Spin-Imbalanced Fermi Gases from 1D to 3D*

A spin-imbalanced Fermi gas confined to 1D tubes using a 2D optical lattice exhibits phase separation; a partially polarized superfluid core adjoins fully polarized or fully paired wings in each 1D tube, depending on the overall spin polarization\footnote{Y.A. Liao et~al., Nature 467, 567 (2010)}. By decreasing the strength of the optical lattice, we vary the tunneling rate between the tubes and decrease the cloud's 1D character. In the absence of a lattice, the 3D cloud separates into a fully paired core surrounded by excess unpaired spins\footnote{G. B. Partridge et~al., Science 311, 503 (2006); Y. Shin et~al., Phys. Rev. Lett. 97, 030401 (2006)}. We report investigations of the spin density in spin-imbalanced Fermi gases confined in a range of lattice depths such that the character of the gas varies from 1D to 3D.