Evidence for universal relations describing a gas with $p$-wave interactions

Thermodynamics provides powerful constraints on physical and chemical systems in equilibrium. However, non-equilibrium dynamics depends on microscopic properties, requiring an understanding beyond thermodynamics. Remarkably, in dilute gases, a set of universal relations is known to connect thermodynamics and microscopics. So far, these "contact" relations have been established only for interactions with $s$-wave symmetry, i.e., without relative angular momentum. We report measurements of two new physical quantities, the "$p$-wave contacts", that are the thermodynamic conjugates to the two parameters describing $p$-wave interactions. Our experiments use an ultracold Fermi gas of $^{40}$K, in which $s$-wave interactions are suppressed by polarising the sample, while $p$-wave interactions are enhanced by working near a scattering resonance. Using time-resolved spectroscopy, we study how correlations in the system develop after "quenching" the atoms into an interacting state. Combining quasi-steady-state measurements with new thermodynamic relations, we infer a $p$-wave interaction energy as large as the Fermi energy. These observations suggest a new way to characterize any gas with $p$-wave interactions, including superfluids with exotic order.