Number statistics of molecules formed from ultra-cold atoms

We calculate the number statistics of a single-mode molecular field excited by photoassociation 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 is a collective process that leads for short times to a coherent molecular state in the quantum optical sense. Atoms in a normal Fermi gas, on the other hand, are converted into molecules independently of each other and result for short times in a molecular state analogous to that 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 increasing gap parameter.