Detecting entrainment in Fermi-Bose mixtures

We propose an experimental protocol to directly detect the Andreev-Bashkin effect (entrainment) in the bulk mixture of a bosonic and fermionic superfluid using a ring geometry. Our protocol involves the interferometric detection of the entrainment-induced phase gradient across a superfluid due to the flow of another in which it is immersed. The choice of ring geometry eliminates variations in the stronger mean-field interaction which can thwart the detection of entrainment in other geometries. A significant enhancement of the entrainment phase shift signal is possible, if the dimer-boson scattering length turns out to be large, which can be measured by tuning the interaction to the limit of miscibility of the two superfluids. With suggested improvements and careful design implementation, one may achieve $\approx 67$% shift in the interferometer fringes.