  The superfluid phases in the resonant dipolar Fermi gases are investigated by
the standard mean-field theory. In contrast to the crossover from Bose-Einstein
condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid in the Fermi
gases with the isotropic interactions, the resonant dipolar interaction leads
to two completely different BEC phases of the tight-binding Fermi molecules on
both sides of the resonance, which are characterized by two order parameters
with the distinct internal symmetries. We point that near the resonance, the
two competitive phases can coexist, and an emergent relative phase between the
two order parameters spontaneously breaks the time-reversal symmetry, which
could be observed in the momentum resolved rf-spectroscopy.
