Frequency domain quantum optimal control under multiple constraints

Optimal control of quantum systems with complex constrained external fields is one of the longstanding theoretical and numerical challenges at the frontier of quantum control research. Here, we present a theoretical method that can be utilized to optimize the control fields subject to multiple constraints while guaranteeing monotonic convergence towards desired physical objectives. This optimization method is formulated in the frequency domain in line with the current ultrafast pulse shaping technique, providing the possibility for performing quantum optimal control simulations and experiments in a unified fashion. For illustrations, this method is successfully employed to perform multiple constraint spectral-phase-only optimization for maximizing resonant multiphoton transitions with desired pulses.