  Stimulated Raman adiabatic passage is a quantum protocol that can be used for
robust state preparation in a three-level system. It has been commonly employed
in quantum optics, but recently this technique has drawn attention also in
circuit quantum electrodynamics. The protocol relies on two slowly varying
drive pulses that couple the initial and the target state via an intermediate
state, which remains unpopulated. Here we study the detrimental effect of the
parasitic couplings of the drives into transitions other than those required by
the protocol. The effect is most prominent in systems with almost harmonic
energy level structure, such as the transmon. We show that under these
conditions in the presence of decoherence there exists an optimal STIRAP
amplitude for population transfer.
