Vortex structure and spectrum of atomic Fermi superfluid in a spherical bubble trap

TL;DR

This paper investigates the structure and spectrum of multiply quantized vortices in a rotating atomic Fermi superfluid confined in a spherical shell trap, revealing vortex behaviors and spectral properties across the BCS-BEC crossover.

Contribution

It provides a detailed analysis of vortex structures and energy spectra in a spherical shell geometry, highlighting phenomena unique to higher vorticity and the BCS regime.

Findings

Higher-vorticity vortices show density peaks and reversed currents.

The energy spectrum's in-gap states correspond to vortex vorticity.

Vortex behavior aligns with topological and geometric constraints.

Abstract

The structures of multiply quantized vortices (MQVs) of an equal-population atomic Fermi superfluid in a rotating spherical bubble trap approximated as a thin shell are analyzed by solving the Bogoliubov-de Gennes (BdG) equation throughout the BCS-Bose Einstein condensation (BEC) crossover. Consistent with the Poincare-Hopf theorem, a pair of vortices emerge at the poles of the rotation axis in the presence of azimuthal symmetry, and the compact geometry provides confinement for the MQVs. While the single-vorticity vortex structure is similar to that in a planar geometry, higher-vorticity vortices exhibit interesting phenomena at the vortex center, such as a density peak due to accumulation of a normal Fermi gas and reversed circulation of current due to in-gap states carrying angular momentum, in the BCS regime but not the BEC regime because of the subtle relations between the order parameter and density. The energy spectrum shows the number of the in-gap state branches corresponds to the vorticity of a vortex, and an explanation based on a topological correspondence is provided.