Phase Diagram of a One-Dimensional Spin-Imbalanced Fermi Gas

We report experimental measurements of spin and density profiles of a two spin mixture of ultracold $^{6}$Li atoms trapped in an array of one dimensional (1D) tubes\footnote{Y. Liao {\it et al.}, Submitted; in collaboration with S. K. Baur and E. J. Mueller.}, a system analogous to electrons in 1D wires. Compared to the three-dimensional case\footnote{G. B. Partridge \textit{et al.}, \textit{Science} 311, 503-505 (2006); G. B. Partridge {\it et al.}, {\it Phys. Rev. Lett.} {\bf 97}, 190407 (2006).}, at finite spin imbalance the 1D system shows an inverted phase separation: a partially polarized core surrounded by wings composed of either a completely paired BCS superfluid or a fully polarized Fermi gas, depending on the degree of polarization. The observations are in quantitative agreement with the Bethe ansatz and numerous other theoretical calculations\footnote{G. Orso, Phys. Rev. Lett. 98, 070402 (2007); H. Hu et. al, Phys. Rev. Lett. 98, 070403 (2007).}, in which the partially polarized phase is found to be a 1D analogue of the FFLO state, a superfluid state with spatially modulated magnetic order.