Photon storage in Λ -type optically dense atomic media. I. Cavity model

In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in Λ-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. In the present paper, we perform the same analysis for the cavity model. In particular, we show that the retrieval efficiency is equal to $C∕(1+C)$ independent of the retrieval technique, where C is the cooperativity parameter. We also derive the optimal strategy for storage and, in particular, demonstrate that at any detuning one can store, with the optimal efficiency of $C∕(1+C)$, any smooth input mode satisfying TCγ⪢1 and a certain class of resonant input modes satisfying TCγ~1, where T is the duration of the input mode and 2γ is the transition linewidth. In the two subsequent papers of the series, we present the full analysis of the free-space model and discuss the effects of inhomogeneous broadening on photon storage.