Dimensional crossover from Quasi-1D to 3D in spin-polarized Fermi superfluids*

We use a zero temperature Bogoliubov de Gennes mean field theory to study the evolution of the exotic FFLO superfluid in a spin-imbalanced Fermi gas as one progresses from quasi-1D to 3D by changing the coupling between an array of tubes. The boundary between the uniform BCS superfluid and the FFLO state is determined by examining the energetics of a single $\pi$-domain wall in the superfluid order parameter. In the quasi-1D limit, each tube contains a single excess particle at the center of each domain wall and the spectrum of single particle excitations is gapped. As one approaches 3D there is a phase transition where this commensurability condition is relaxed and gapless single particle excitations can be found. [1] M. M. Parish, S. K. Baur, E. J. Mueller, and D. A. Huse, arXiv:0709.1120