“…Population control in quantum systems, namely transfer of electrons from an ensemble of atoms all in the same initial state to specified final states, is used in problems ranging from coherent population trapping [1, 2,3,4,5], including electromagnetically induced transparency [6,7,8,9], and quantum computing [10,11,12,13,14,15,16], to chemical dynamics [17,18]. These problems are modeled in terms of an n-level (often 3-level) atom interacting with a strong external field [19,20,21,22,23,24].…”