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Physical Review Letters

Electromagnetic Wave Dynamics in Matter-Wave Superradiant Scattering

L. Deng, M. G. Payne, E. W. Hagley

Published Feb 2, 2010• 29 citations
Publisher

Abstract

We present a small-signal wave propagation theory on matter-wave superradiant scattering. We show, in a longitudinally excited condensate, that the backward-propagating, superradiantly generated optical field propagates with ultraslow group velocity and that the small-signal gain profile has a Bragg resonance. We further show a unidirectional suppression of optical superradiant scattering, and explain why matter-wave superradiance can occur only when the pump laser is red detuned. This is the first analytical theory on field propagation in matter-wave superradiance that can explain all matter-wave superradiance experiments to date that used a single-frequency, long-pulse, red-detuned laser.

DOI
10.1103/physrevlett.104.050402

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

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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.

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We present a small-signal wave propagation theory on matter-wave superradiant scattering. We show, in a longitudinally excited condensate, that the backward-propagating, superradiantly generated optical field propagates with ultraslow group velocity and that the small-signal gain profile has a Bragg resonance. We further show a unidirectional suppression of optical superradiant scattering, and explain why matter-wave superradiance can occur only when the pump laser is red detuned. This is the first analytical theory on field propagation in matter-wave superradiance that can explain all matter-wave superradiance experiments to date that used a single-frequency, long-pulse, red-detuned laser.
We show that a Bragg resonance is substantially incapacitated in short-pulse, matter-wave superradiant scatterings and both positive- and negative-order scatterings contribute equally. We further show that propagation gain is small and scattering events primarily occur at the ends of the condensate where the generated field has maximum strength. This explains the apparent ``asymmetry'' in the scattered components with respect to the condensate center. In contrast to long-pulse excitation, we prove that the generated field travels near the speed of light in vacuum and show that this has a significant impact on scattering. Finally, we show that when the excitation rate increases, the front-edge steepening and forward shifting of the peak of the generated field are due to depletion of the condensate.
We study superradiant scattering off Bose-Einstein condensates by solving the semiclassical Maxwell-Schr\"odinger equations describing the coupled dynamics of matter-wave and optical fields. Taking the spatial dependence of these fields along the condensate axis into account, we are able to reproduce and explain many of the characteristic features observed in the experiments of Inouye et al. [Science 285, 571 (1999)] and Schneble et al. [Science 300, 475 (2003)], such as the shape of the atomic side-mode distributions for forward and backward scattering, the spatial asymmetry between forward and backward side modes, and the depletion of the condensate center observed for forward scattering.
We present the first experimental evidence supporting the postulation that an optical-dipole potential in a condensate undergoing superradiant scattering modifies the structure factor of the system and significantly impacts the scattering. Several consequences of this new detuning-dependent mechanism are discussed and verified experimentally. Our experiments indicate that whenever the generation and propagation growth of a new field are significant, the dynamic response of the condensate can have a profound impact on the scattering process.
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.
We propose a setup to generate giant Kerr nonlinearity and polaritonic solitons via matter-wave superradiant scattering. The system we consider is a long cigar-shaped Bose-Einstein condensate (BEC), pumped by a red-detuned laser field with a space-dependent intensity distribution in transverse directions. The pump and the scattered fields propagate along the longitudinal direction. We show that by means of the atom-photon and atom-atom interactions in the system it is possible to produce a giant nonlinear optical effect. We further show that a backward scattering of the laser field from the BEC is favorable for the formation and stable propagation of polaritonic solitons, which are collective nonlinear excitations of the BEC coupled with the scattered laser field. In the case of backward Stokes (anti-Stokes) scattering the system may support robust bright (dark) polaritonic solitons propagating with superluminal (subluminal) velocity.
The interaction of short and strong laser pulses with an atomic Bose-Einstein condensate is found to generate patterns of recoiling atoms that are different from those seen in previous light-scattering experiments. This phenomenon can only be explained by optical stimulation, showing that the previous description of superradiance as atomic stimulation is incomplete and that matter-wave amplification in Bose-Einstein condensates is suppressed at short times. Our experiments clarify the nature of bosonic stimulation in the four-wave mixing of light and atoms.