Photon storage in Λ-type optically dense atomic media.: II.: Free-space model

In a recent paper [Gorshkov , Phys. Rev. Lett. 98, 123601 (2007)], we presented a universal physical picture for describing a wide range of techniques for storage and retrieval of photon wave packets in Lambda-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo based techniques. This universal picture produced an optimal control strategy for photon storage and retrieval applicable to all approaches and yielded identical maximum efficiencies for all of them. In the present paper, we present the full details of this analysis as well some of its extensions, including the discussion of the effects of non-degeneracy of the two lower levels of the Lambda system. The analysis in the present paper is based on the intuition obtained from the study of photon storage in the cavity model in the preceding paper [Gorshkov , previous paper, Phys. Rev. A. 76, 033804 (2007)].