A theoretical model describing the Raman scattering process in atomic vapors is constructed. The treatment investigates the low-excitation regime suitable for modern experimental applications. Despite the incorporated decoherence effects (possibly mode dependent) it allows for a direct separation of the time evolution from the spatial degrees of freedom. The impact of noise on the temporal properties of the process is examined. The model is applied in two experimentally relevant situations of ultra-cold and room-temperature atoms. The spatial eigenmodes of the Stokes photons and their coupling to atomic excitations are computed. Similarly, dynamics and the waveform of the collective atomic state are derived for quantum memory implementations.
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