Ground-state description of a single vortex in an atomic Fermi gas: From BCS to Bose-Einstein condensation

We use Bogoliubov-de Gennes (BdG) theory to describe a vortex in a neutral fermionic gas, for an attractive interaction that can be arbitrarily tuned to exhibit a crossover from BCS to Bose-Einstein condensation (BEC). We adopt the BCS-Leggett mean-field ground state for which a BdG approach is microscopically justified, and for which a Gross-Pitaevskii description emerges in the BEC limit. The local density of fermionic states is used to provide insight into the particle density depletion from BCS to BEC. We relate this depletion to the presence of unoccupied discrete states at the core center, as well as to a suppression of negative energy continuum states.