Strong-Coupling Effects and Shear Viscosity in an Ultracold Fermi Gas

We theoretically investigate the shear viscosity η, as well as the entropy density s, in the normal state of an ultracold Fermi gas. Including pairing fluctuations within the framework of a T-matrix approximation, we calculate these quantities in the Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensation (BEC) crossover region. We also evaluate η/ s, to compare it with the lower bound of this ratio, conjectured by Kovtun, Son, and Starinets (KSS bound). In the weak-coupling BCS side, we show that the shear viscosity η is remarkably suppressed near the superfluid phase transition temperature T_c, due to the so-called pseudogap phenomenon. In the strong-coupling BEC side, we find that, within the neglect of the vertex corrections, one cannot correctly describe η. We also show that η/ s decreases with increasing the interaction strength, to become very close to the KSS bound, ħ/ 4 πk_B, on the BEC side.