Comment on ""Electromagnetic Wave Dynamics in Matter- Wave Superradiant Scattering"

The Letter by Deng et al. [1] presents an analytic theoretical description of matter-wave superradiance [2] which claims to go beyond previous theoretical frameworks. I show here that the theory presented in this Letter 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 super-radiance. Two additional new findings of the Letter 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. The theory of Raman (or Rayleigh) amplifiers is well known. For the situation of matter-wave superradiance in a Bose-Einstein condensate it was summarized in Ref. [3]. If a medium is illuminated with a pump laser beam then there is Raman gain which is described, e.g., by Eq. (1) of Ref. [3]. Since the Raman resonance is narrow, it is accompanied by a narrow dispersive feature that leads to a slow group velocity of the amplified beam [3]. The main result of Ref. [1], Eq. (7), describes just this phenomenon in the form of a propagation equation for the amplified probe beam. The only addition is the inclusion of a weak loss term due to off-resonant Rayleigh scattering of the probe beam [parametrized by 0 in Eq. (7) of [1]] which is completely negligible in the experimental studies. As described in Ref. [3], superradiance is a nonlinear process where the build up of a matter wave grating enhances the Raman gain beyond the perturbative description used in [1]. Positive feedback leads then to a runaway situation: At the threshold for superradiance, the optical Raman gain diverges, and superradiance starts spontaneously without any probe laser input. The perturbative treatment of Ref. [1] (which explicitly assumes a classical seed laser field) does not include such feedback, and can therefore not describe any nonlinear regime including the onset of superradiance. The threshold in Ref. [1] called ''super-radiantly generated field gain threshold'' is the point at which the perturbative Raman gain exceeds the (negligible) off-resonant absorption of the probe laser beam. However, it has nothing to do with superradiance, and only depends on density. In contrast, the superradiant threshold …