Coherent population trapping and dynamical instability in coupled atom-molecule condensates

Coherent population trapping (CPT) is an important concept in many subfields of physics and chemistry. Here we analyze the collective excitation spectrum of the CPT states in a coupled atom-molecule condensate system. We find that collisions between particles can cause the CPT state to be dynamically unstable, which is a unique feature of the nonlinear system. We obtain a set of analytical criteria for determining the stability properties of the CPT state in the long-wavelength limit. We construct stability diagrams and provide a systematic classification of various instabilities according to collisional interaction strengths.