6533b834fe1ef96bd129d26b

RESEARCH PRODUCT

Contrôle quantique optimal et robuste dans des systèmes de petite dimension

subject

description

Optimal control theory (OCT) is the basic and comprehensive method to obtain the optimal solutions of quantum systems controlled by external fields. It provides a powerful set of tools and concepts. One of the goals of the thesis is to design the technique of OCT in two- and three-state quantum systems taking into account losses and robustness, which is of primary importance for the implementation of control techniques in a broad class of platforms.Based on inverse-engineering techniques and the Pontryagin maximum principle (PMP), we establish and test the different optimal strategies showing how to control the transfer in three-level quantum systems considering energy- and time-minimum optimal solutions taking into account losses. These results, in particular, show that the usual adiabatic passage in such systems, known as stimulated Raman adiabatic passage (STIRAP), which leads to imperfect transfer, can be made exact thus achieving stimulated Raman exact passage (STIREP) while reducing the energy and the duration costs respectively of the controls.We next combine robustness with optimization. Instead of using a direct optimization procedure from OCT, we develop a technique of geometric optimization that allows the derivation of optimal and robust solutions from an inverse optimization. The method named robust inverse optimization (RIO) allows one to obtain numerical trajectories that can be made as accurate as required. The method is versatile and can be applied to various types of errors and of quantum control problems.