Superfluidity in 1D and 3D Spin-Imbalanced Fermi Gases

The phase separation between superfluid and normal phases (both polarized and unpolarized) in trapped Fermi gases in the BEC-BCS crossover reveals the interplay between superfluid pairing, interactions, and dimensionality. We measure density profiles of both spins of a two-component, spin-polarized gas of $^6$Li atomic fermions cooled to $\sim 100$~nK. In a 3D gas, an unpolarized superfluid core is surrounded by a polarized shell. We observe gradual suppression of this core as interactions are weakened from unitarity. For a 1D gas in an optical lattice, the phase separation matches exactly-solved 1D models, where the central phase is partially polarized, and is predicted to exhibit FFLO correlations\footnote{Y.A. Liao et al., Nature {\bf 467}, 567 (2010).}. By increasing the inter-tube tunneling rate, we investigate the dimensional crossover between 1D and 3D Fermi gases. In this regime, the FFLO order parameter is predicted to be correlated between tubes\footnote{K. Sun, and C. J. Bolech, PRA {\bf 87}, 053622 (2013)}, and its modulation length constant over larger regions of the trap\footnote{M. M. Parish, et al., PRL {\bf 99}, 250403 (2007)}. These features are predicted to enhance the observable signatures of FFLO correlations; we report progress towards such measurements.