The authors calculate thermal transport and the damping of sound in a unitary Fermi gas. In the quantum critical regime, thermal diffusion follows a universal scaling law and reaches a limit set by the uncertainty principle of quantum mechanics
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 m. 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. 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 C. For the spin susceptibility ${\ensuremath{\chi}}_{s}(T)$ we find no downturn in the normal phase.
Transport of strongly interacting fermions is crucial for the properties of modern materials, nuclear fission, the merging of neutron stars, and the expansion of the early Universe. Here, we observe a universal quantum limit of diffusivity in a homogeneous, strongly interacting atomic Fermi gas by studying sound propagation and its attenuation through the coupled transport of momentum and heat. In the normal state, the sound diffusivity D monotonically decreases upon lowering the temperature, in contrast to the diverging behavior of weakly interacting Fermi liquids. Below the superfluid transition temperature, D attains a universal value set by the ratio of Planck's constant and the particle mass. Our findings inform theories of fermion transport, with relevance for hydrodynamic flow of electrons, neutrons, and quarks.
Recent experiments on sound waves in a unitary Fermi gas reveal many transport properties about strongly interacting fermions. Sound propagates through the coupling of momentum and heat transport, and attenuates strongly with the presence of a phase transition. In this work, focusing on the temperature regimes near and below the superfluid critical temperature [Formula: see text] in the BCS-BEC crossover, we present a Kubo-based microscopic calculation of thermal conductivity [Formula: see text], which has not attracted much attention compared to the shear viscosity. Our approach primarily addresses the contributions of the fermionic quasiparticles to thermal transport and our results return to the kinetic descriptions at high temperatures. [Formula: see text] drops upon crossing the pseudogap temperature [Formula: see text], and its temperature dependence changes below [Formula: see text]. The drops become more pronounced on the weakly coupled BCS side, where the Pauli blocking causes the upturn of [Formula: see text] above [Formula: see text]. Our calculations fit well with the sound measurement on the damping rate.
Strongly interacting two-dimensional Fermi systems are one of the great remaining challenges in many-body physics due to the interplay of strong local correlations and enhanced long-range fluctuations. Here, we probe the thermodynamic and transport properties of a 2D Fermi gas across the BEC-BCS crossover by studying the propagation and damping of sound modes. We excite particle currents by imprinting a phase step onto homogeneous Fermi gases trapped in a box potential and extract the speed of sound from the frequency of the resulting density oscillations. We measure the speed of sound across the BEC-BCS crossover and compare the resulting dynamic measurement of the equation of state both to a static measurement based on recording density profiles and to quantum Monte Carlo calculations and find reasonable agreement between all three. We also measure the damping of the sound mode, which is determined by the shear and bulk viscosities as well as the thermal conductivity of the gas. We find that the damping is minimal in the strongly interacting regime and the diffusivity approaches the universal quantum bound ℏ/m of a perfect fluid.
The thermodynamic and transport properties of the unitary Fermi gas at finite temperature T are governed by a quantum critical point at T=0 and zero density. We compute the universal shear viscosity to entropy ratio $\ensuremath{\eta}/s$ in the high-temperature quantum critical regime $T\ensuremath{\gg}|\ensuremath{\mu}|$ and find that this strongly coupled quantum fluid comes close to perfect fluidity $\ensuremath{\eta}/s=\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})$. Using a controlled large-N expansion, we show that already at the first nontrivial order the equation of state and the Tan contact density C agree well with the most recent experimental measurements and theoretical Luttinger-Ward and bold diagrammatic Monte Carlo calculations.