Adiabatic theorem for a condensate system in an atom-molecule dark state

We consider the adiabatic evolution of an atom-molecule dark state in a collisional two-color Raman photoassociation condensate system. By linking nonadiabaticity with the population growth in the collective excitations of the dark state, we develop an adiabatic theorem where we have consistently addressed the issues related to the Goldstone mode and the biorthonormality of the collective modes. We apply this theorem to specific examples to demonstrate its use in designing pulses that can optimize the yield of ground molecule production in the stimulated Raman adiabatic passage process.