Density fingerprint of giant vortices in Fermi gases near a Feshbach resonance

The structure of multiply quantized or giant vortex states in atomic Fermi gases across a Feshbach resonance is studied within the context of self-consistent Bogoliubov–de Gennes theory. The particle density profile of vortices with $\kappa >1$ flux quanta is calculated. Owing to $\kappa$ discrete branches of vortex-core bound states, inside the core the density oscillates as a function of the distance from the vortex line and displays a nonmonotoic dependence on the interaction strengths, in marked contrast to the singly quantized case, in which the density depletes monotonically. This feature can make a direct visualization of the giant vortices in atomic Fermi gases.

Figure 1

(Color online) Particle density profiles, normalized by $n_{TF}=\sqrt{N}∕\pi a_{ho}^{-2}$, for several values of the interaction strengths: $E_a=0.1E_F$ (solid lines), $E_a=0.2E_F$ (dashed lines), $E_a=0.5E_F$ (dotted lines), and $E_a=2.0E_F$ (dash-dotted lines).

Figure 2

(Color online) Center particle density as a function of the number of flux quanta (a) and the interaction strengths (b). The symbols in the left panel denote different values of the interaction strengths: $E_a=0.1E_F$ (BCS side, squares), $E_a=0.5E_F$ (crossover point, circles), and $E_a=1.5E_F$ (BEC side, triangles). The lines in the right panel show the results with different numbers of flux quanta: $\kappa =1$ (solid line), $\kappa =2$ (dashed line), and $\kappa =3$ (dash-dotted line).

Figure 3

(Color online) Local fermionic density of states at the vortex axis for (a) $E_a=0.1E_F$, (b) $E_a=0.5E_F$, (c) and $E_a=1.5E_F$.

Figure 4

(Color online) Spatial variations of the local density of states for $\kappa =4$ and $\kappa =5$ at several values of the interaction strengths as labeled.

Figure 5

(Color online) Order parameter profiles and current distributions at the vortex core for several values of the interaction strengths: $E_a=0.1E_F$ (solid lines), $E_a=0.2E_F$ (dashed lines), $E_a=0.5E_F$ (dotted lines), and $E_a=1.5E_F$ (dash-dotted lines). The currents are in units of $n_{TF}{v}_F$, where $v_F=\hslash k_F∕m$ is the Fermi velocity.