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arXiv:cond-mat/0401585 · Physical Review A

Experimental study of the thermodynamics of an interacting trapped Bose-Einstein condensed gas

Fabrice Gerbier, Joseph H. Thywissen, S. Richard, Mathilde Hugbart, Philippe Bouyer, Alain Aspect

Published Jul 19, 2004• 98 citations
arXivHTMLPDF

Abstract

We have investigated experimentally the finite-temperature properties of a Bose-Einstein condensed cloud of ${}^{87}\mathrm{Rb}$ atoms in a harmonic trap. Focusing primarily on condensed fraction and expansion energy, we measure unambiguous deviations from ideal-gas thermodynamics and obtain good agreement with a Hartree-Fock description of the mixed cloud. Our results offer clear evidence of the mutual interaction between the condensed and thermal components. To probe the low-temperature region unaccessible to the usual time-of-flight technique, we use coherent Bragg scattering as a filtering technique for the condensate. This allows us to separate spatially the condensed and normal components in time of flight and to measure reliably temperatures as low as $0.2{T}_{c}^{0}$ and thermal fractions as low as 10%. Finally, we observe evidence for the limitations of the usual image analysis procedure, pointing out to the need for a more elaborate model of the expansion of the mixed cloud.

DOI
10.1103/physreva.70.013607

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We measure the ground-state occupation and energy of a dilute Bose gas of 87Rb{}^{87}\mathrm{Rb}87Rb atoms as a function of temperature. The ground-state fraction shows good agreement with the predictions for an ideal Bose gas in a 3D harmonic potential. The measured transition temperature is 0.94(5)To0.94(5){T}_{o}0.94(5)To​, where To{T}_{o}To​ is the value for a noninteracting gas in the thermodynamic limit. We determine the energy from a model-independent analysis of the velocity distribution, after ballistic expansion, of the atom cloud. We observe a distinct change in slope of the energy-temperature curve near the transition, which indicates a sharp feature in the specific heat.
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We present measurements of finite-temperature atom clouds cooled below the transition temperature for Bose-Einstein condensation. We study the dynamics of the interface region between the Bose condensed and noncondensed components of the atom clouds, where the time-dependent density profile is highly sensitive to interactions between the two components. We observe directly the effects of repulsion from the condensate on the dynamics of noncondensed atoms. The measurements are compared to calculations based on Hartree-Fock-Bogoliubov mean-field theory. We infer a value for the spatial second-order correlation function for noncondensed atoms of g 0,NC (2) ( r = 0) = 1.8 ± 0.3.
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