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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 explicitly on microscopic properties, requiring an understanding beyond thermodynamics. Remarkably, in dilute gases, a set of universal relations is known to connect thermodynamics directly with microscopic properties. 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", and present evidence that they encode the universal aspects of $p$-wave interactions through recently proposed relations. 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 contact relations, we infer an attractive $p$-wave interaction energy as large as half the Fermi energy. Our results reveal new ways to understand and characterise the properties of a resonant $p$-wave quantum gas.