Phase Diagram of A One Dimensional Spin-Imbalanced Fermi Gas

We study a 1D polarized Fermi gas by confining a two spin-component Fermi gas of $^{^{6}}$Li atoms in a 2D optical lattice. The lattice forms an array of tubes with weak axial confinement. Polarization is varied by changing the relative spin populations. In 3D, we observed phase separation in which an unpolarized superfluid core was surrounded by a normal polarized gas\footnote{G. B. Partridge et al., Science 311, 503-505 (2006); G. B. Partridge {\it et al.}, {\it Phys. Rev. Lett.} {\bf 97}, 190407 (2006).}. In 1D, however, theory predicts an inverted phase separation, where a central partially polarized (FFLO) superfluid is surrounded by wings that are either fully polarized or an unpolarized superfluid depending on the spin imbalance\footnote{G. Orso, Phys. Rev. Lett. 98, 070402 (2007); H. Hu et. al, Phys. Rev. Lett. 98, 070403 (2007)}. We will present our results and compare with the theoretical phase diagram.