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 problem, quantum systems, hamiltonian identification, optimal identification
Bris, Claude Le ; Mirrahimi, Mazyar ; Rabitz, Herschel 1 ; Turinici, Gabriel 2
@article{COCV_2007__13_2_378_0,
author = {Bris, Claude Le and Mirrahimi, Mazyar and Rabitz, Herschel and Turinici, Gabriel},
title = {Hamiltonian identification for quantum systems : well-posedness and numerical approaches},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {378--395},
year = {2007},
publisher = {EDP Sciences},
volume = {13},
number = {2},
doi = {10.1051/cocv:2007013},
mrnumber = {2306642},
zbl = {1123.93040},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2007013/}
}
TY - JOUR AU - Bris, Claude Le AU - Mirrahimi, Mazyar AU - Rabitz, Herschel AU - Turinici, Gabriel TI - Hamiltonian identification for quantum systems : well-posedness and numerical approaches JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 378 EP - 395 VL - 13 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2007013/ DO - 10.1051/cocv:2007013 LA - en ID - COCV_2007__13_2_378_0 ER -
%0 Journal Article %A Bris, Claude Le %A Mirrahimi, Mazyar %A Rabitz, Herschel %A Turinici, Gabriel %T Hamiltonian identification for quantum systems : well-posedness and numerical approaches %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 378-395 %V 13 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2007013/ %R 10.1051/cocv:2007013 %G en %F COCV_2007__13_2_378_0
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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