Perfect fluids and bad metals: insights from ultracold Fermi gases

Abstract

In this paper, we examine in a unified-fashion dissipative transport in strongly correlated systems. We thereby demonstrate the connection between ‘bad metals’ (such as high-temperature superconductors) and ‘perfect fluids’ (such as ultracold Fermi gases, near unitarity). One aim of this paper is to communicate to the high-energy physics community some of the central unsolved problems in high-Tc superconductors. Because of the interest in the nearly perfect fluidity of cold gases and because of new tools such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, the communication may lead to significant progress in a variety of different fields. A second aim is to draw attention to the great power of transport measurements, which reflect the excitation spectrum more directly than, say, thermodynamics, and therefore strongly constrain microscopic theories of correlated fermionic superfluids. Our calculations show that bad metal and perfect fluid behavior is associated with the presence of a normal state excitation gap that suppresses the effective number of carriers leading to anomalously low conductivity and viscosity above the transition temperature Tc. Below Tc, we demonstrate that the condensate collective modes (‘phonons’) do not couple to transverse probes, such as shear viscosity or conductivity. As a result, our calculated shear viscosity at low T becomes arbitrarily small, as observed in experiments. In both homogeneous and trap calculations, we do not find the upturn in η or η/s (where s is the entropy density) that is found in most theories. In the process of these studies, we demonstrate compatibility with the transverse sum rule and find reasonable agreement with viscosity experiments.