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arXiv:1307.5175 · Physical Review A

Transverse spin diffusion in strongly interacting Fermi gases

Tilman Enss

Published Sep 27, 2013• 19 citations
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Abstract

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.

DOI
10.1103/physreva.88.033630

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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∥{D}_{\ensuremath{\parallel}}D\ensuremath∥​ depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity D\ensuremath⊥{D}_{\ensuremath{\perp}}D\ensuremath⊥​ has a strong polarization dependence and approaches a finite value for T\ensuremath→0T\ensuremath{\rightarrow}0T\ensuremath→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 \ensuremathℏ/m\ensuremath{\hbar}/m\ensuremathℏ/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⊥{D}_{\ensuremath{\perp}}D\ensuremath⊥​ attains a minimum at strong coupling \ensuremath−1\ensuremath≲ln(kFa2D)\ensuremath≲1\ensuremath{-}1\ensuremath{\lesssim}\mathrm{ln}({k}_{F}{a}_{2D})\ensuremath{\lesssim}1\ensuremath−1\ensuremath≲ln(kF​a2D​)\ensuremath≲1 and reaches D\ensuremath⊥\ensuremath∼0.2...0.3\ensuremathℏ/m{D}_{\ensuremath{\perp}}\ensuremath{\sim}0.2...\phantom{\rule{0.16em}{0ex}}0.3\phantom{\rule{0.16em}{0ex}}\ensuremath{\hbar}/mD\ensuremath⊥​\ensuremath∼0.2...0.3\ensuremathℏ/m at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.
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 HHH. 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 3He^{3}\mathrm{He}3He and 3He^{3}\mathrm{He}3He- 4He^{4}\mathrm{He}4He mixtures.
We compute spin transport in the unitary Fermi gas using the strong-coupling Luttinger-Ward theory. In the quantum degenerate regime the spin diffusivity attains a minimum value of ${D}_{s}\ensuremath{\simeq}1.3\ensuremath{\hbar}/m$ approaching the quantum limit of diffusion for a particle of mass mmm. Conversely, the spin drag rate reaches a maximum value of ${\ensuremath{\Gamma}}_{\mathrm{sd}}\ensuremath{\simeq}1.2{k}_{B}{T}_{F}/\ensuremath{\hbar}$ in terms of the Fermi temperature TF{T}_{F}TF​. The frequency-dependent spin conductivity ${\ensuremath{\sigma}}_{s}(\ensuremath{\omega})$ exhibits a broad Drude peak, with spectral weight transferred to a universal high-frequency tail ${\ensuremath{\sigma}}_{s}(\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty})={\ensuremath{\hbar}}^{1/2}C/3\ensuremath{\pi}(m\ensuremath{\omega}{)}^{3/2}$ proportional to the Tan contact density CCC. For the spin susceptibility ${\ensuremath{\chi}}_{s}(T)$ we find no downturn in the normal phase.
We solve a recently derived kinetic equation for a dilute quantum system at arbitrary degeneracy and polarization, M. From this equation we develop a spin hydrodynamic equation that allows the generalization of the treatment of spin waves and the Leggett-Rice effect to polarized degenerate Fermi gases. We find a transverse spin-diffusion collision time ${\ensuremath{\tau}}_{\ensuremath{\perp}}$ that is often shorter than the corresponding longitudinal collision time ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\parallel}}}$ that is often shorter than the corresponding longitudinal collision time ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. As T\ensuremath{\rightarrow}0, ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\parallel}}}$ approaches T-independent value, in constrast to ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\sim}1/T2{\mathit{T}}^{2}T2. Spin waves would thus continue to be damped even to T=0 K.
We examine spin diffusion in a two-component homogeneous Fermi gas in the normal phase. Using a variational approach, analytical results are presented for the spin diffusion coefficient and the related spin relaxation time as a function of temperature and interaction strength. For low temperatures, strong correlation effects are included through the Landau parameters, which we extract from Monte Carlo results. We show that the spin diffusion coefficient has a minimum for a temperature somewhat below the Fermi temperature with a value that approaches the quantum limit ∼ℏ/ m in the unitarity regime, where m is the particle mass. Finally, we derive a value for the low-temperature shear viscosity in the normal phase from the Landau parameters.
Transport measurement is one of the most important ways to study the properties of matter. In this article, we discuss recent experiments in ultracold atomic gases where the analog of Landauer transport in mesoscopic devices is realized and spin dynamics in a strongly interacting Fermi gas is probed. In the latter case, we pay special attention to the peculiarity of spin dynamics due to identical spin rotation effect which leads to a novel form of spin diffusion current. This modifies the usual diffusion equation into a more complicated form and leads to important consequence for, in particular, transverse spin diffusion in ultracold Fermi gases.
We measure the transport properties of two-dimensional ultracold Fermi gases during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of a spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector k_{F}^{-1}, we find that the bare transverse spin diffusivity reaches a minimum of 1.7(6)ℏ/m, where m is the bare particle mass. The rate of demagnetization is also reflected in the growth rate of the s-wave contact, observed using time-resolved spectroscopy. The contact rises to 0.28(3)k_{F}^{2} per particle, which quantifies how scaling symmetry is broken by near-resonant interactions, unlike in unitary three-dimensional systems. Our observations support the conjecture that, in systems with strong scattering, the local relaxation rate is bounded from above by k_{B}T/ℏ.