  We consider the STIRAP process in a three-level atom. Viewed as a closed
system, no geometric phase is acquired. But in the presence of spontaneous
emission and/or collisional relaxation we show numerically that a
non-vanishing, purely real, geometric phase is acquired during STIRAP, whose
magnitude grows with the decay rates. Rather than viewing this
decoherence-induced geometric phase as a nuisance, it can be considered an
example of "beneficial decoherence": the environment provides a mechanism for
the generation of geometric phases which would otherwise require an extra
experimental control knob.
