technique, developed recently by the author, analytic and numerical solutions are obtained for the spontaneous emission from a single two-level atom interacting with a three-dimensional multimode radiation field with a narrow frequency range in a damped cavity.
DOI
10.1364/josab.2.001687

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We present a numerical and analytical study of a multimode Jaynes-Cummings model describing the spontaneous decay of a single atom in a high-Q cavity. The theory of cavity-modified spontaneous emission is discussed in terms of quantities that have clear physical interpretations: the photon wave packet radiated by the atom, its reflection by the cavity boundaries, and its reabsorption by the atom. Multimode corrections to the single-mode Jaynes-Cummings model are calculated. The multimode corrections are formulated in terms of quantities that may be calculated by solving the single-mode equations of motion.
The dynamics of the much studied Jaynes–Cummings model, of a single two-level atom interacting with a single quantized field mode, is simple to solve for because the number of quanta in the system is strictly conserved. Including the effects of cavity damping makes the model significantly more difficult to treat. Here we present a simple derivation of the evolution of the atomic inversion in the presence of cavity damping. This will enable us to explain the physical meaning of the solution, first derived more than 20 years ago, and also to show that it is valid for much stronger damping than was appreciated at that time.
As a continuation of the previous paper 'Collapse and revival in the damped Jaynes-Cummings model' [Chin. Phys. Lett. 16 (1999) 895], at present the problem is solved under the condition that the atomic spontaneous emission is included. In the case of no damping, c = 0,γ 1 ≠ 0,γ 2 ≠ 0, the half atomic inversion operator ⟨σ z ⟩ possesses an analytic solution, whereas in the general case c ≠ 0, the problem is reduced to the numerical evaluation of first-order nonlinear differential equations. The final results show that with the increase of γ 1 and γ 2 , the kinetic quantities converge rapidly to stationary solutions.