Adiabatic population transfer via multiple intermediate states

This paper discusses a generalization of stimulated Raman adiabatic passage (STIRAP) in which the single intermediate state is replaced by N intermediate states. Each of these states is connected to the initial state ψᵢ with a coupling proportional to the pump pulse and to the final state ψf with a coupling proportional to the Stokes pulse, thus forming a parallel multi-{Λ} system. It is shown that the dark (trapped) state exists only when the ratio between each pump coupling and the respective Stokes coupling is the same for all intermediate states. We derive the conditions for existence of a more general adiabatic-transfer state that includes transient contributions from the intermediate states but still transfers the population from state ψᵢ to state ψf in the adiabatic limit. We present various numerical examples for success and failure of multi-{Λ} STIRAP, which illustrate the analytic predictions. Our results suggest that in the general case of arbitrary couplings, it is most appropriate to tune the pump and Stokes lasers either just below or just above all intermediate states.