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

A 3D trapped spin polarized Fermi gas has been shown to phase separate into a fully paired core and a polarized shell.\footnote{G.B. Partridge \textit{et al.}, Science \textbf{311}, 503(2006); Y. Shin \textit{et al.} Phys. Rev. Lett. 97, 030401 (2006).} Motivated by a search for FFLO pairing we have obtained the phase diagram of a 1D spin-imbalanced Fermi gas confined to an array of tubes created by a 2D optical lattice. It exhibits three phases with an inverted structure compared to 3D: a partially polarized superfluid, a fully paired phase and a fully polarized phase, depending on the degree of spin polarization.\footnote{Y.A. Liao \textit{et al}., Nature \textbf{467}, 567(2010).} We investigate the transition from a 3D to 1D gas by smoothly varying the depth of our 2D optical lattice. This changes the tunneling between the 1D tubes allowing us to study how the spin density varies with inter-tube coupling. By varying the lattice depth quickly, we can also measure spin transport in a strongly interacting system.