Spin Mixing in Spinor Fermi Gases

We study a spinor fermionic system under the effect of spin-exchange interaction. We focus on the interplay between the spin-exchange interaction and the effective quadratic Zeeman shift. We examine the static and the dynamic properties of both two- and many-body system. We find that the spin-exchange interaction induces coherent Rabi oscillation in the two-body system, but the oscillation is quickly damped when the system is extended to the many-body case.