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

TL;DR

This paper investigates how strong anisotropy in trapping potentials causes the local density approximation to fail in describing phase separation in cold fermionic systems, revealing new density and shape phenomena.

Contribution

It demonstrates the breakdown of the local density approximation in anisotropic traps and predicts novel density and shape features in polarized fermionic gases.

Findings

Double-peak structure in axial density difference

Polarization-dependent aspect ratio of minority species

Breakdown of local density approximation in phase-separated regime

Abstract

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.