Exact solutions and magnetic monopoles in adiabatic three level systems

We investigate the geometrical phase associated to the Schr\"odinger equation in a three level system in Stimulated Raman Adiabatic Passage (STIRAP). We solve explicitly a dual model, in which the pulses are applied in the counterintuitive and intuitive order. We show that when the pulse areas are finite, a pair of magnetic monopoles with opposite charges are created resulting the oscillations of the populations on the final states. The applications of the phase shift include, for example, phase gates in quantum computing, phase manipulation in quantum cryptography and phase interactions in quantum interference.