Zero-Temperature Theory of Collisionless Rapid Adiabatic Passage from a Fermi Degenerate Gas of Atoms to a Bose-Einstein Condensate of Molecules

We theoretically examine a zero-temperature system of Fermi degenerate atoms coupled to bosonic molecules via collisionless rapid adiabatic passage across a Feshbach resonance, focusing on saturation of the molecular conversion efficiency at the slowest magnetic-field sweep rates. Borrowing a novel {\em many-fermion} Fock-state theory, we find that a proper model of the magnetic-field sweep can systematically remove saturation. We also debunk the common misconception that many-body effects are responsible for molecules existing above the two-body threshold.