This work explores the relationship between optimal control theory and
adiabatic passage techniques in quantum systems. The study is based on a
geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin
Maximum Principle. In a three-level quantum system, we show that the Stimulated
Raman Adiabatic Passage technique can be associated to a peculiar Hamiltonian
singularity. One deduces that the adiabatic pulse is solution of the optimal
control problem only for a specific cost functional. This analysis is extended
to the case of a four-level quantum system.Comment: 19 pages, 6 figure