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We show how additional constraints, restricting the spectrum of the optimizedpulse or confining the system dynamics, can be used to steer optimization inquantum control towards distinct solutions. Our examples are multi-photonexcitation in atoms and vibrational population transfer in molecules. We showthat a spectral constraint is most effective in enforcing non-resonanttwo-photon absorption pathways in atoms and avoiding unnecessarily broadspectra in Raman transitions in molecules. While a constraint restricting thesystem to stay in an allowed subspace is also capable of identifyingnon-resonant excitation pathways, it does not avoid spurious peaks in the pulsespectrum. Both constraints are compatible with monotonic convergence but implydifferent additional numerical costs.

Steering the optimization pathway in the control landscape using constraints