Spin-Imbalance in a 1-Dimensional Trapped Fermi-Gas*

Spin-polarized trapped Fermi gases have been observed to phase separate into normal and superfluid phases\footnote{G. B. Partridge et al., Science 311, 503-505 (2006); C.H. Schunck et al., Science 316, 867-870 (2007)}. The elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, predicted more than 40 years ago has, however, not yet been found in the 3-dimensional gas. Theory predicts that the FFLO phase occupies only a small part of the phase diagram in 3D\footnote{D.E. Sheehy, L. Radzihovsky, Ann. Phys. 332(8), 1790 (2006)}, whereas in a 1D gas it is expected to be more prominent and is further expected to exhibit an interesting dimensional crossover\footnote{G. Orso, Phys. Rev. Lett. 98, 070402 (2007); H. Hu et. al, Phys. Rev. Lett. 98, 070403 (2007)}. We have implemented a 2D optical lattice to create an array of 1D tubes in order to explore the phase diagram of the 1D polarized Fermi gas. Our progress will be reported.