In order to clarify the structure of a singly quantized vortex in a superfluid fermion gas near the Feshbach resonance, we numerically solve the generalized Bogoliubov-de Gennes equation in the boson-fermion model. The superfluid gap, which contains contributions from both condensed fermion pairs and condensed bosons, is self-consistently determined, and the quasiparticle excitation levels bound in the vortex core are explicitly shown. We find that the boson condensate contributes to enhance the matter density depletion and the discreteness of localized quasiparticle spectrum inside the core. It is predicted that the matter density depletion and the discrete core levels are detectable in the vicinity of the BCS-Bose-Einstein condensation crossover point.
In atomic Fermi gases, the pairing character changes from BCS‐like to BEC‐like when one decreases the threshold energy of the Feshbach resonance. With this crossover, the system enters the strong‐coupling regime through the population enhancement of diatom molecules, and the vortex structure becomes much different from well‐known core structures in BCS superfluid since the superfluid order parameter is given by a sum of BCS pairs and BEC molecular condensates. In this paper, we study the structure of a vortex by numerically solving the generalized Bogoliubov‐de Gennes equation derived from the fermion‐boson model and clarify how the vortex structure changes with the threshold energy of the Feshbach resonance. We find that the diatom boson condensate enhances the matter density depletion inside the vortex core and the discreteness of localized quasi‐particle spectrum.
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.
A self-consistent theory is derived to describe the BCS--Bose-Einstein-condensate crossover for a strongly interacting Fermi gas with a Feshbach resonance. In the theory the fluctuation of the dressed molecules, consisting of both preformed Cooper pairs and ``bare'' Feshbach molecules, has been included within a self-consistent
T-matrix approximation, beyond the Nozi\`eres and Schmitt-Rink strategy considered by Ohashi and Griffin. The resulting self-consistent equations are solved numerically to investigate the normal-state properties of the crossover at various resonance widths. It is found that the superfluid transition temperature
Tc increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor
Zm of the molecule's Green function and a complex effective mass have been determined to characterize the fraction and lifetime of Feshbach molecules at
Tc. Our many-body calculations of
Zm agree qualitatively well with recent measurments of the gas of
6Li atoms near the broad resonance at
834G. The crossover from narrow to broad resonances has also been studied.
In order to understand what kind of information can be extracted from the vortex-core structure in superfluid fermion-atom gases we make a systematic study for the core structure of a singly quantized vortex in the range of broad Feshbach resonance, solving numerically the generalized Bogoliubov--de Gennes equation derived from the fermion-boson model. Numerical calculations reveal that the vortex core can be well characterized by three length scales from the spatial variation of the fermionic and bosonic gap functions. We also predict that the profile of matter depletion and the quasiparticle spectrum show distinctive differences between the BCS and Bose-Einstein Condensate regimes.
We investigate the single-particle properties at
T=0 of a trapped superfluid gas of Fermi atoms with a Feshbach resonance. A tunable pairing interaction associated with the Feshbach resonance leads to the BCS--Bose-Einstein condensate (BEC) crossover, where the character of superfluidity continuously changes from the BCS-type to a BEC of composite bosons. In this paper, we extend our previous work for a uniform superfluid Fermi gas [Y. Ohashi and A. Griffin, Phys. Rev. A 67, 063612 (2003)] to include the effect of a harmonic trap. We do not use the local density approximation (LDA), but directly solve the Bogoliubov--de Gennes (BdG) coupled equations. While our explicit numerical solutions are for a weak (narrow) Feshbach resonance, we argue that the single-particle BdG excitation spectrum will exhibit the same features for a strong (broad) Feshbach resonance. Using these equations, we find self-consistent values for the spatially dependent local density
n(r) as well as the composite BCS order parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(\mathbf{r})$, the latter describing both the Cooper-pair and molecular condensate contributions. Using these results, we calculate the single-particle density of states in the crossover region, and from this determine the true single-particle energy gap
(Eg) of the trapped Fermi superfluid. This is associated with the in-gap (or Andreev) states in the low-density region at the edge of the trap. We calculate the laser-induced tunneling current $I(\ensuremath{\omega})$ into another hyperfine state, as measured in recent rf spectroscopy experiments. This rf spectrum gives a direct probe of the quasiparticle spectrum. We show how the high-energy part of $I(\ensuremath{\omega})$ gives information about $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(r=0)$ at the center of the trap (which is comparable to the Fermi energy ${\ensuremath{\epsilon}}_{F}$ in the crossover region). We show that $I(\ensuremath{\omega})$ is very dependent on the spatial profile of the pair potential $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(r)$ that is used. We also emphasize that the narrow ``unpaired atom" peak in the rf data gives information about
Eg and the low-energy $(⪡{\ensuremath{\epsilon}}_{F})$ in-gap states of a Fermi superfluid. While our calculations are limited to
T=0, we use them to discuss the recent data of Chin et al. and the LDA calculations of T\"orm\"a and co-workers. The LDA, while useful, can lead to an incorrect physical picture of the low-density surface region of the Fermi superfluid.