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

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