dorsal/arxiv
View SchemaResonance of Minimizers for $n$-level Quantum Systems with an Arbitrary Cost
| Authors | Ugo Boscain, Gregoire Charlot |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0308103 |
| URL | https://arxiv.org/abs/quant-ph/0308103 |
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 $S^{2n-1}\subset\C^n$ one is reduced to look just for minimizers on the sphere $S^{n-1}\subset \R^n$. Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer.
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"abstract": "We consider an optimal control problem describing a laser-induced population\ntransfer on a $n$-level quantum system.\n For a convex cost depending only on the moduli of controls (i.e. the lasers\nintensities), we prove that there always exists a minimizer in resonance. This\npermits to justify some strategies used in experimental physics. It is also\nquite important because it permits to reduce remarkably the complexity of the\nproblem (and extend some of our previous results for $n=2$ and $n=3$): instead\nof looking for minimizers on the sphere $S^{2n-1}\\subset\\C^n$ one is reduced to\nlook just for minimizers on the sphere $S^{n-1}\\subset \\R^n$. Moreover, for the\nreduced problem, we investigate on the question of existence of strict abnormal\nminimizer.",
"arxiv_id": "quant-ph/0308103",
"authors": [
"Ugo Boscain",
"Gregoire Charlot"
],
"categories": [
"quant-ph"
],
"title": "Resonance of Minimizers for $n$-level Quantum Systems with an Arbitrary Cost",
"url": "https://arxiv.org/abs/quant-ph/0308103"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "0b622952-d5f2-422f-ae52-721eecd2f4da",
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"variant": "snapshot-2026-03-01",
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