Dynamics of Fermi gases near $s$-wave and $p$-wave Feshbach resonances

Using a Fermi gas of potassium atoms, we explore different regimes of dynamics by varying the strength of $s$-wave and $p$-wave interactions. Near the zero crossing of the $s$-wave Feshbach resonance, we observe magnetization dynamics using a Ramsey sequence of radio-frequency pulses. For sufficiently weak interactions, the motional degrees of freedom are fixed, and the cloud realizes a quantum simulation of the collective Heisenberg lattice spin model in harmonic oscillator mode space. This system exhibits a dynamical phase transition between a ferromagnetic phase with long-lived magnetization, and a fast-decaying paramagnetic state. We also investigate the behavior of a spin-polarized cloud tuned near a $p$-wave Feshbach resonance. We report on the effects of strong confinement on energetics of the cloud, observed through loss features and radio-frequency spectroscopy. These studies have implications for the stability of Fermi gases with strong $p$-wave interactions.