  We study the process of Stimulated Raman Adiabatic Passage (STIRAP) under the
influence of a non-trivial solid-state environment, particularly the effect of
two-level fluctuators (TLFs) as they are frequently present in solid-state
devices. When the amplitudes of the driving-pulses used in STIRAP are in
resonance with the level spacing of the fluctuators the quality of the
protocol, i.e., the transferred population decreases sharply. In general the
effect can not be reduced by speeding up the STIRAP process. We also discuss
the effect of a structured noise environment on the process of Coherent
Tunneling by Adiabatic Passage (CTAP). The effect of a weakly structured
environment or TLFs with short coherence times on STIRAP and CTAP can be
described by the Bloch-Redfield theory. For a strongly structured environment a
higher-dimensional approach must be used, where the TLFs are treated as part of
the system.
