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We find conditions required to achieve complete population transfer, viacoherent population trapping, from an initial state to a designated final stateat a designated time in a degenerate 3-level atom, where transitions are causedby an external interaction. Complete population transfer from an initiallyoccupied state 1 to a designated state 2 occurs under two conditions. First,there is a constraint on the ratios of the transition matrix elements of theexternal interaction. Second, there is a constraint on the action integral overthe interaction, or "area", corresponding to the phase shift induced by theexternal interaction. Both conditions may be expressed in terms of simple oddintegers.Comment: 22 pages, 4 figure

Complete population transfer in a degenerate three-state atom