Detecting FFLO Pairs in a 1D Spin-Polarized Fermi Gas by Time-of-Flight Expansion

We previously reported the experimental phase diagram of a 1D spin-imbalanced Fermi gas consisting of ultracold $^6$Li atoms prepared in two unequally-populated hyperfine sublevels \footnote{Y. A. Liao \textit{et al}., Nature \textbf{467}, 567 (2010).}. This system exhibits three phases: a uniformly paired phase, a fully-polarized phase consisting of only spin-up atoms, and a partially-polarized phase that is predicted to be the elusive FFLO superfluid. The FFLO state accommodates the mismatched Fermi surfaces by forming atom pairs with nonzero center-of-mass momentum, which we aim to directly characterize via time-of-flight expansion imaging. We confine the atoms in an array of 1D tubes formed from a 2D optical lattice. A blue-detuned anti-trapping laser beam will be applied to exactly cancel the axial harmonic confinement, allowing the atoms to freely expand in 1D. We will report the progress of our experiment.