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Physical Review Letters

Viscosity increase upon spin polarization of a dilute Fermi gas

Donald Candela, L-J. Wei, D. R. McAllaster, William J. Mullin

Published Jul 15, 1991• 20 citations
Publisher

Abstract

A vibrating-wire technique has been used to directly measure the viscosity increase in a dilute $^{3}\mathrm{\ensuremath{-}}^{4}$He solution caused by brute-force spin polarization up to 40%. The viscosity of a solution with degeneracy temperature ${\mathit{T}}_{\mathit{F}}$=19.5 mK was measured over the temperature range 6.1--100 mK in magnetic fields of 1.00 and 7.96 T. Spin polarization caused a marked decrease in the mechanical Q of the viscometer at low temperatures. The observed viscosity is compared with calculations of the transport coefficients of dilute quantum gases for all temperatures and spin polarizations.

DOI
10.1103/physrevlett.67.330

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A vibrating-wire technique has been used to directly measure the viscosity increase in a dilute 3\ensuremath−4^{3}\mathrm{\ensuremath{-}}^{4}3\ensuremath−4He solution caused by brute-force spin polarization up to 40%. The viscosity of a solution with degeneracy temperature TF{\mathit{T}}_{\mathit{F}}TF​=19.5 mK was measured over the temperature range 6.1--100 mK in magnetic fields of 1.00 and 7.96 T. Spin polarization caused a marked decrease in the mechanical Q of the viscometer at low temperatures. The observed viscosity is compared with calculations of the transport coefficients of dilute quantum gases for all temperatures and spin polarizations.
We carried out experiments on a spin polarized 3He- 4He mixture with 3He concentration x 3 = 6.26 × 10−4, and on pure 3He liquid. Spin polarization affects the transport properties of these Fermi systems. The effect on momentum transport was studied by using a vibrating-wire viscometer to measure viscosity of the 3He-4He mixture over the temperature range 6.09 mK–100 mK in 7.96 T and 1.00 T magnetic fields. A large viscosity increase was observed upon application of the 7.96 T magnetic field for temperature T < TF(TF = 19.5 mK is the Fermi temperature). The observed viscosity is in very good agreement with theoretical calculations for a dilute Fermi gas by Jeon and Mullin [1988, 1989] and Mullin and Jeon [1992]. The polarization effect on spin transport was investigated by measuring the transverse diffusion coefficient D ⊥ in pure 3He liquid at saturated vapor pressure and at 15.85 bar over the temperature range 4.5 mK–159 mK in a 7.96 T magnetic field. We used a pulsed NMR spin echo technique in a field gradient of 16.0 G/cm to do the measurements and fits to the Leggett equations [1970] to obtain D⊥. For T < 20 mK, we found D⊥ is less than measured in earlier experiments at lower magnetic fields. D⊥ does not increase with decreasing temperature as 1/T2, but appears to approach a constant as T → 0 while it is expected that the longitudinal spin diffusion coefficient D∥ ∝ 1/ T2. This is called spin diffusion anisotropy and it was observed for the first time in our 3He liquid experiments. The anisotropy temperature we determined for 3He liquid was Ta = 16.4 ± 2.2 mK at saturated vapor pressure and in a 7.96 T magnetic field. The transverse spin diffusion in 3 He results agree qualitatively with theories proposed by Meyerovich and Musaeflan [1992, 1994]. They also agree qualitatively with theories proposed by Golosov and Ruckenstein [1995, 1998] by extrapolation of the dilute theory to a strongly interacting system.
We present vibrating - wire viscosity measurements on a very dilute 3 He -4 He mixture (χ3 = 150 ppm ) in fields up to 14.8 T and temperatures down to 3 mK. The 3 He spin polarization is greater than 99% for the highest field and lowest temperature used. In these conditions, the s-wave scattering rate decreases due to a lack of quasiparticles with the minority spin state. This enhances all transport coefficients including the viscosity. At the lowest temperature, the hydrodynamic damping of the viscometer in a 14.8 T field was more than 10 times larger than in low fields. This indicates a many-fold increase in the mixture viscosity due to spin polarization.
The viscosity is measured for a Fermi liquid, a dilute $^{3}\mathrm{He}\mathrm{\text{\ensuremath{-}}}^{4}\mathrm{He}$ mixture, under extremely high magnetic field/temperature conditions ($B\ensuremath{\le}14.8\text{ }\text{ }\mathrm{T}$, $T\ensuremath{\ge}1.5\text{ }\text{ }\mathrm{mK}$). The spin-splitting energy $\ensuremath{\mu}B$ is substantially greater than the Fermi energy kBTF{k}_{B}{T}_{F}kB​TF​; as a consequence the polarization tends to unity and sss-wave quasiparticle scattering is suppressed for $T\ensuremath{\ll}{T}_{F}$. Using a novel composite vibrating-wire viscometer an enhancement of the viscosity is observed by a factor of more than 500 over its low-field value. Good agreement is found between the measured viscosity and theoretical predictions based upon a ttt-matrix formalism.
The transport properties of one-dimensional Fermi gases at low temperatures are often described by the Luttinger liquid (LL) model. However, to study dissipative effects, one needs to examine interactions beyond the LL model. In this work, we provide a simple model that allows for a direct microscopic calculation of the bulk viscosity, namely, the one-dimensional spin polarized ppp-wave Fermi gas. To leading order in the finite interaction strength, we find that the bulk viscosity is finite and consistent with the requirement of scale symmetry. We further show that the bulk viscosity satisfies the Bose-Fermi duality relating the weakly interacting limit of the spin polarized Fermi gas to the strongly interacting limit of the Lieb-Liniger model and vice versa. This work establishes the bulk viscosity to leading order in scale-breaking interactions in both the strongly and weakly interacting limits for both high and low temperatures.
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)].
Using kinetic theory, we calculate the shear viscosity and the spin-diffusion coefficient as well as the associated relaxation times for a two-component Fermi gas in two dimensions, as a function of temperature, coupling strength, polarization, and mass ratio of the two components. It is demonstrated that the minimum value of the viscosity decreases with the mass ratio, since Fermi blocking becomes less efficient. We furthermore analyze recent experimental results for the quadrupole mode of a two-dimensional gas in terms of viscous damping, obtaining a qualitative agreement using no fitting parameters.