  We study bosonic atoms near a Feshbach resonance, and predict that in
addition to a standard normal and atomic superfluid phases, this system
generically exhibits a distinct phase of matter: a molecular superfluid, where
molecules are superfluid while atoms are not. We explore zero- and
finite-temperature properties of the molecular superfluid (a bosonic,
strong-coupling analog of a BCS superconductor), and study quantum and
classical phase transitions between the normal, molecular superfluid and atomic
superfluid states.
