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Degenerate Fermi gas interacting with molecules near Feshbach resonance isunstable with respect to formation of a mixed state in which atoms andmolecules coexist as a coherent superposition. Theory of this state isdeveloped using a mapping to the Dicke model, treating molecular field in thesingle mode approximation. The results are accurate in the strong couplingregime relevant for current experimental efforts. The exact solution of theDicke model is exploited to study stability, phase diagram, and nonadiabaticdynamics of molecular field in the mixed state.Comment: 5 pages, 2 figure

Atom-Molecule Coexistence and Collective Dynamics Near a Feshbach Resonance of Cold Fermions