# Resonance of minimizers for n-level quantum systems with an arbitrary cost

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 10, Issue: 4, page 593-614
- ISSN: 1292-8119

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topBoscain, Ugo, and Charlot, Grégoire. "Resonance of minimizers for n-level quantum systems with an arbitrary cost." ESAIM: Control, Optimisation and Calculus of Variations 10.4 (2010): 593-614. <http://eudml.org/doc/90745>.

@article{Boscain2010,

abstract = {
We consider an optimal control problem describing a
laser-induced
population transfer on a n-level quantum system. For a convex cost depending only on the moduli
of controls (i.e. the lasers intensities),
we prove that there always exists a minimizer in
resonance. This permits to justify
some strategies used in experimental physics. It is also quite
important
because it permits to reduce remarkably
the complexity of the problem (and extend some of our previous
results
for n=2 and n=3): instead of looking for minimizers on the
sphere $S^\{2n-1\}\subset\mathbb\{C\}^n$ one is reduced to look just for
minimizers on the sphere $S^\{n-1\}\subset \mathbb\{R\}^n$. Moreover, for the reduced problem,
we investigate on the question of existence of strict
abnormal
minimizer.
},

author = {Boscain, Ugo, Charlot, Grégoire},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Control of quantum systems; optimal control;
sub-Riemannian geometry;
resonance; pontryagin maximum principle; abnormal extremals;
rotating wave approximation.; atomic levels; molecular levels; control of quantum systems; sub-Riemannian geometry; resonance; Pontryagin maximum principle; rotating wave approximation},

language = {eng},

month = {3},

number = {4},

pages = {593-614},

publisher = {EDP Sciences},

title = {Resonance of minimizers for n-level quantum systems with an arbitrary cost},

url = {http://eudml.org/doc/90745},

volume = {10},

year = {2010},

}

TY - JOUR

AU - Boscain, Ugo

AU - Charlot, Grégoire

TI - Resonance of minimizers for n-level quantum systems with an arbitrary cost

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 10

IS - 4

SP - 593

EP - 614

AB -
We consider an optimal control problem describing a
laser-induced
population transfer on a n-level quantum system. For a convex cost depending only on the moduli
of controls (i.e. the lasers intensities),
we prove that there always exists a minimizer in
resonance. This permits to justify
some strategies used in experimental physics. It is also quite
important
because it permits to reduce remarkably
the complexity of the problem (and extend some of our previous
results
for n=2 and n=3): instead of looking for minimizers on the
sphere $S^{2n-1}\subset\mathbb{C}^n$ one is reduced to look just for
minimizers on the sphere $S^{n-1}\subset \mathbb{R}^n$. Moreover, for the reduced problem,
we investigate on the question of existence of strict
abnormal
minimizer.

LA - eng

KW - Control of quantum systems; optimal control;
sub-Riemannian geometry;
resonance; pontryagin maximum principle; abnormal extremals;
rotating wave approximation.; atomic levels; molecular levels; control of quantum systems; sub-Riemannian geometry; resonance; Pontryagin maximum principle; rotating wave approximation

UR - http://eudml.org/doc/90745

ER -

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