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