Observing the 1D-3D Crossover in a Spin-Imbalanced Fermi Gas

Trapped two-component Fermi gases phase separate into superfluid and normal phases when their spin populations are imbalanced. In 3D, a balanced superfluid core is surrounded by shells of partially polarized and normal phases\footnote{B. A. Olsen et al., Phys. Rev. A. 92, 063616 (2015).}, while in 1D, the balanced superfluid occupies the low density wings\footnote{Y.A. Liao et al., Nature 467, 567 (2010).}. We explored the crossover from 3D to 1D using a two-spin component ultracold atomic gas of $^{6}$Li prepared in the lowest two hyperfine sublevels, where the interactions are tuned by a Feshbach resonance. The atoms are confined to 1D tubes where the tunneling rate $t$ between tubes is varied by changing the depth of a 2D optical lattice. We observe the transition from 1D to 3D-like phase separation by varying $t$ and interaction strength which changes the pair binding energy $\epsilon_{B}$. We find a universal scaling of the dimensional crossover with $t/\epsilon_{B}$, in agreement with previous theory\footnote{M. Parish et al., PRL 99, 250403 (2007).}. The crossover region is believed to be the most promising to find the exotic FFLO superfluid phase.