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Interaction-induced instability and chaos in the photoassociative stimulated Raman adiabatic passage from atomic to molecular Bose-Einstein condensates

We study the effect of interactions on the conversion of atomic -to molecular Bose-Einstein condensates via stimulated Raman adiabatic passage. Both energetic instability during avoided crossings and dynamical instability during chaotic intervals limit adiabaticity and impose {\em low} sweep-rate boundaries on the efficiency of the process. For the diabatic traverse of avoided crossings, we find a reciprocal power-law dependence of the final unconverted population on sweep rate. For the traverse of chaos, we find a sharp low-rate boundary determined by the dynamical instability parameters. The interplay of these two mechanisms determines which instability controls the failure of molecular production. A judicious choice of sweep parameters is hence required to restore the process efficiency.