  We model combined photoassociation and Feshbach resonances in a Bose-Einstein
condensate, where the shared dissociation continuum allows for quantum
interference in losses from the condensate, as well as a dispersive-like shift
of resonance. A simple analytical model, based on the limit of weakly bound
molecules, agrees well with numerical experiments that explicitly include
dissociation to noncondensate modes. For a resonant laser and an off-resonant
magnetic field, constructive interference enables saturation of the
photoassociation rate at user-friendly intensities, at a value set by the
interparticle distance. This rate limit is larger for smaller condensate
densities and, near the Feshbach resonance, approaches the rate limit for
magnetoassociation alone. Also, we find agreement with the unitary limit--set
by the condensate size--only for a limited range of near-resonant magnetic
fields. Finally, for a resonant magnetic field and an off-resonant laser,
magnetoassociation displays similar quantum interference and a dispersive-like
shift. Unlike photoassociation, interference and the fieldshift in resonant
magnetoassociation is tunable with both laser intensity and detuning. Also, the
dispersive-like shift of the Feshbach resonance depends on the size of the
Feshbach molecule, and is a signature of non-universal physics in a strongly
interacting system.
