Slow rotation of a superfluid trapped fermi gas

The moment of inertia, Theta 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 Theta 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 h omega is of the same order of magnitude as the gap Delta. It turns out that Theta 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 h expansion. Quantitatively we find deviations from the two-fluid model due to the small system size.