Evolution of the vortex state in the BCS-BEC crossover of a quasi two-dimensional superfluid Fermi gas

We use the path-integral formalism to investigate the vortex properties of a quasi-two dimensional (2D) Fermi superfluid system trapped in an optical lattice potential. Within the framework of mean-field theory, the cooper pair density, the atom number density, and the vortex core size are calculated from weakly interacting BCS regime to strongly coupled while weakly interacting BEC regime. Numerical results show that the atoms gradually penetrate into the vortex core as the system evolves from BEC to BCS regime. Meanwhile, the presence of the optical lattice allows us to analyze the vortex properties in the crossover from three-dimensional (3D) to 2D case. Furthermore, using a simple re-normalization procedure, we find that the two-body bound state exists only when the interaction is stronger than a critical one denoted by G_c which is obtained as a function of the lattice potential's parameter. Finally, we investigate the vortex core size and find that it grows with increasing interaction strength. In particular, by analyzing the behavior of the vortex core size in both BCS and BEC regimes, we find that the vortex core size behaves quite differently for positive and negative chemical potentials.