Fermi surface of a trapped dipolar Fermi gas

TL;DR

This paper uses semiclassical theory and numerical calculations to analyze the Fermi surface deformation in a trapped dipolar Fermi gas, revealing how interactions influence its shape, energy, and stability.

Contribution

It provides a detailed numerical study of Fermi surface deformation and stability boundaries in dipolar Fermi gases, comparing ellipsoidal approximations with full calculations.

Findings

Fermi surfaces are stretched along the dipolar attraction direction.

Deformed Fermi surfaces can be approximated by ellipsoids with slight density dependence.

Ellipsoidal approximation is accurate for weak interactions but less so under strong interactions.

Abstract

Under the framework of the semiclassical theory, we investigate the equilibrium-state properties of a spin polarized dipolar Fermi gas through full numerical calculation. We show that the Fermi surfaces in both real and momentum spaces are stretched along the attractive direction of dipolar interaction. We further verify that the deformed Fermi surfaces can be well approximated by ellipsoids. In addition, the deformation parameters slightly depend on the local real- and momentum-space densities. We also study the interaction strength dependence of the energy and real- and momentum-space densities. By comparing them with variational results, we find that the ellipsoidal ansatz usually generates accurate results for weak dipolar interaction, while under strong dipolar interaction limit, notable discrepancy can be observed. Finally, we map out the stability boundary of the system.