Abstract: 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 due to spin-dependent harmonic potential, 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 demonstrate a new protocol for the study of information scrambling for a sample of 6 x 10^4 atoms, employing an inverse Abel-transform to extract energy-resolved out-of-time-order correlation functions (OTOC) from the spatial profile of the spin density. To fit the observed energy-resolved dependent structure, the scattering length in the model must be increased by a factor of 2.6 compared to the measured value. These results suggest that beyond mean-field treatment is needed to correctly predict the observed OTOC measurements. The ability to access energy-resolved OTOC under a wide variety of conditions in a large system will motivate new cold atom approaches to simulate “out-of-equilibrium” dynamics in spin-lattice systems, information propagation site-resolved measurements, and “fast scrambling”.
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