Time-dependent projection operator technique in superradiance theory

The modifield Robertson method derived and applied in previous papers is extended to the case of the Bonifacio-Schwendimann-Haake model of superradiance where both interacting systems, the system of N identical atoms and the radiation field, are of interest. A special noncanonical density operator is constructed to determine the expectation values of a set of operators containing the collective atomic operators, their twofold products, and the photon-number operator. Moreover, this density operator completely takes into account the two-atom correlations in expectation values of threefold products of collective operators. For the expectation values of the set of operators mentioned, exact closed equations of motion are derived. By taking the Born approximation these equations reduce to a set of closed integro-differential equations which are applicable also in cases where the emitted photons feed themselves back into atomic excitation. The Markov approximation is used in cases of very strong field damping and leads to a set of closed differential equations for the expectation values. (Auth.)