  We show that the physical mechanism of population transfer in a 3-level
system with a closed loop of coherent couplings (loop-STIRAP) is not equivalent
to an adiabatic rotation of the dark-state of the Hamiltonian but coresponds to
a rotation of a higher-order trapping state in a generalized adiabatic basis.
The concept of generalized adiabatic basis sets is used as a constructive tool
to design pulse sequences for stimulated Raman adiabatic passage (STIRAP) which
give maximum population transfer also under conditions when the usual condition
of adiabaticty is only poorly fulfilled. Under certain conditions for the
pulses (generalized matched pulses) there exists a higher-order trapping state,
which is an exact constant of motion and analytic solutions for the atomic
dynamics can be derived.
