Breathing modes of a fast rotating Fermi gas

TL;DR

This paper analyzes the frequency spectrum of compressional oscillations in a rotating Fermi superfluid with vortices, covering various regimes and geometries using a hydrodynamic approach.

Contribution

It derives the oscillation frequencies for a superfluid at zero temperature with a polytropic equation of state, including limiting cases and conditions for quantum Hall regimes.

Findings

Derived frequency spectrum for different regimes

Analyzed effects of rotation and geometry

Discussed conditions for quantum Hall regimes

Abstract

We derive the frequency spectrum of the lowest compressional oscillations of a 3D harmonically trapped Fermi superfluid in the presence of a vortex lattice, treated in the diffused vorticity approximation within a hydrodynamic approach. We consider the general case of a superfluid at T=0 characterized by a polytropic equation of state ($\sim{n}^\gamma$), which includes both the Bose-Einstein condensed regime of dimers ($\gamma=1$) and the unitary limit of infinite scattering length ($\gamma=2/3$). Important limiting cases are considered, including the centrifugal limit, the isotropic trapping and the cigar geometry. The conditions required to enter the lowest Landau level and quantum Hall regimes at unitarity are also discussed.