Sound Velocity and Eigenfrequencies of a Disk-Shaped Harmonically Trapped Superfluid Fermi Gas in the BCS-BEC Crossover

摘要

The analytical expressions for the zero-temperature sound velocity and low-energy eigenfrequencies of a disk-shaped harmonically trapped three-dimensional superfluid Fermi gas are derived on the basis of the hydrodynamic theory in the regimes along the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Theoretically, by plotting the sound velocity as a function of 1/(k F a), it finds that there is an obvious flat behavior for the sound velocity in a disk-shaped trap around unitarity. However, there is no such flat behavior for a cigar-shaped Fermi gas at the same superfluid regime. Here, k F is the Fermi wave vector and a is the s-wave scattering length.