Vortex lattice in spin-imbalanced unitary Fermi gas

We investigate the properties of a spin-imbalanced and rotating unitary Fermi gas. Using a density functional theory (DFT), we provide insight into states that emerge as a result of a competition between Abrikosov lattice formation, spatial phase separation and the emergence of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. A confrontation of the experimental data [M. Zwierlein et al., Science 311, 492 (2006)] with theoretical predictions provides a remarkable qualitative agreement. In case of gas confined in a harmonic trap, the phase separation into a superfluid core populated by the Abrikosov lattice and a spin-polarized corona is the dominant process. Changing confinement to a box-like trap, reverts the spatial location of the component: gas being in the normal state is surrounded by superfluid threaded by quantum vortices. The vortex lattice no longer exhibits the triangular symmetry, and emergence of exotic geometries may be an indirect signature of the FFLO-like state formation in the system.