We survey results on the creation of heteronuclear Fermi molecules by tuning
a degenerate Bose-Fermi mixture into the neighborhood of an association
resonance, either photoassociation or Feshbach, as well as the subsequent
prospects for Cooper-like pairing between atoms and molecules. In the simplest
case of only one molecular state, corresponding to either a Feshbach resonance
or one-color photoassociation, the system displays Rabi oscillations and rapid
adiabatic passage between a Bose-Fermi mixture of atoms and fermionic
molecules. For two-color photoassociation, the system admits stimulated Raman
adiabatic passage (STIRAP) from a Bose-Fermi mixture of atoms to stable Fermi
molecules, even in the presence of particle-particle interactions. By tailoring
the STIRAP sequence it is possible to deliberately convert only a fraction of
the initial atoms, leaving a finite fraction of bosons behind to induce
atom-molecule Cooper pairing via density fluctuations; unfortunately, this
enhancement is insufficient to achieve a superfluid transition with present
ultracold technology. We therefore propose the use of an association resonance
that converts atoms and diatomic molecules (dimers) into triatomic molecules
(trimers), which leads to a crossover from a Bose-Einstein condensate of
trimers to atom-dimer Cooper pairs. Because heteronuclear dimers may possess a
permanent electric dipole moment, this overall system presents an opportunity
to investigate novel microscopic physics.Comment: 10 pages, 5 figures, 77+ references, submitted to Euro. Phys. J.
topical issue on "Ultracold Polar Molecules: Formation and Collisions