Abstract
We study the effects of quantum statistics on the counting statistics of ultracold heteronuclear molecules formed by Feshbach-assisted photoassociation (Search and Meystre 2004 Phys. Rev. Lett. 93 140405). Exploiting the formal similarities with sum frequency generation and using quantum optics methods, we consider the cases where the molecules are formed from atoms out of two Bose–Einstein condensates (BEC), out of a BEC and a gas of degenerate fermions, and out of two degenerate Fermi gases with and without superfluidity. Bosons are treated in a single-mode approximation and fermions in a degenerate model. In these approximations, we can numerically solve the master equations describing the system's dynamics and thus we find the full counting statistics of the molecular modes. The full quantum dynamics calculations are complemented by mean-field calculations and short time perturbative expansions. While the molecule production rates are very similar in all three cases at this level of approximation, differences show up in the counting statistics of the molecular fields. The intermediate field of closed-channel molecules is, for short times, second-order coherent if the molecules are formed from two BECs or a Bose–Fermi mixture. They show counting statistics similar to a thermal field if formed from two normal Fermi gases. The coherence properties of molecule formation in two superfluid Fermi gases are intermediate between the two previous cases. In all cases, the final field of deeply bound molecules is found to be twice as noisy as that of the intermediate state. This is a consequence of its coupling to the lossy optical cavity in our model, which acts as an input port for quantum noise, much like the situation in an optical beam splitter.