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

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.