Complete population transfer in a degenerate three-state atom

We have found conditions required to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate three-state atom, where transitions are caused by an external interaction. Complete population transfer from an initially occupied state one to a designated state two occurs under two conditions. First, there is a constraint on the ratios of the transition matrix elements of the external interaction. Second, there is a constraint on the action integral over the interaction, or “area,” corresponding to the phase shift induced by the external interaction. Both conditions may be expressed in terms of simple odd integers. Some specific examples are discussed.