Tunable viscosity across the BCS-BEC crossover

Tunable interactions make ultracold quantum gases a unique platform for exploring hydrodynamic properties in the strongly correlated regime. Of particular interest are turbulent flows possible in the regime of high Reynolds numbers. Since the system size and flow velocity are limited in experimentally realistic systems, we propose an alternative approach to enhance the Reynolds numbers in an ultracold Fermi gas by minimizing the shear viscosity in the vicinity of the Feshbach resonance. By employing the Keldysh formulation of the linear response theory, we theoretically demonstrate that the shear viscosity can vary by several orders of magnitude in the vicinity of the BCS-BEC crossover. It is also shown that while Drude-like contributions generally dominate at large Feshbach detunings, higher-order vertex corrections, including the Maki-Thompson contribution, become significant and suppress singular behavior in the near-resonant regime. Our results provide a roadmap for achieving tunable Reynolds numbers in ultracold quantum fluids, which can serve as table-top turbulence simulators.