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

Abstract

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.