Perturbative and nonperturbative processes in adiabatic population transfer

With the help of superadiabatic techniques for quantum systems depending slowly on time: we demonstrate how the total transition amplitude, tracked in time in the usual adiabatic basis, can be decomposed into a perturbative part consisting of terms proportional to powers of the adiabaticity parameter, and a nonperturbative component. The interference of both components underlies the oscillations that accompany transitions in the adiabatic basis. Whereas for traditionally considered systems the final non adiabatic transition probability is determined by the nonperturbative part alone, this is no longer correct for models describing stimulated Raman adiabatic passage (STIRAP). We explain the recently discovered breakdown of the Dykhne-Davis-Pechukas formula on general grounds, and provide simple, but accurate approximations for transition amplitudes in STIRAP systems.