Non-equilibrium spin dynamics in a trapped Fermi gas with effective spin-orbit interaction

We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and non-trivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive non-equilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to the harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters.