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Size dependence of single-photon superradiance of cold and dilute atomic ensembles

We report a theoretical investigation of angular distribution of a single-photon superradiance from cold and dilute atomic clouds. In the present work we focus our attention on the dependence of superradiance on the size and shape of the cloud. We analyze the dynamics of the afterglow of atomic ensemble excited by pulse radiation. Two theoretical approaches are used. The first is the quantum microscopic approach based on a coupled-dipole model. The second approach is random walk approximation. We show that the results obtained in both approaches coincide with a good accuracy for incoherent fluorescence excited by short resonant pulses. We also show that the superradiance decay rate changes with size differently for radiation emitted into different directions.