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We investigate the geometrical phase associated to the Schr\"odinger equationin a three level system in Stimulated Raman Adiabatic Passage (STIRAP). Wesolve explicitly a dual model, in which the pulses are applied in thecounterintuitive and intuitive order. We show that when the pulse areas arefinite, a pair of magnetic monopoles with opposite charges are createdresulting the oscillations of the populations on the final states. Theapplications of the phase shift include, for example, phase gates in quantumcomputing, phase manipulation in quantum cryptography and phase interactions inquantum interference.

Exact solutions and magnetic monopoles in adiabatic three level systems