Efficient control of molecular rotations — time and controllability

• Applicant: Professorin Dr. Christiane Koch
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 505622963

In this project, we seek to elucidate the role of time in quantum control, using the important benchmark of molecular rotations as testbed. Quantum control refers to the ability to manipulate dynamical processes at the atomic or molecular scale using external electromagnetic fields. Typical control tasks require a minimum time to be carried out, and estimating this time is important in view of both practical applications and fundamental understanding. To date, these estimates can only be obtained empirically, save for a few exceptional cases. We will leverage controllability analysis to tackle the role of time in quantum control, combining physical intuition from the control of molecular rotations with recent advances of mathematical methods. Our goals are three-fold: (i) We seek to identify the conditions for controllability in case of a perturbative treatment of the interaction with the external fields; time will emerge naturally via the perturbation order. (ii) We aim to compute the controllability diameter, and thus the minimum time for control, by suitable decompositions of the system evolution in Galerkin approximations. (iii) We shall determine the conditions under which the chattering phenomenon, referring to the pathological case of an infinite number of times an external field is switched in a finite time interval, occurs in quantum control. Our proposal is built on a proven track record of joint and interdisciplinary work and the long-standing expertise of the French and German partners in quantum control, combining pioneering development of mathematical methods with successful demonstrations of control at the forefront of AMO physics. If successful, our project will provide a systematic approach to determine the minimum time for quantum control and improve our fundamental understanding of whether and how practical quantum control is affected by a mathematical pathology. For our testbed of molecular rotations, it will open new routes for control-relevant to applications from ultrafast molecular physics to tests of fundamental physics or molecule-based quantum information science.

• DFG Programme: Research Grants
• International Connection: France
• Partner Organisation: Agence Nationale de la Recherche / The French National Research Agency
• Cooperation Partners: Professor Dr. Ugo Boscain; Professor Dr. Gabriele Ciaramella; Professor Dr. Jean-Michel Coron; Professor Dr. Olivier Faucher