Breakdown of the local density approximation in interacting systems of cold fermions in strongly anisotropic traps

We consider spin-polarized mixtures of cold fermionic atoms on the BEC side of the Feshbach resonance. We demonstrate that a strongly anisotropic confining potential can give rise to a double-peak structure in the axial distribution of the density difference and a polarization-dependent aspect ratio of the minority species. Both phenomena appear as a result of the breakdown of the local density approximation for the phase-separated regime. We speculate on the implications of our findings for the unitary regime