Ground State Description of a Single Vortex in an Atomic Fermi gas: From BCS to Bose-Einstein Condensation

TL;DR

This paper models a single vortex in an atomic Fermi gas across the BCS-BEC crossover using a BdG approach, revealing the vortex structure and density depletion at unitarity.

Contribution

It provides a microscopic BdG analysis of vortex states in fermionic gases across the BCS-BEC crossover, connecting to bosonic vortex descriptions at strong coupling.

Findings

Density depletion at the vortex core in the unitary regime.

Analytic equivalence of BdG and Gross-Pitaevskii descriptions at strong coupling.

Presence of unoccupied quasi-bound states at the vortex center.

Abstract

We use a Bogoliubov-de Gennes (BdG) formulation to describe a single vortex in a neutral fermionic gas. It is presumed that the attractive pairing interaction can be arbitrarily tuned to exhibit a crossover from BCS to Bose-Einstein condensation. Our starting point is the BCS-Leggett mean field ground state for which a BdG approach is microscopically justified. At strong coupling, we demonstrate that this approach is analytically equivalent to the Gross-Pitaevskii description of vortices in true bosonic systems. We analyze the sizable density depletion found for the unitary regime and relate it to the presence of unoccupied (positive energy) quasi-bound states at the core center.