Observation of deviations from ideal gas thermodynamics in a trapped Bose-Einstein condensed gas

We have investigated experimentally the finite-temperature properties of a Bose-Einstein condensed cloud of $^{87}$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 for the first time 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 $0.2 T_{\rm c}^0$ 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.