Geodesic
Hamiltonian identification for quantum systems : well-posedness and numerical approaches
Bris, Claude Le  ; Mirrahimi, Mazyar  ; Rabitz, Herschel1 ; Turinici, Gabriel2 
1 Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009;
2 INRIA Rocquencourt, Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 378-395

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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.

DOI : 10.1051/cocv:2007013
Classification : 93B30, 65K10
Keywords: inverse problem, quantum systems, hamiltonian identification, optimal identification

Bris, Claude Le  ; Mirrahimi, Mazyar  ; Rabitz, Herschel 1 ; Turinici, Gabriel 2

1 Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009;
2 INRIA Rocquencourt, Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France. 
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     title = {Hamiltonian identification for quantum systems : well-posedness and numerical approaches},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {378--395},
     publisher = {EDP-Sciences},
     volume = {13},
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     year = {2007},
     doi = {10.1051/cocv:2007013},
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     zbl = {1123.93040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007013/}
}
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Bris, Claude Le; Mirrahimi, Mazyar; Rabitz, Herschel; Turinici, Gabriel. Hamiltonian identification for quantum systems : well-posedness and numerical approaches. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 378-395. doi: 10.1051/cocv:2007013

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