  We examine the topology of eigenenergy surfaces characterizing the population
transfer processes based on adiabatic passage. We show that this topology is
the essential feature for the analysis of the population transfers and the
prediction of its final result. We reinterpret diverse known processes, such as
stimulated Raman adiabatic passage (STIRAP), frequency-chirped adiabatic
passage and Stark-chirped rapid adiabatic passage (SCRAP). Moreover, using this
picture, we display new related possibilities of transfer. In particular, we
show that we can selectively control the level which will be populated in
STIRAP process in Lambda or V systems by the choice of the peak amplitudes or
the pulse sequence.
