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Optica Acta International Journal of Optics

Exact Equations of Motion and Numerical Results for Two-atom Spontaneous Emission in a Damped Cavity

JOSIP SEKE, G. Adam, Otto Hittmaır

Published Jun 1, 1986• 16 citations
Publisher

Abstract

By using a new technique developed recently, exact closed equations of motion for expectation values for the spontaneous emission from two two-level atoms in a resonant damped cavity are derived. These equations are solved numerically for different values of the cavity damping. Moreover, different atom and field fluctuations are calculated numerically. A comparison is made with results obtained by Bonifacio, Schwendimann and Haake in the case of strong damping.

DOI
10.1080/713822011

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By using a new technique developed recently, exact closed equations of motion for expectation values for the spontaneous emission from two two-level atoms in a resonant damped cavity are derived. These equations are solved numerically for different values of the cavity damping. Moreover, different atom and field fluctuations are calculated numerically. A comparison is made with results obtained by Bonifacio, Schwendimann and Haake in the case of strong damping.
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An exact closed system of linear differential equations of the first order, which can be expressed by a simple recurrence equation, is derived for matrix elements of the statistical density operator. This exact recurrence equation opens the way for numerical solutions for collective many-atom spontaneous emission in cavities with arbitrary damping and detuning. For the first time to the authors’ knowledge, numerical results are presented for N = 10 and N = 15. Moreover, the influence of the cavity damping and detuning on the collective spontaneous emission is discussed. New effects, such as the suppression of the superfluorescent effects in strongly detuned cavities, are also pointed out.
In this paper the equations of motion for open systems, derived recently by one of the present authors, are applied to the case of spontaneous emission from a system of NNN identical two-level atoms. Three different observation levels of the atomic system are considered. First, exact closed integrodifferential equations for the expectation values of each observation level are obtained. Second, making the standard approximations---Born, Markov, and long-time approximations, we find that these equations reduce to closed differential equations for the expectation values. The quality of the Born approximation for different observation levels is also discussed. Moreover, in the obtained equations no kind of rotating-wave approximation was made.