Nonlinear spin diffusion and spin rotation in a trapped Fermi gas

TL;DR

This paper investigates nonlinear effects in spin diffusion and spin rotation in a trapped Fermi gas, revealing inhomogeneous spin states and saturation of diffusivity and spin-rotation parameters consistent with experimental observations.

Contribution

It introduces a numerical solution to nonlinear spin diffusion equations in a trapped Fermi gas, highlighting inhomogeneous spin states and the behavior of spin-rotation parameters.

Findings

Microscopic diffusivity and gamma increase at weak coupling.

Apparent values from trap-averaged magnetization saturate.

Inhomogeneous spin states emerge even at spin echo time.

Abstract

Transverse spin diffusion in a polarized, interacting Fermi gas leads to the Leggett-Rice effect, where the spin current precesses around the local magnetization. With a spin-echo sequence both the transverse diffusivity and the spin-rotation parameter $\gamma$ are obtained; the sign of $\gamma$ reveals the repulsive or attractive character of the effective interaction. In a trapped Fermi gas the spin diffusion equations become nonlinear, and their numerical solution exhibits an inhomogeneous spin state even at the spin echo time. While the microscopic diffusivity and $\gamma$ increase at weak coupling, their apparent values inferred from the trap-averaged magnetization saturate in agreement with a recent experiment for a dilute ultracold Fermi gas.