Search for the FFLO Phase in the 1D-3D Crossover of a Spin-Imbalanced Fermi Gas

The Fulde-–Ferrell-–Larkin-–Ovchinnikov (FFLO) type superconductor is exotic since it simultaneously supports superfluid and magnetic order, and thus, is a supersolid. This phase has yet to be conclusively observed either in condensed matter or in ultracold atomic gases. In one-dimension (1D), the FFLO phase is found in a large region of the phase diagram\footnote{Y.-A. Liao et al. Nature. 467, 567-569 (2010)} - unlike in 3D where it is believed to occupy only a small region, if any. The FFLO phase is expected to be more robust against quantum and thermal fluctuations, however, 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).}. We confine a spin-imbalanced Fermi gas of $^6$Li to 1D tubes using a 2D optical lattice. By increasing the inter-tube tunneling rate, we bring the system into the dimensional crossover, while interactions are tuned via an s-wave Feshbach resonance. We present our progress towards direct observation of the periodic domain walls which would be a definitive signature of the FFLO phase.