We analyze the properties of a Raman quantum light-atom interface in longatomic ensemble and its applications as a quantum memory or two-mode squeezedstate generator. We consider the weak-coupling regime and include both Stokesand anti-Stokes scattering and the effects of Doppler broadening in buffer gasassuming frequent velocity-averaging collisions. We find the Green functionsdescribing multimode transformation from input to output fields of photons andatomic excitations. Proper mode basis is found via singular value decompositionfor short interaction times. It reveals that triples of modes are coupled by atransformation equivalent to a combination of two beamsplitters and a two-modesqueezing operation. We analyze the possible transformations on an example ofwarm rubidium-87 vapor. The model we present bridges the gap between the Stokesonly and anti-Stokes only interactions providing simple, universal descriptionin a temporally and longitudinally multimode situation. Our results alsoprovide an easy way to find an evolution of the states in a Schr\"odingerpicture thus facilitating understanding and design.
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