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Complete population transfer in a degenerate 3-level atom
We find 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 3-level atom, where transitions are caused
by an external interaction. Complete population transfer from an initially
occupied 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 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.Comment: 22 pages, 4 figure