Reference Trajectory Tracking for Locally Designed Coherent Quantum Controls

Local time control methods are used in the simulation of quantum control phenomena because they conveniently ensure an increase of a predefined performance index and also avoid singularities associated with tracking procedures. However, the drawback of the existing implementations is that they only take into account one-photon, direct transitions and may stop at nonoptimal values of the index. We propose in this paper a modification of the currently used algorithms that addresses this issue and explain how the convergence is improved. Furthermore, when iterations are required, we show that this approach can be inserted into a monotonically convergent algorithm.