Ultracold strongly coupled gas: A near-ideal liquid

Abstract

Feshbach resonances of trapped ultracold alkali-metal atoms allow to vary the atomic scattering length $a$. At very large values of $a$ the system enters an universal strongly coupled regime in which its properties---the ground-state energy, pressure, etc.---become independent of $a$. We discuss the transport properties of such systems. In particular, the universality arguments imply that the shear viscosity of ultracold Fermi atoms at the Feschbach resonance is proportional to the particle number density $n$ and the Plank constant $\ensuremath{\hbar}$: $\ensuremath{\eta}=\ensuremath{\hbar}n{\ensuremath{\alpha}}_{\ensuremath{\eta}}$, where ${\ensuremath{\alpha}}_{\ensuremath{\eta}}$ is a universal constant. Using Heisenberg uncertainty principle and Einstein's relation between diffusion and viscosity we argue that the viscosity has the lower bound given by ${\ensuremath{\alpha}}_{\ensuremath{\eta}}\ensuremath{\leqslant}{(6\ensuremath{\pi})}^{\ensuremath{-}1}$. We relate the damping of low-frequency density oscillations of ultracold optically trapped $^{6}\mathrm{Li}$ atoms to viscosity and find that the value of the coefficient ${\ensuremath{\alpha}}_{\ensuremath{\eta}}$ is about 0.3. We also show that such a small viscosity cannot be explained by kinetic theory based on binary scattering. We conclude that the system of ultracold atoms near the Feshbach resonance is a near-ideal liquid.