Abstract
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.
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