Coherent population transfer beyond the adiabatic limit: Generalized matched pulses and higher-order trapping states

We show that the physical mechanism of population transfer in a three-level system with a closed loop of coherent couplings is not equivalent to an adiabatic rotation of the dark state of the Hamiltonian, but corresponds 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, which also give maximum population transfer 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.