Probing the critical exponent of the superfluid fraction in a strongly interacting Fermi gas

Abstract

We theoretically investigate the critical behavior of second sound mode in a harmonically trapped ultracold atomic Fermi gas with resonant interactions. Near the superfluid phase transition with critical temperature Tc, the frequency or the sound velocity of second sound mode depends crucially on the critical exponent β of superfluid fraction. In an isotropic harmonic trap, we predict that the mode frequency diverges like (1 − T /Tc) β−1/2 when β < 1/2. In a highly elongated trap, the speed of second sound reduces by a factor 1/ √ 2β + 1 from that in a homogeneous three-dimensional superfluid. Our prediction could be readily tested by measurements of second sound wave propagation in a setup such as that exploited by Sidorenkov et al. [Nature 498, 78 (2013)] for resonantly interacting lithium-6 atoms, once the experimental precision is improved.