1D-3D Crossover in a Spin-Imbalanced Fermi Gas

We experimentally study the phases of an ultracold two-spin component gas of atomic fermions ($^{6}$Li) confined to 1D tubes formed by a 2D optical lattice. The atoms are prepared in the lowest two hyperfine sublevels where their interactions are tuned by a Feshbach resonance. We previously observed phase separation into a partially-polarized superfluid core and either fully-paired or fully-polarized wings (depending on the spin polarization)\footnote{Y.A. Liao et al., Nature 467, 567 (2010).}. In 3D, the phase separation is inverted, such that the cloud center is fully paired\footnote{G. B. Partridge et al., Science 311, 503 (2006); Y. Shin et al., Phys. Rev. Lett. 97, 030401 (2006).}. We investigate the transition from a 1D to 3D gas by varying the lattice depth and interaction strength which changes the ratio of the tunneling rate between the tubes to the pair binding energy. We are exploring a region of parameter space that is believed to be the most promising region for the exotic FFLO superfluid phase\footnote{M. Parish et al., PRL 99, 250403 (2007).}.