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Physical Review A

Off-resonance light scattering from Bose condensates in traps

András Csordás, Robert Graham, P. Szépfalusy

Published Oct 1, 1996• 18 citations
Publisher

Abstract

The density-density correlation function determining off-resonance light scattering in weakly interacting Bose-condensed gases in a trapping potential is calculated in the Bogoliubov approximation. The evaluation of the necessary matrix elements is carried out for positive scattering length in the WKB approximation using the Thomas-Fermi approximation for the condensate.

DOI
10.1103/physreva.54.r2543

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The density-density correlation function determining off-resonance light scattering in weakly interacting Bose-condensed gases in a trapping potential is calculated in the Bogoliubov approximation. The evaluation of the necessary matrix elements is carried out for positive scattering length in the WKB approximation using the Thomas-Fermi approximation for the condensate.
The Bogoliubov equations of the quasiparticle excitations in a weakly interacting trapped Bose condensate are solved in the WKB approximation in an isotropic harmonic trap, determining the discrete quasiparticle energies and wave functions by torus (Bohr-Sommerfeld) quantization of the integrable classical quasiparticle dynamics. The results are used to calculate the position and strengths of the peaks in the dynamic structure function, which can be observed by off-resonance inelastic light scattering.
Bose-Einstein condensates of 10485Rb{10}^{4}{}^{85}\mathrm{Rb}10485Rb atoms in a cylindrical trap are studied using a recently proposed approach based on a local-density approximation. Since the existence of a Feshbach resonance allows for widely tuning the scattering length of the atoms, values of the peak gas parameter xpk{x}_{\mathrm{pk}}xpk​ of the order of ${10}^{\ensuremath{-}2}$ may be attained and the standard analysis based on Gross-Pitaevskii and/or Thomas-Fermi equations may result in being questionable. Energy functionals derived from the correlated basis functions theory and the low-density expansion for a homogeneous hard-spheres gas are used to estimate corrections to the Gross-Pitaevskii equation. The two functionals give similar results, both showing large differences with respect to the Thomas-Fermi and Gross-Pitaevskii ones. The column densities at z=0z=0z=0 may differ by as much as $\ensuremath{\sim}30%$ and the half maximum radius by $\ensuremath{\sim}20%.$ The scattering lengths estimated by fitting the half maximum radius may differ by $\ensuremath{\sim}40%$ from those given by a Thomas-Fermi-based analysis of the experimental data.