Decoherence-induced geometric phase in a multilevel atomic system

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 numerically show that a non-vanishing, purely real, geometric phase is acquired during STIRAP, whose magnitude grows with the decay rates. We speculate that 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.