Weakly-Interacting Fermi Gases as Chains of Interacting Spins

In a weakly-interacting (a_s < ~15 Bohr) Fermi gas, the energies of individual atoms are conserved on the order of minutes. As pairs of atoms forward-scatter, the spin states are mutually affected, producing long-range spin coherence and spin waves. This system may be described as a spin chain in energy space, with site-to-site couplings that are controlled either magnetically or optically. We discuss our progress in developing new methods to characterize this system.