Shortcut to a Fermi-Degenerate Gas of Molecules via Cooperative Association

We theoretically examine the creation of a Fermi-degenerate gas of molecules by considering a photoassociation or Feshbach resonance applied to a degenerate Bose-Fermi mixture of atoms. This problem raises interest because, unlike bosons, fermions in general do not behave cooperatively, so that the collective conversion of a degenerate gas atoms into a macroscopic number of diatomic molecules is not to be expected. Nevertheless, we find that the coupled Fermi system displays collective Rabi-like oscillations and a rapid adiabatic passage between atoms and molecules, thereby mimicking Bose-Einstein statistics. Cooperative association of a degenerate mixture of Bose and Fermi gases could therefore serve as a shortcut to a degenerate gas of Fermi molecules.