Title: Time Optimal Control of Nonlinear Bloch Equations
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-19-00012; Volume 2 / Issue 2 / Year 2020, Pages 49-57
Document Type: Research Paper
Author(s): Irigo Edouard Zibo a , Rachida El Assoudi-Baikari b , Nicolas Forcadel c
aINSA Rouen Normandie, LMI. Avenue de l’université . 76801 Saint Étienne du Rouvray, France
bINSA Rouen Normandie, LMI. Avenue de l’université . 76801 Saint Étienne du Rouvray, France
cINSA Rouen Normandie, LMI. Avenue de l’université . 76801 Saint Étienne du Rouvray, France
Received: 12 December 2019, Accepted: 6 May 2020, Available online: 23 September 2020.
Corresponding Author: Irigo Edouard Zibo (Email address: edouard.zibo@insa-rouen.fr)
Full Text: PDF
Abstract
We deal with time optimal control of nonlinear Bloch equations describing the influence of Coulomb parameters on particle dynamics. The dynamic is analyzed using tools of geometric optimal control theory. We present different time optimal syntheses by varying the parameters of a two energy levels quantum dots system. We show the nontrivial role of Coulomb parameters on the time minimal trajectories.
Keywords: Geometric optimal control, Optimal control synthesis, Quantum dots
References:- B. Bidégaray-Fesquet and K. Keita, A nonlinear Bloch model for Coulomb interaction in quantum dots, Journal of Mathematical Physics, 55 (2), 021501, 2014.
- U. Boscain and P. Mason, Time minimal trajectories for a spin ½ particle in a magnetic field, Journal of Mathematical Physics, 47(6), 602101, 2006.
- U. Boscain and B. Piccoli, Optimal Synthesis for Control Systems on 2-D Manifolds, Springer-Verlag, Berlin Heidelberg, Vol. 43, 2004.
- A. Bressan and B. Piccoli, A generic classification of time-optimal planar stabilizing feedbacks, SIAM J. Control Optim, 36 (1), 12-32, 1998.
- E. Brüning, H. Mäkelä and A. Messina, Parameterizations of density matrices, Journal of Modern, Journal of Modern Optics, 59 (1), 1-20, 2011.
- F. Grillot, Contribution à l’étude de la dynamique des diodes lasers à nanostructures quantiques, Université Paris-VII Denis Diderot.
- M. Lapert, E. Assemat, Y. Zhang, S.J. Glaser and D. Sugny, Time-optimal control of spin ½ particles with dissipative and generalized radiation-damping effects, Physical Review A, 87 (4), 043417, 2013.
- B. Piccol, Regular time-optimal syntheses for smooth planar systems, Rendiconti del Seminario Matematico della Universita, Vol. 95, 59-79, 1996.
- D. Sugny, C. Kontz and H.R. Jauslin, Time-optimal control of a two-level dissipative quantum system, Phys. Rev. A, 76 (2), 023419, 2007.
- H.J. Sussmann, Regular synthesis for time-optimal control of single-input real analytic systems in the plane, SIAM J. Control Optim, 25 (5), 1145-1162, 1987.
- C. Tonin, Manipulation cohérente de l’émission résonnante d’une boîte quantique unique, Université Pierre et Marie Curie-Paris VI, 2012.