Slow rotation of a superfluid trapped Fermi gas

TL;DR

This paper investigates how the moment of inertia of a trapped superfluid Fermi gas varies with temperature below the critical point, highlighting the effects of small system size and deviations from traditional models.

Contribution

It provides a detailed analysis of the temperature dependence of the moment of inertia in small superfluid Fermi gases, accounting for finite size effects beyond leading-order approximations.

Findings

Moment of inertia decreases slowly below T_c

Small system size causes deviations from the two-fluid model

Transport approach needs correction for finite systems

Abstract

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 hbar omega is of the same order of magnitude as the gap Delta. It is shown that the usual transport approach, corresponding to the leading order of an expansion in powers of hbar, is not accurate in this case. It turns out that Theta does not change rapidly if T becomes smaller than T_c, but it rather decreases slowly. Qualitatively this behavior can be explained within the two-fluid model, which again corresponds to the leading order in hbar. Quantitatively we find deviations from the two-fluid model due to the small system size.