The internal Josephson effect in a Fermi gas near a Feshbach resonance

We consider a two-component system of Fermi atoms and molecular bosons in the vicinity of a Feshbash resonance. We derive an effective action for the system, which has a term describing coherent tunneling of the molecular bosons into Cooper pairs and vice versa. In the equilibrium state, global phase coherence may be destroyed by thermal or quantum phase fluctuations. In the non-equilibrium regime, the system may show an internal AC Josephson effect leading to real time oscillations in the number of molecular bosons.