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Monotonically convergent optimal control theory of quantum systems under a nonlinear interaction with the control field

Lapert, Marc; Tehini, R.; Turinici, Gabriel; Sugny, Dominique (2008), Monotonically convergent optimal control theory of quantum systems under a nonlinear interaction with the control field, Physical Review. A, Atomic, Molecular and Optical Physics, 78, 2, p. 023408. http://dx.doi.org/10.1103/PhysRevA.78.023408

Type
Article accepté pour publication ou publié
Date
2008-02
Journal name
Physical Review. A, Atomic, Molecular and Optical Physics
Volume
78
Number
2
Publisher
American Physical Society
Pages
023408
Publication identifier
Metadata
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Author(s)
Lapert, Marc
Laboratoire Interdisciplinaire Carnot de Bourgogne [LICB]
Tehini, R.
Laboratoire Interdisciplinaire Carnot de Bourgogne [LICB]
Turinici, Gabriel cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Sugny, Dominique
Laboratoire Interdisciplinaire Carnot de Bourgogne [LICB]
Abstract (EN)
We consider the optimal control of quantum systems interacting nonlinearly with an electromagnetic field. We propose monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a nonstandard choice of the cost, which is not quadratic in the field. These algorithms can be constructed for pure- and mixed-state quantum systems. The efficiency of the method is shown numerically for molecular orientation with a nonlinearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well approximated by pulses that could be implemented experimentally.
Subjects / Keywords
Schrodinger equation; quantum theory; quantum optics; Fourier transforms; convergence of numerical methods