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EDP Sciences, ESAIM: Control, Optimisation and Calculus of Variations, 2(13), p. 378-395, 2007

DOI: 10.1051/cocv:2007013

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

Journal article published in 2007 by Claude Le Bris, Mazyar Mirrahimi, Herschel Rabitz, Gabriel Turinici ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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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.