Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates

Abstract

We present a detailed theoretical analysis of superradiant Rayleigh scattering from atomic Bose-Einstein condensates. A thorough investigation of the spatially resolved time-evolution of optical and matter-wave fields is performed in the framework of the semiclassical Maxwell-Schrödinger equations. Our theory is not only able to explain many of the known experimental observations, e.g., the behavior of the atomic side-mode distributions, but also provides further detailed insights into the coupled dynamics of optical and matter-wave fields. To work out the significance of propagation effects, we compare our results to other theoretical models in which these effects are neglected.

Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate

“…In this way, we investigate the effect of the detuning of the pump beam in the process, and move between the case where the pump beam remains essentially undepleted by the scattering, to the situation where superradiant scattering is 'clamped' by a lack of photons in the pump beam. Crucial to these dynamics is the structure that builds up along the long axis of the condensate, demonstrating characteristics from 'Dicke' superradiance from extended samples [6,7,8], a fact recognized recently both experimentally [9,10] and theoretically [11,12,13,14]. Contrary to most earlier experimental work on the subject [9,15,16,17], we end-pump along * hilliard@nbi.dk the long axis with a beam mode-matched to the transverse cross-section of the BEC in order to optimize the coupling between pump photons and atoms.…”

“…The situation of SLS from a BEC was derived in [11,12], and we follow closely their notation. In the endpumped geometry, the Maxwell-Schrödinger equations read:…”

“…The boundary conditions for the light fields were typically taken to be e + (0, τ ) = e i and e − (k l L, τ ) = 0. Note that |e − (0, τ )| 2 is proportional to the back-scattered light intensity measured in experiment, and that the total photon flux is conserved: (2) and (3) contain no explicit noise term to instigate superradiant scattering, we seed the process by taking a non-zero first order momentum component ψ 2 = ψ 0 / √ N at , corresponding to a single delocalized atom in the first side-mode [12]. The random nature of the initiation of superradiant scattering may be modeled in the present formalism by using random initial conditions but here we focus on the large scale dynamics of the system rather than its noise properties [20].…”

High Order Momentum States by Light Wave Scattering

“…Several theoretical descriptions of these cooperative scattering in BEC with single-frequency pump have also been presented (Guo et al, 2008;Moore & Meystre, 1999;Pu et al, 2003;Zobay & Nikolopoulos, 2006).…”

“…In the superradiant Rayleigh scattering (Bar-Gill et al, 2007;Guo et al, 2008;Inouye et al, 1999;Kozuma, Suzuki et al, 1999;Moore & Meystre, 1999;Pu et al, 2003;Sadler et al, 2007;Schneble et al, 2003;Slama et al, 2007;Zobay & Nikolopoulos, 2006), the spatial and time evolutions of superradiant scattering are studied for a weak pump beam with different frequency components traveling along the long axis of an elongated Bose-Einstein condensate. Through the analysis of the mode competition between the different resonant channels and the local depletion of the spatial distribution, we can get a large number of high-order forward modes by resonant frequency components of the pump beam ).…”