Condensed Fraction of an Atomic Bose Gas Induced by Critical Correlations

We study the condensed fraction of a harmonically trapped atomic Bose gas at the critical point predicted by mean-field theory. The nonzero condensed fraction f₀ is induced by critical correlations which increase the transition temperature T_c above T. Unlike the T_c shift in a trapped gas, f₀ is sensitive only to the critical behavior in the quasiuniform part of the cloud near the trap center. To leading order in the interaction parameter a/₀, where a is the s-wave scattering length and ₀ the thermal wavelength, we expect a universal scaling f₀(a/₀)⁴. We experimentally verify this scaling using a Feshbach resonance to tune a/₀. Further, using the local density approximation, we compare our measurements with the universal result obtained from Monte Carlo simulations for a uniform system, and find excellent quantitative agreement.