Tkachenko modes in a superfluid Fermi gas at unitarity

TL;DR

This paper calculates Tkachenko oscillation frequencies in a superfluid Fermi gas at unitarity, highlighting how Fermi pressure enables large vortex lattices and potential experimental observation of these modes.

Contribution

It introduces a detailed elasto-hydrodynamic model accounting for elastic constants and density profiles to predict vortex oscillation frequencies in a superfluid Fermi gas.

Findings

Large vortex lattices are achievable at unitarity due to Fermi pressure.

Vortex oscillation frequencies can approach the Tkachenko law in certain regimes.

Experimental observation of these modes is feasible with current technology.

Abstract

We calculate the frequencies of the Tkachenko oscillations of a vortex lattice in a harmonically trapped superfluid Fermi gas. We use the elasto-hydrodynamic theory by properly accounting for the elastic constants, the Thomas-Fermi density profile of the atomic cloud, and the boundary conditions. Thanks to the Fermi pressure, which is responsible for larger cloud radii with respect to the case of dilute Bose-Einstein condensed gases, large vortex lattices are achievable in the unitary limit of infinite scattering length, even at relatively small angular velocities. This opens the possibility of experimentally observing vortex oscillations in the regime where the dispersion relation approaches the Tkachenko law for incompressible fluids and the mode frequency is almost comparable to the trapping frequencies.