Weakly interacting Fermi gases provide a rich platform for investigating information spreading and spin coherence in a large many-body quantum system with effective long-range interactions. Using quantum degenerate clouds of 6Li, first, I will present complex time-dependent spin-density profiles, and show that a one-dimensional mean-field model, without additional simplifying approximations, quantitatively predicts the observed fine structure. For this weakly interacting system, single-atom energies are conserved over experimental time scales of seconds, creating an effective "spin-lattice," where the "sites" are labeled by the fixed single-atom energies. Second, I show that the collective spin vector can be determined as a function of energy from the measured spin density, enabling general energy-space resolved protocols. By measuring out-of-time-order correlation functions in this system, I demonstrate the energy dependence of the many-body coherence, which is not fully substantiated by our collective spin vector model.
