Anisotropic expansions of a strongly interacting Fermi superfluid containing a vortex

We present a study of static and expansion properties of strongly interacting Fermi superfluids containing a vortex initially trapped by cylindrically symmetric potentials. Based on the order-parameter equation in the framework of the Gross-Pitaevskii equation, a unified expression for the energy of a vortex line in the crossover from a Bardeen-Cooper-Schrieffer superfluid to a molecular Bose-Einstein condensate is analytically presented. Numerical simulations show that the combined effects of interactions and trap configurations lead to an interesting property that the free expansion rate of the vortex core radius is smaller than that of the radius of the superfluid in the radial direction, when the strongly interacting Fermi superfluid containing a vortex is released from a cigar-shaped trap. The effects of the trap anisotropy and vortex on the Efimovian expansions of a unitary Fermi superfluid in real experimental setups are also predicted.