Spin diffusion in ultracold spin-orbit coupled $^{40}$K gas

We investigate the steady-state spin diffusion for ultracold spin-orbit coupled $^{40}$K gas by the kinetic spin Bloch equation approach. It is found that the behaviors of the steady-state spin diffusion are determined by three characteristic lengths in the system: the mean free path, the Zeeman oscillation length and the spin-orbit coupling oscillation length. It is further revealed that by tuning the scattering strength, the system can be divided into {\it five} regimes, in which the behaviors of the spacial evolution of the steady-state spin polarization shows different dependencies on the scattering strength, Zeeman field and spin-orbit coupling strength. These rich behaviors of the spin diffusions in different regimes are hard to be understood in the framework of the simple drift-diffusion model or the direct inhomogeneous broadening picture in the literature. However, almost all these rich behaviors can be well understood by means of our {\it modified} drift-diffusion model and/or {\it modified} inhomogeneous broadening picture. Specifically, several anomalous features of the spin diffusion are revealed, which are in contrast to those obtained from {\it both} the simple drift-diffusion model and the direct inhomogeneous broadening picture.