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 (MF) theory. The non-zero 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 behaviour in the quasi-uniform part of the cloud near the trap centre. 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 $f_0 \propto (a/\lambda_0)^4$. 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.