Abstract of "Resonance
of Minimizers for n-level
Quantum Systems with an Arbitrary Cost"
We consider an optimal control problem describing a laser-induced
population transfer on a $n$-level quantum system.
For a convex cost depending only on the moduli of controls (i.e. the
lasers intensities), we prove that there always exists a minimizer in
resonance. This permits to justify some strategies used in
experimental physics. It is also quite important because it permits to
reduce remarkably the complexity of the problem (and extend some of our
previous results for n=2 and n=3): instead of looking for minimizers on
the sphere $S^{2n-1}\subset\C^n$ one is reduced to look just for
minimizers on the sphere $S^{n-1}\subset \R^n$.
Moreover, for the reduced problem, we investigate on the question of
existence of strict abnormal minimizer.
Keywords: Control of Quantum Systems, Optimal Control, Sub-Riemannian
Geometry, Resonance, Pontryagin Maximum Principle, Abnormal
Extremals, Rotating Wave Approximation.