  We consider a dilute atomic gas of two species of fermions with unequal
concentrations under a Feshbach resonance. We find that the system can have
distinct properties due to the unbound fermions. The uniform state is stable
only when either (a) beyond a critical coupling strength, where it is a gapless
superfluid, or (b) when the coupling strength is sufficiently weak, where it is
a normal Fermi gas mixture. Phase transition(s) must therefore occur when the
resonance is crossed.
