Origin of nonlinear contribution to the shift of the critical temperature in atomic Bose-Einstein condensates

Abstract

We discuss a possible origin of the experimentally observed nonlinear contribution to the shift $\Delta T_c=T_c-T_c^0$ of the critical temperature $T_c$ in an atomic Bose-Einstein condensate (BEC) with respect to the critical temperature $T_c^0$ of an ideal gas. We found that accounting for a nonlinear (quadratic) Zeeman effect (with applied magnetic field closely matching a Feshbach resonance field $B_0$) in the mean-field approximation results in a rather significant renormalization of the field-free nonlinear contribution $b_2$, namely $\Delta T_c/T_c^0\simeq b_2^{\ast }(a/{\lambda }_T{)}^2$ (where $a$ is the s-wave scattering length, ${\lambda }_T$ is the thermal wavelength at $T_c^0$) with $b_2^{\ast }={\gamma }^2{b}_2$ and $\gamma =\gamma (B_0)$. In particular, we predict $b_2^{\ast }\simeq 42.3$ for the $B_0\simeq 403G$ resonance observed in the ${}^{39}K$ BEC.

arXiv commentAccepted for publication in JETP Letters

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