2002/04/18 by Ugo Boscain, Boscain, Ugo, Thomas Chambrion +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #49j15 #81p68 #Analysis of PDEs (math.AP) #FOS: Mathematics #Laser-Matter Interactions and Applications #Optimization and Control (math.OC) #Protein Interaction Studies and Fluorescence Analysis #Quantum optics and atomic interactions #math.AP #math.OC #msc:49j15 #msc:81p68
paper · pdf · doi:10.48550/arxiv.math/0204233
19 pages, 1 figure
arxiv created 2002/04/18 · openalex publication_date 2002/04/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply techniques of subriemannian geometry on Lie groups to laser-induced population transfer in a three-level quantum system. The aim is to induce transitions by two laser pulses, of arbitrary shape and frequency, minimizing the pulse energy. We prove that the Hamiltonian system given by the Pontryagin Maximum Principle is completely integrable, since this problem can be stated as a ``\k⊕\p problem'' on a simple Lie group. Optimal trajectories and controls are exhausted. The main result is that optimal controls correspond to lasers that are ``in resonance''.