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It has recently been discovered that the optical analogue of a gradient echoin an optically thick material could form the basis of a optical memory that isboth completely efficient and noise free. Here we present analyticalcalculation showing this is the case. There is close analogy between theoperation of the memory and an optical system with two beam splitters. We canuse this analogy to calculate efficiencies as a function of optical depth for anumber of quantum memory schemes based on controlled inhomogeneous broadening.In particular we show that multiple switching leads to a net 100% retrievalefficiency for the optical gradient echo even in the optically thin case.

Analytic treatment of CRIB Quantum Memories for Light using Two-level Atoms