  We investigate the relationship between stability, adiabaticity and transfer
efficiency in a \Lambda-type atom-molecule coupling system via a nonlinear
stimulated Raman adiabatic passage. We find that only when the pump and control
lasers overlap in time domain, the coherent population trapping (CPT) state
could become unstable. If the overlapping time of the two lasers is short so
that unstable growth of the deviation from the CPT state is negligible, then
good adiabaticity of the CPT state could be maintained even in the unstable
region. In this case, a high atom-molecule transfer efficiency could be
obtained by chirping applied laser pulses to elegantly compensate the frequency
shift induced by intra-atomic collision. Our results could be useful for
efficiently photoassociating ground-state molecules from a cold atomic gas with
strong atom-atom collisional interaction.
