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Hamiltonian identification for quantum systems: well-posedness and numerical approaches

Published online by Cambridge University Press:  12 May 2007

Claude Le Bris ,
Mazyar Mirrahimi ,
Herschel Rabitz  and
Gabriel Turinici
Claude Le Bris
Affiliation:
INRIA Rocquencourt, Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France. CERMICS-ENPC, 6 & 8 Av. B. Pascal, 77455 Marne la Vallée Cedex, France; lebris@cermics.enpc.fr
Mazyar Mirrahimi
Affiliation:
INRIA Rocquencourt, Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France. École des Mines de Paris, CAS, 60 Bd Saint-Michel, 75272 Paris Cedex 06, France; mazyar.mirrahimi@ensmp.fr
Herschel Rabitz
Affiliation:
Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009; hrabitz@princeton.edu
Gabriel Turinici
Affiliation:
INRIA Rocquencourt, Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France. CEREMADE, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France; Gabriel.Turinici@dauphine.fr
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Abstract

This paper considers the inversion problem related to the manipulation of quantum systems using laser-matter interactions. The focus is on the identification of the field free Hamiltonian and/or the dipole moment of a quantum system. The evolution of the system is given by the Schrödinger equation. The available data are observations as a function of time corresponding to dynamics generated by electric fields. The well-posedness of the problem is proved, mainly focusing on the uniqueness of the solution. A numerical approach is also introduced with an illustration of its efficiency on a test problem.

Keywords

Inverse problemquantum systemsHamiltonian identificationoptimal identification
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 2 , April 2007 , pp. 378 - 395
Copyright
© EDP Sciences, SMAI, 2007

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