Stability of a Fully Polarized Ultracold Fermi Gas near Zero-Crossing of a p-wave Feshbach Resonance

TL;DR

This paper investigates the stability of a fully polarized ultracold Fermi gas near zero-crossing of a p-wave Feshbach resonance, revealing that the system remains stable under typical conditions but can be unstable under tight confinement.

Contribution

It provides a detailed analysis of the effective interaction and stability criteria of a polarized Fermi gas near zero p-wave scattering length using a two-channel model.

Findings

Effective attraction at zero scattering length.

Critical particle number is very large under typical trapping.

Instability can occur under tight confinement.

Abstract

We consider a fully polarized ultracold Fermi gas interacting through a p-wave Feshbach resonance. Using a two-channel model, we find the effective potential at the point where the p-wave scattering length goes to zero. Here the effective interaction provides attraction and one can therefore ask about the stability of the system. We calculate the energy density of the system in the Thomas-Fermi approximation, determine the profile of the gas, and the critical number of particle in the system as function of the relevant interaction parameters. The instability can be deduced from a simple breathing mode argument which explains the scaling found numerically. The critical particle number turns out to be extremely large unless the external confinement is very tight. We therefore conclude that the effect is insignificant for standard trapping potentials and that the magnetic dipole interaction is the important term at zero scattering length. However, for tight confinement as in an optical lattice higher-order corrections can become important.