Search for the FFLO phase in the dimensional crossover of an imbalanced fermi gas

The exotic Fulde– Ferrell– Larkin– Ovchinnikov (FFLO) magnetized superconductor has never been conclusively observed. It fills a large region of the one-dimensional (1D) phase diagram and is believed to occupy only a small region, if any, in 3D. The FFLO phase should be more robust, however, against quantum and thermal fluctuations in higher dimensions. These considerations motivated the proposal to search for FFLO near the 1D-3D dimensional crossover\footnote{M. M. Parish et al. Phys. Rev. Lett. 99, 250403 (2007).}, which we have identified and characterized\footnote{M. C. Revelle et al. Phys. Rev. Lett. 117, 235301 (2016).}. Using a 2D optical lattice, we confine a spin-imbalanced Fermi gas of $^6$Li to 1D tubes. We bring the system to the dimensional crossover by tuning the inter-tube tunneling rate and the interaction strength in the BEC-BCS crossover regime. Domain walls carrying the excess unpaired spins would constitute direct evidence for FFLO pairs. These are expected to become more visible in a 1D time-of-flight expansion, which we induce with a blue-detuned laser beam. We report our progress.