We present a finite temperature calculation of the transverse spin-diffusion coefficient ${D}_{\ensuremath{\perp}}$ in a dilute degenerate Fermi gas, in the presence of a small external magnetic field $H$ . While the longitudinal diffusion coefficient displays the conventional Fermi-liquid dependence, ${D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$, the behavior of ${D}_{\ensuremath{\perp}}$ shows three separate regimes: (a) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{H}^{\ensuremath{-}2}$ for $T\ensuremath{\ll}H$, (b) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{T}^{\ensuremath{-}2}$, $\frac{{D}_{\ensuremath{\perp}}}{{D}_{\ensuremath{\parallel}}}\ensuremath{\ne}1$ for $T\ensuremath{\gg}H$ and large spin-rotation parameter $\ensuremath{\xi}\ensuremath{\gg}1$, and (c) ${D}_{\ensuremath{\perp}}={D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$ for $T\ensuremath{\gg}H$ and $\ensuremath{\xi}\ensuremath{\ll}1$. Our results are qualitatively consistent with the experimental data in weakly spin-polarized $^{3}\mathrm{He}$ and $^{3}\mathrm{He}$ - $^{4}\mathrm{He}$ mixtures.We present a finite temperature calculation of the transverse spin-diffusion coefficient ${D}_{\ensuremath{\perp}}$ in a dilute degenerate Fermi gas, in the presence of a small external magnetic field $H$. While the longitudinal diffusion coefficient displays the conventional Fermi-liquid dependence, ${D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$, the behavior of ${D}_{\ensuremath{\perp}}$ shows three separate regimes: (a) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{H}^{\ensuremath{-}2}$ for $T\ensuremath{\ll}H$, (b) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{T}^{\ensuremath{-}2}$, $\frac{{D}_{\ensuremath{\perp}}}{{D}_{\ensuremath{\parallel}}}\ensuremath{\ne}1$ for $T\ensuremath{\gg}H$ and large spin-rotation parameter $\ensuremath{\xi}\ensuremath{\gg}1$, and (c) ${D}_{\ensuremath{\perp}}={D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$ for $T\ensuremath{\gg}H$ and $\ensuremath{\xi}\ensuremath{\ll}1$. Our results are qualitatively consistent with the experimental data in weakly spin-polarized $^{3}\mathrm{He}$ and $^{3}\mathrm{He}$- $^{4}\mathrm{He}$ mixtures.

arXiv:cond-mat/9406101Physical Review LettersFeb 27, 199519 citations

Transverse spin diffusion in strongly interacting Fermi gases

Tilman Enss

We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization, and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity ${D}_{\ensuremath{\parallel}}$ depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity ${D}_{\ensuremath{\perp}}$ has a strong polarization dependence and approaches a finite value for $T\ensuremath{\rightarrow}0$ in the Fermi liquid phase. For a 3D unitary Fermi gas at infinite scattering length, the diffusivities reach a minimum near the quantum limit of diffusion $\ensuremath{\hbar}/m$ in the quantum degenerate regime and are strongly suppressed by medium scattering, and we discuss the importance of the spin-rotation effect. In two dimensions, ${D}_{\ensuremath{\perp}}$ attains a minimum at strong coupling $\ensuremath{-}1\ensuremath{\lesssim}\mathrm{ln}({k}_{F}{a}_{2D})\ensuremath{\lesssim}1$ and reaches ${D}_{\ensuremath{\perp}}\ensuremath{\sim}0.2...\phantom{\rule{0.16em}{0ex}}0.3\phantom{\rule{0.16em}{0ex}}\ensuremath{\hbar}/m$ at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization, and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity ${D}_{\ensuremath{\parallel}}$ depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity ${D}_{\ensuremath{\perp}}$ has a strong polarization dependence and approaches a finite value for $T\ensuremath{\rightarrow}0$ in the Fermi liquid phase. For a 3D unitary Fermi gas at infinite scattering length, the diffusivities reach a minimum near the quantum limit of diffusion $\ensuremath{\hbar}/m$ in the quantum degenerate regime and are strongly suppressed by medium scattering, and we discuss the importance of the spin-rotation effect. In two dimensions, ${D}_{\ensuremath{\perp}}$ attains a minimum at strong coupling $\ensuremath{-}1\ensuremath{\lesssim}\mathrm{ln}({k}_{F}{a}_{2D})\ensuremath{\lesssim}1$ and reaches ${D}_{\ensuremath{\perp}}\ensuremath{\sim}0.2...\phantom{\rule{0.16em}{0ex}}0.3\phantom{\rule{0.16em}{0ex}}\ensuremath{\hbar}/m$ at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.

arXiv:1307.5175Physical Review ASep 27, 201319 citations

A Diffusion Monte Carlo study of spin polarized Fermi gases

Sumita Datta

APSOct 1, 20080 citations

Nonlinear spin diffusion and spin rotation in a trapped Fermi gas

Tilman Enss

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 $\ensuremath{\gamma}$ are obtained; the sign of $\ensuremath{\gamma}$ 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 $\ensuremath{\gamma}$ 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.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 $\ensuremath{\gamma}$ are obtained; the sign of $\ensuremath{\gamma}$ 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 $\ensuremath{\gamma}$ 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.

arXiv:1501.02677Physical Review AFeb 17, 20157 citations

H

. While the longitudinal diffusion coefficient displays the conventional Fermi-liquid dependence, ${D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$, the behavior of ${D}_{\ensuremath{\perp}}$ shows three separate regimes: (a) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{H}^{\ensuremath{-}2}$ for $T\ensuremath{\ll}H$, (b) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{T}^{\ensuremath{-}2}$, $\frac{{D}_{\ensuremath{\perp}}}{{D}_{\ensuremath{\parallel}}}\ensuremath{\ne}1$ for $T\ensuremath{\gg}H$ and large spin-rotation parameter $\ensuremath{\xi}\ensuremath{\gg}1$, and (c) ${D}_{\ensuremath{\perp}}={D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$ for $T\ensuremath{\gg}H$ and $\ensuremath{\xi}\ensuremath{\ll}1$. Our results are qualitatively consistent with the experimental data in weakly spin-polarized

^{3}\mathrm{He}

and

^{3}\mathrm{He}

^{4}\mathrm{He}

mixtures.