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arXiv:1504.02560 · Physical Review A

Perfect-fluid behavior of a dilute Fermi gas near unitary

Gabriel Wlazłowski, Wei Quan, Aurel Bulgac

Published Dec 21, 2015• 19 citations
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Abstract

We present an ab initio calculation of the shear viscosity as a function of interaction strength in a two-component unpolarized Fermi gas near the unitary limit, within a finite temperature quantum Monte Carlo (QMC) framework and using the Kubo linear-response formalism. The shear viscosity decreases as we tune the interaction strength $\frac{1}{a{k}_{F}}$ from the Bardeen-Cooper-Schrieffer side of the Feshbach resonance towards Bose-Einstein condensation limit and it acquires the smallest value for $\frac{1}{a{k}_{F}}\ensuremath{\approx}0.4$, with a minimum value of ${\frac{\ensuremath{\eta}}{s}|}_{\text{min}}\ensuremath{\approx}0.2\frac{\ensuremath{\hbar}}{{k}_{B}}$, which is about twice as small as the value reported for experiments in quark-gluon plasma ${\frac{\ensuremath{\eta}}{s}|}_{\text{QGP}}\ensuremath{\lesssim}0.4\frac{\ensuremath{\hbar}}{{k}_{B}}$. The Fermi gas near unitarity thus emerges as the most ``perfect fluid'' observed so far in nature. The clouds of dilute Fermi gas near unitarity exhibit the unusual attribute that, for the sizes realized so far in the laboratory, or larger (less than ${10}^{9}$ atoms), can sustain quantum turbulence below the critical temperature, but at the same time the classical turbulence is suppressed in the normal phase.

DOI
10.1103/physreva.92.063628

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We present an ab initio calculation of the shear viscosity as a function of interaction strength in a two-component unpolarized Fermi gas near the unitary limit, within a finite temperature quantum Monte Carlo (QMC) framework and using the Kubo linear-response formalism. The shear viscosity decreases as we tune the interaction strength 1akF\frac{1}{a{k}_{F}}akF​1​ from the Bardeen-Cooper-Schrieffer side of the Feshbach resonance towards Bose-Einstein condensation limit and it acquires the smallest value for 1akF\ensuremath≈0.4\frac{1}{a{k}_{F}}\ensuremath{\approx}0.4akF​1​\ensuremath≈0.4, with a minimum value of \ensuremathηs∣min\ensuremath≈0.2\ensuremathℏkB{\frac{\ensuremath{\eta}}{s}|}_{\text{min}}\ensuremath{\approx}0.2\frac{\ensuremath{\hbar}}{{k}_{B}}s\ensuremathη​∣min​\ensuremath≈0.2kB​\ensuremathℏ​, which is about twice as small as the value reported for experiments in quark-gluon plasma \ensuremathηs∣QGP\ensuremath≲0.4\ensuremathℏkB{\frac{\ensuremath{\eta}}{s}|}_{\text{QGP}}\ensuremath{\lesssim}0.4\frac{\ensuremath{\hbar}}{{k}_{B}}s\ensuremathη​∣QGP​\ensuremath≲0.4kB​\ensuremathℏ​. The Fermi gas near unitarity thus emerges as the most ``perfect fluid'' observed so far in nature. The clouds of dilute Fermi gas near unitarity exhibit the unusual attribute that, for the sizes realized so far in the laboratory, or larger (less than 109{10}^{9}109 atoms), can sustain quantum turbulence below the critical temperature, but at the same time the classical turbulence is suppressed in the normal phase.
We present an ab initio determination of the shear viscosity $\ensuremath{\eta}$ of the unitary Fermi gas, based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism. We determine the temperature dependence of the shear viscosity-to-entropy density ratio $\ensuremath{\eta}/s$. The minimum of $\ensuremath{\eta}/s$ appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being $(\ensuremath{\eta}/s{)}_{\mathrm{min}}\ensuremath{\approx}0.2\ensuremath{\hbar}/{k}_{B}$, which is close the Kovtun-Son-Starinets universal value $\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})$.
We present an ab initio determination of the shear viscosity for the unitary Fermi gas based on finite temperature quantum Monte Carlo (QMC) calculations and the Kubo linear-response formalism. The results are confronted with the bound for the shear viscosity originating from hydrodynamic fluctuations. Assuming smoothness of the frequency dependent shear viscosity $\ensuremath{\eta}(\ensuremath{\omega})$, we show that the bound is violated in the low temperature regime and the violation occurs simultaneously with the onset of the Cooper pairing in the system. In order to preserve the hydrodynamic bound in QMC $\ensuremath{\eta}(\ensuremath{\omega})$ has to possess a sharp structure located in the vicinity of zero frequency which is not resolved by an analytic continuation procedure.
We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T . We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏ n is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.
We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T. We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏn is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.
We study the shear viscosity of a dilute Fermi gas as a function of the scattering length in the vicinity of the unitarity limit. The calculation is based on kinetic theory, which provides a systematic approach to transport properties in the limit in which the fugacity $z=n{\ensuremath{\lambda}}^{3}/2$ is small. Here, nnn is the density of the gas and $\ensuremath{\lambda}$ is the thermal wavelength of the fermions. At leading order in the fugacity expansion, the shear viscosity is independent of density, and the minimum shear viscosity is achieved at unitarity. At the next order, medium effects modify the scattering amplitude as well as the quasiparticle energy and velocity. We show that these effects shift the minimum of the shear viscosity to the Bose-Einstein condensation side of the resonance, in agreement with the result of recent experiments.
We confirm and expand on work by Chafin and Sch\"afer [Phys. Rev. A 87, 023629 (2013)] on hydrodynamic fluctuations in the unitary Fermi gas. Using the result for the equation of state from a recent MIT experiment, we derive lower bounds for $\ensuremath{\eta}/n$ and $\ensuremath{\eta}/s$ as a function of temperature. Reanalyzing recent quantum Monte Carlo data for the shear-viscosity spectral function, we point out a possible resolution for the tension between the viscosity bound $\ensuremath{\eta}/n\ensuremath{\gtrsim}0.3$ from Chafin and Sch\"afer and the quantum Monte Carlo results $\ensuremath{\eta}/n\ensuremath{\lesssim}0.2$ from Wlazlowski, Magierski, and Drut [Phys. Rev. Lett. 109, 020406 (2012)] near the critical temperature.