Observing spin-energy correlation in weakly interacting Fermi gases.

Active manipulation of electron spin and spin current can be used to transport information with low dissipation and for creating quantum-entangled states. 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. In the experiments, a uniform cloud containing a coherent superposition of spin states is created by radio-frequency pulse. After 800 ms, we observe spontaneous spatial separation of the spin-up and spin-down density profiles, for both quantum-degenerate and thermal Fermi gases. These results are explained by a collision-less mean-field model of spin-energy correlation. We also determine the temperature dependence of the magnetic field at which the s-wave scattering length vanishes and spin segregation ceases, providing new constraints on models of the molecular potentials.