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Physical Review A

Peak in the static structure factor of a Bose-Einstein condensate

Jeff Steinhauer, Roee Ozeri, Nadav Y. Katz, Nir Davidson

Published Aug 15, 2005• 6 citations
Publisher

Abstract

A peak in the static structure factor of a Bose-Einstein condensate is computed, both near and far from a Feshbach resonance. A low-density approximation is made, allowing for an analytic result. A Monte Carlo calculation shows that the peak is larger than predicted by the low-density approximation, for the upper range of densities considered here. The peak could be measured by a probe beam of cold atoms.

DOI
10.1103/physreva.72.023608

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A peak in the static structure factor of a Bose-Einstein condensate is computed, both near and far from a Feshbach resonance. A low-density approximation is made, allowing for an analytic result. A Monte Carlo calculation shows that the peak is larger than predicted by the low-density approximation, for the upper range of densities considered here. The peak could be measured by a probe beam of cold atoms.
We consider the total density and spin density fluctuations of a uniform spin-1 Bose-Einstein condensate within the Bogoliubov formalism. We present results for the total density and spin density static structure factors for all four magnetic phases. A key result of our work is a set of analytic predictions for the structure factors in the large- and small-momentum limits. These results will be useful in current experiments aiming to develop a better understanding of the excitations and fluctuations of spinor condensates.
We explore the zero-temperature statics of an atomic Bose-Einstein condensate in which a Feshbach resonance creates a coupling to a second condensate component of quasibound molecules. Using a variational procedure to find the equation of state, the appearance of this binding is manifest in a collapsing ground state, where only the molecular condensate is present up to some critical density. Further, an excited state is seen to reproduce the usual low-density atomic condensate behavior in this system, but the molecular component is found to produce a coherent, many-body decay, quantified by the imaginary part of the chemical potential. Most importantly, the unique decay rate dependencies on density (approximately rho (3/2)) and on scattering length (approximately (5/2)) can be measured in experimental tests of this result.
Bogoliubov modes and the static structure factor for a two-species Bose–Einstein condensate were investigated within the framework of mean field approximation. We find that both quantities are strongly affected due to atomic collisions between the two species. The inter-species interaction not only changes the density distributions of the two species, but also modifies the Bogoliubov modes. As a consequence, the static structure factor exhibits a measurable difference. For a binary mixture of 87Rb and 23Na, our numerical results suggest that such an effect can be observed experimentally.
A path integral Monte Carlo method was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at T = 0.77 K, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9 before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. Finally, a surface dispersion relation was calculated from imaginary-time density-density correlations.
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.