Analytic properties and effective two-level problems in stimulated Raman adiabatic passage

We demonstrate that various properties of population transfer by delayed pulses in three-level systems on two-photon resonance can be deduced analytically and for general pulse shapes. We use the fact that the three-level system reduces to effective two-level problems at large intermediate-level detuning Delta, on resonance (Delta=0) and for completely overlapping pulses. Special attention is paid to the effect of the pulse order on the population transfer efficiency. We show that on resonance the transfer efficiency depends substantially on the pulse order, while at large Delta it does not. We also find that under some natural restrictions on the symmetry of the problem, the population of the initial level does not depend on the pulse order at any Delta. Furthermore, we demonstrate that the population transfer in the three-level system can be viewed as a level-crossing problem in an equivalent two-level system not only at large Delta (which is known) but also on resonance, Delta=0. The effective on-resonance two-level problem is interesting by itself as it shows that a level crossing and adiabatic evolution do not necessarily lead to complete population inversion. As examples throughout the paper, we present several analytically solvable models.