Universal Properties of a Strongly Interacting Fermi Gas at a $p$-wave Resonance

TL;DR

This paper explores the universal properties of a strongly interacting spinless Fermi gas near a $p$-wave resonance, identifying two key contacts that govern its momentum distribution and can be experimentally measured.

Contribution

It introduces two adiabatic theorems linking the energy variation to $p$-wave scattering parameters and evaluates the contacts at high temperature using virial expansion.

Findings

Universal momentum distribution behaviors ($ ext{~}1/k^2$ and $ ext{~}1/k^4$) determined by the two contacts.

Experimental methods for measuring the contacts via radio-frequency, Bragg, and photo-association spectroscopies.

High-temperature contacts evaluated through virial expansion.

Abstract

In this letter, we investigate the properties of a strongly interacting spinless Fermi gas close to a $p$-wave resonance. We show that the universal properties at a $p$-wave resonance are captured by two contacts, which are related respectively to the variation of energy with the $p$-wave scattering volume $v$ and with the effective range $R$ in the two adiabatic theorems derived. We show how the two contacts determine the leading and sub-leading asymptotic behavior of the momentum distribution ($\sim 1/k^2$ and $\sim 1/k^4$) and how they can be measured experimentally by radio-frequency, Bragg, and photo-association spectroscopies. Finally, we evaluate the two contacts at high temperature via the virial expansion.