High temperature thermodynamics of strongly interacting s-wave and p-wave Fermi gases in a harmonic trap

TL;DR

This paper develops a theoretical framework using the second order quantum virial expansion to analyze the high-temperature thermodynamics of strongly interacting s-wave and p-wave Fermi gases in harmonic traps, accounting for finite-range effects.

Contribution

It introduces a method to calculate the second virial coefficient for p-wave interactions in harmonic traps, extending previous s-wave studies and considering finite-range effects.

Findings

Second virial coefficient depends on scattering length and effective range.

Thermodynamics are significantly affected by finite-range interaction effects.

Results are relevant for high-precision experiments near p-wave Feshbach resonances.

Abstract

We theoretically investigate the high-temperature thermodynamics of a strongly interacting trapped Fermi gas near either s-wave or p-wave Feshbach resonances, using a second order quantum virial expansion. The second virial coefficient is calculated based on the energy spectrum of two interacting fermions in a harmonic trap. We consider both isotropic and anisotropic harmonic potentials. For the two-fermion interaction, either s-wave or p-wave, we use a pseudopotential parametrized by a scattering length and an effective range. This turns out to be the simplest way of encoding the energy dependence of the low-energy scattering amplitude or phase shift. This treatment of the pseudopotential can be easily generalized to higher partial-wave interactions. We discuss how the second virial coefficient and thermodynamics are affected by the existence of these finite-range interaction effects. The virial expansion result for a strongly interacting s -wave Fermi gas has already been proved very useful. In the case of p-wave interactions, our results for the high-temperature equation of state are applicable to future high-precision thermodynamic measurements for a spin-polarized Fermi gas near a p-wave Feshbach resonance.