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Quantum time ordering and degeneracy. II: Coherent population transfer between degenerate states

Kh. Yu. Rakhimov·Kh. Kh. Shakov·J. H. McGuire
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Abstract

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 $n$-state atom, where transitions are caused by an external interaction. In systems with degenerate states there is no time ordering. Analytic expressions have been found for transition probabilities in a degenerate $n$-state atom interacting with a strong external field that gives a common time dependence to all of the transition matrix elements. Except for solving a simple $n^{th}$ order equation to determine eigenvalues of dressed states, the method is entirely analytic. These expressions may be used to control electron populations in degenerate $n$-state atoms. Examples are given for $n=2$ and $n=3$.

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Kh. Yu. Rakhimov, Kh. Kh. Shakov, J. H. McGuire. 2003-08-02. Quantum time ordering and degeneracy. II: Coherent population transfer between degenerate states. https://arxiv.org/abs/quant-ph/0308015

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