Spin-Energy Correlation in Degenerate Weakly-Interacting Fermi Gases*

Very weakly interacting Fermi gases offer a new paradigm for exploring the interplay between spin, motion, Fermi statistics, and interactions in many-body systems. We study the formation of spin-energy correlations in a very weakly interacting Fermi gas of $^6$Li contained in an optical trap with a spin-dependent potential. Measuring time dependent spin density profiles for coherently prepared, quantum degenerate clouds of $^6$Li, we find that the profiles are in very good agreement with a one-dimensional mean field description for small s-wave scattering lengths, where the energy changing collision rate is negligible. For temperatures in the classical Boltzmann regime, we observe a modified spin density patterns arising from the energy dependence of the scattering length and measure the zero crossing shift in the scattering length.