  We model combined photoassociation and Feshbach resonances in a Bose-Einstein
condensate. When the magnetic field is far-off resonance, cross coupling
between the two target molecules--enabled by the shared dissociation
continuum--leads to an anomalous dispersive shift in the position of laser
resonance, as well as unprecedented elimination and enhancement of resonant
photoassociation via quantum interference. For off-resonant lasers, a
dispersive shift and quantum interference appear similarly in resonant
three-body Feshbach losses, except that the Feshbach node is tunable with
intensity.
