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

TL;DR

This paper critically analyzes Deng et al.'s theoretical work on matter-wave superradiance, clarifying its limitations and correcting two key claims, emphasizing that it describes a Raman amplifier rather than true superradiance.

Contribution

It clarifies that Deng et al.'s theory is a perturbative treatment of a Raman amplifier, not a comprehensive description of superradiance, and corrects two inaccuracies in their claims.

Findings

Deng et al.'s theory is a limiting case of known superradiance treatments.

Adiabatic elimination of the excited state is not restricted to slow probe pulses.

Superradiance does not depend on the sign of the pump laser detuning.

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.