Pair density waves and vortices in an elongated spin-1/2 Fermi gas.

We study the vortex structures of a (pseudo)spin-1/2 Fermi gas experiencing a uniform effective magnetic field in an anisotropic trap that interpolates between quasi-one dimensional (1D) and quasi-two dimensional (2D). At a fixed chemical potential, reducing the anisotropy (or equivalently increasing the attractive interactions or increasing the magnetic field) leads to instabilities towards pair density waves and vortex lattices. Reducing the chemical potential stabilizes the system. We calculate the phase diagram and explore the density and pair density. The structures are similar to those predicted for superfluid Bose gases. We further calculate the paired fraction, showing how it depends on the chemical potential and anisotropy.