Slow Rotation of a Superfluid Trapped Fermi Gas

The moment of inertia, Θ, is one of the possible observables for the experimental determination whether a trapped Fermi system has reached the BCS transition or not. In this article we investigate in detail the temperature dependence of Θ below the critical temperature T_c. Special care is taken to account for the small size of the system, i.e., for the fact that the trapping frequency ħω is of the same order of magnitude as the gap Δ. It turns out that Θ does not change rapidly if T becomes smaller than T_c, but it rather decreases smoothly. Qualitatively this behavior can be explained within the two-fluid model, which corresponds to the leading order of an ħ expansion. Quantitatively we find deviations from the two-fluid model due to the small system size.