Number statistics of molecules formed from ultracold atoms

We calculate the number statistics of a single-mode molecular field excited by photo-association or via a Feshbach resonance from an atomic Bose-Einstein condensate (BEC), a normal atomic Fermi gas, and a Fermi system with pair correlations (BCS state). We find that the molecule formation from a BEC leads for short times to a coherent molecular state in the quantum optical sense. Atoms in a normal Fermi gas, on the other hand, result for short times in a molecular field analog of a classical chaotic light source. The BCS situation is intermediate between the two and goes from producing an incoherent to a coherent molecular field with an increasing gap parameter. This distinct signature of the initial atomic state in the resulting molecular field makes single molecule counting into a powerful diagnostic tool.