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arXiv:1208.6580 · Physical Review A

Heat and spin transport in a cold atomic Fermi gas

HyungWon Kim, David A. Huse

Published Nov 8, 2012• 20 citations
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Abstract

Motivated by recent experiments measuring the spin transport in ultracold unitary atomic Fermi gases [Sommer et al., Nature (London) 472, 201 (2011); Sommer et al., New J. Phys. 13, 055009 (2011)], we explore the theory of spin and heat transport in a three-dimensional spin-polarized atomic Fermi gas. We develop estimates of spin and thermal diffusivities and discuss magnetocaloric effects, namely the the spin Seebeck and spin Peltier effects. We estimate these transport coefficients using a Boltzmann kinetic equation in the classical regime and present experimentally accessible signatures of the spin Seebeck effect. We study an exactly solvable model that illustrates the role of momentum-dependent scattering in the magnetocaloric effects.

DOI
10.1103/physreva.86.053607

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Motivated by recent experiments measuring the spin transport in ultracold unitary atomic Fermi gases [Sommer et al., Nature (London) 472, 201 (2011); Sommer et al., New J. Phys. 13, 055009 (2011)], we explore the theory of spin and heat transport in a three-dimensional spin-polarized atomic Fermi gas. We develop estimates of spin and thermal diffusivities and discuss magnetocaloric effects, namely the the spin Seebeck and spin Peltier effects. We estimate these transport coefficients using a Boltzmann kinetic equation in the classical regime and present experimentally accessible signatures of the spin Seebeck effect. We study an exactly solvable model that illustrates the role of momentum-dependent scattering in the magnetocaloric effects.
We study the spin-Seebeck effect in a strongly interacting, two-component Fermi gas and propose an experiment to measure this effect by relatively displacing spin-up and spin-down atomic clouds in a trap using spin-dependent temperature gradients. We compute the spin-Seebeck coefficient and related spin-heat transport coefficients as functions of temperature and interaction strength. We find that, when the interspin scattering length becomes larger than the Fermi wavelength, the spin-Seebeck coefficient changes sign as a function of temperature, and hence so does the direction of the spin separation. We compute this zero-crossing temperature as a function of interaction strength and in particular in the unitary limit for the interspin scattering.
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.
Hydrodynamics governs diverse collective phenomena in nature, from the expansion of a quarkgluon plasma to viscous electron flow in quantum materials. In strongly interacting hydrodynamic fluids, the transport of spin remains poorly understood. Here, we investigate spin transport in the hydrodynamic regime of a spin-imbalanced unitary Fermi gas confined in a uniform optical box. By quenching a spatially periodic optical potential that modulates both the density and spin polarization, we observe the relaxation of the many-body system, which determines both the spin diffusivity and the spin Seebeck/Peltier coefficients in a homogeneous quantum gas. Our measurements provide parameter-free benchmarks for microscopic theories and establish an ultracold atom platform for studying spin caloritronics in strongly correlated matter.
We investigate the temperature dependence of the shear viscosity and spin diffusion in a two-dimensional Fermi gas with contact interactions, as realized in ultracold atomic gases. We describe the transport coefficients in terms of a Boltzmann equation and present a full numerical solution for the degenerate gas. In contrast to previous works we take the medium effects due to finite density fully into account. This effect reduces the viscosity-to-entropy ratio $\ensuremath{\eta}/s$ by a factor of 3, and similarly for spin diffusion. The trap-averaged viscosity agrees well with recent measurements by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].
We address recent spin transport experiments in ultracold unitary Fermi gases. We provide a theoretical understanding for how the measured temperature dependence of the spin diffusivity at low TTT can disagree with the expected behavior of a Fermi liquid (FL), while the spin susceptiblity, following the experimental protocols, is consistent with a FL picture. We show that the experimental protocols for extracting the spin susceptibility implicitly reflect a FL viewpoint; relaxing this leads to consistency within but not proof of a pseudogap-based theory. Our transport calculations yield insight into the observed suppression of the spin diffusion constant at lower TTT.
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.