Steering the optimization pathway in the control landscape using constraints

We show how additional constraints, restricting the spectrum of the optimized pulse or confining the system dynamics, can be used to steer optimization in quantum control towards distinct solutions. Our examples are multiphoton excitation in atoms and vibrational population transfer in molecules. We show that a spectral constraint is most effective in enforcing nonresonant two-photon absorption pathways in atoms and avoiding unnecessarily broad spectra in Raman transitions in molecules. While a constraint restricting the system to stay in an allowed subspace is also capable of identifying nonresonant excitation pathways, it does not avoid spurious peaks in the pulse spectrum. Both constraints are compatible with monotonic convergence but imply different additional numerical costs.