Hydrodynamic theory of giant vortices in trapped unitary Fermi gases

The rotational properties are studied for a unitary superfluid gas of fermions at zero temperature. Using a hydrodynamic approach, the conditions for the formation of a giant vortex are discussed. It is found that in the present approximation, an anharmonic addition to the usual harmonic-oscillator type of trap potential is necessary for the energetic stability of a giant vortex. To determine the conditions quantitatively, a Thomas-Fermi approach is compared with numerical solutions in three dimensions.

Figure 1

Density plots of a unitary Fermi gas with $N=1000$, $\alpha =1.0$, $\nu =1.0$, and $\Omega =3.0$. Left panel: cross-section in the $x\text{−}y$ plane with $z=0$. Right panel: cross-section in the $y\text{−}z$ plane with $x=0$.

Figure 2

Same as Fig. 1, with $\Omega =3.2$, close to the expected transition.

Figure 3

Same as Fig. 1, with $\Omega =3.5$, above the expected transition.

Figure 4

Same as Fig. 1, with $\Omega =7.3$.