Controlling molecular processes by shaped laser pulses is a long-standing goal in Molecular Physics and Chemistry. Here, we suggest a direct optimal control approach based on a simultaneous simulation and optimization paradigm, meaning that the equations of motion are discretized in time and converted into a set of holonomic constraints for a nonlinear optimization problem given by the control functional. This approach uses automatic differentiation, offering as advantages final time and model parameter optimization, as well as a wide range of terms in the performance functional and constraints that could be easily implemented in a plug-and-play fashion.
First, the method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential. The wavepacket was parameterized in terms of a single Gaussian function and field optimization was performed for a wide range of particle masses and lengths of the control interval. Using the optimized field in a full quantum propagation still produced reasonable control yields for most of the considered cases. Analysis of the deviations leads to conditions that must be fulfilled to make the semiclassical single Gaussian approximation meaningful for field optimization.
Additionally, we have studied the case of exact wavepacket propagation using the example of a generic Fermi-resonance model. In particular, we addressed the question of how the population of the involved overtone state can be avoided such as to reduce the effect of intramolecular vibrational energy redistribution. A methodological advantage is that our approach offers great flexibility when choosing the running cost since there is no need to compute functional derivatives and coupling terms as in the case of indirect optimal control. We exploit this fact to include state populations in the running cost, which allows for their optimization.
Finally, the approach was applied to a model system describing H-atom transfer in a lossy Fabry–Pérot cavity under vibrational strong coupling conditions. Specifically, final time and cavity coupling strength optimization are demonstrated, allowing us to minimize cavity-induced decay and obtain better control strategies.