Trapped fermionic clouds distorted from the trap shape due to many-body effects

We present a general approach for calculating densities and other local quantities of trapped Fermi gases, when the cloud shape is distorted with respect to the trap shape due to global energy considerations. Our approach provides a consistent way to explore physics beyond the local density approximation, if this is necessary due to the distortion. We illustrate this by analyzing in detail experimentally observed distortions in an imbalanced Fermi mixture in an elongated trap. In particular, we demonstrate in that case dramatic deviations from ellipsoidal cloud shapes arising from the competition between surface and bulk energies.