Vortex arrays in neutral trapped Fermi gases through the BCS–BEC crossover

Vortex arrays in type-II superconductors reflect the translational symmetry of an infinite system. There are cases, however, such as ultracold trapped Fermi gases and the crust of neutron stars, where finite-size effects make it complex to account for the geometrical arrangement of vortices. Here, we self-consistently generate these arrays of vortices at zero and finite temperature through a microscopic description of the non-homogeneous superfluid based on a differential equation for the local order parameter, obtained by coarse graining the Bogoliubov–de Gennes (BdG) equations. In this way, the strength of the inter-particle interaction is varied along the BCS–BEC crossover, from largely overlapping Cooper pairs in the Bardeen–Cooper–Schrieffer (BCS) limit to dilute composite bosons in the Bose–Einstein condensed (BEC) limit. Detailed comparison with two landmark experiments on ultracold Fermi gases, aimed at revealing the presence of the superfluid phase, brings out several features that make them relevant for other systems in nature as well. The formation of vortex arrays in rotating Fermi gases is not limited to ultracold gases but may be relevant in nuclei and neutron stars, so it is important to be able to calculate their properties in a realistic fashion.