  We study the collective radiation properties of cold, trapped ensembles of
atoms. We consider the high density regime with the mean interatomic distance
being comparable to, or smaller than, the wavelength of the resonant optical
radiation emitted by the atoms. We find that the emission rate of a photon from
an excited atomic ensemble is strongly enhanced for an elongated cloud. We
analyze collective single-excitation eigenstates of the atomic ensemble and
find that the absorption/emission spectrum is broadened and shifted to lower
frequencies as compared to the non-interacting (low density) or single atom
spectrum. We also analyze the spatial and temporal profile of the emitted
radiation. Finally, we explore how to efficiently excite the collective
super-radiant states of the atomic ensemble from a long-lived storage state in
order to implement matter-light interfaces for quantum computation and
communication applications.
