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 f(0) is induced by critical correlations which increase the transition temperature T(c) above T(c)(MF). Unlike the T(c) shift in a trapped gas, f(0) 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/lambda(0), where a is the s-wave scattering length and lambda(0) the thermal wavelength, we expect a universal scaling f(0) (alpha) (a/lambda(0))(4). We experimentally verify this scaling using a Feshbach resonance to tune a/lambda(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.