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

摘要

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