Macroscopic periodic tunneling of Fermi atoms in the BCS-BEC crossover

We study the macroscopic quantum tunneling of two weakly linked superfluids made of interacting fermionic atoms. We derive atomic Josephson junction equations and find that zero-mode and pi-mode frequencies of coherent atomic oscillations depend on the tunneling coefficient and the sound velocity of the superfluid. By considering a superfluid of K-40 atoms, we calculate these oscillation frequencies in the crossover from the Bardeen-Cooper-Schrieffer state of weakly bound Cooper pairs to the Bose-Einstein condensate of strongly bound molecular dimers.