Spin-Imbalanced Quasi-Two-Dimensional Fermi Gases

We measure the density profiles for a Fermi gas of Li-6 containing N-1 spin-up atoms and N-2 spin-down atoms, confined in a quasi-two-dimensional geometry. The spatial profiles are measured as a function of spin imbalance N-2/N-1 and interaction strength, which is controlled by means of a collisional (Feshbach) resonance. The measured cloud radii and central densities are in disagreement with mean-field Bardeen-Cooper-Schrieffer theory for a true two-dimensional system. We find that the data for normal-fluid mixtures are reasonably well fit by a simple two-dimensional polaron model of the free energy. Not predicted by the model is a phase transition to a spin-balanced central core, which is observed above a critical value of N-2/N-1. Our observations provide important benchmarks for predictions of the phase structure of quasi-two-dimensional Fermi gases.