The first part of this presentation is dedicated to the study of a 3-level optimal quantum control problem. Using V. F. Borisov and M. I. Zelikin's results, we prove the existence of a chattering phenomenon and provide numerical tools to study the optimal synthesis. To the best of the author knowledge, this is the first example of such a phenomenon in a quantum setting.
The second part of this talk tackles the compatibility between the Rotating Wave Approximation (RWA) and Adiabatic Approximation (AA). Both approximations are widely used 'in cascade' in many experiments and papers to provide robust controls on a quantum system. The purpose of this work is to study how the cascade of the two approximations can be rigorously justified.
These are joint works with N. Augier, U. Boscain, M. Sigalotti and D. Sugny.