Adiabatic fidelity for atom-molecule conversion in a nonlinear three-level Λ system

By generalizing the definition of fidelity for the nonlinear system, we investigate the dynamics and adiabaticity of the population transfer for atom-molecule three-level Lambda system on a stimulated Raman adiabatic passage (STIRAP). We find that the adiabatic fidelity for the coherent population trapping state or dark state, as the function of the adiabatic parameter, approaches to unit in a power law. The power exponent, however, is much less than the prediction of the linear adiabatic theorem. We further discuss how to achieve higher adiabatic fidelity for the dark state through optimizing the external parameters of the STIRAP.