Shape of the Normal-Superfluid Boundary in Polarized Fermi Gases

We model the normal-superfluid boundary in a trapped polarized Fermi gas as an elastic membrane and calculate the density profile. For weak trapping anisotropy, the normal-superfluid boundary remains elliptical, in agreement with the LDA. However, for strong anisotropy, the boundary becomes distorted into a capsule-like shape. As one moves axially from the edge of the trap to the center, the radius of the boundary almost discontinuously jumps. In addition to full numerical calculations, we present a simple model that predicts the density profile in the limit of large trapping anisotropy.