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The paper by Deng et al. (Phys. Rev. Lett. 104, 050402 (2010)) presents ananalytic theoretical description of matter-wave superradiance (Phys. Rev. Lett.85, 4225-4228 (2000)) which claims to go beyond previous theoreticalframeworks. I show here that the theory presented in this paper is not adescription of superradiance per se, but rather an elegant perturbativedescription of a Raman amplifier far away from the superradiant threshold. Assuch, it merely is a limiting case of previously known treatments ofsuperradiance. Two additional new findings of the paper are incorrect: (1) Theclaim that adiabatic elimination of the excited state of the atoms is onlypossible when the probe pulse propagates slowly. (2) The prediction thatsuperradiance has a dependence on the sign of the detuning of the pump laserdue to a phase-matching condition.

Comment on the paper "Electromagnetic Wave Dynamics in Matter-Wave Superradiant Scattering" by L. Deng, M.G. Payne, and E.W. Hagley