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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 321, Pages 237–251
DOI: https://doi.org/10.4213/tm4321
(Mi tm4321)
 

This article is cited in 1 scientific paper (total in 1 paper)

Some Controllable and Uncontrollable Degenerate Four-Level Quantum Systems

Anastasia A. Myachkova, Alexander N. Pechen

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (263 kB) Citations (1)
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Abstract: We analyze the controllability of three quantum systems that belong to a specific class of four-level quantum systems with twice degenerate highest excited energy level and with forbidden transition between the two remaining non-degenerate levels. For this purpose we perform numerical computation, construct the dynamical Lie algebras generated by all commutators of the free and interaction Hamiltonians, and show that two quantum systems are irreducible and controllable while the third system is reducible and hence uncontrollable. The reducibility and uncontrollability are proved by constructing a conserved Hermitian operator (physical quantity). The controllability is proved by constructing the dynamical Lie algebra and showing that it has maximal rank. These findings indicate that depending on the values of certain particular matrix entries of the interaction Hamiltonian, quantum systems in the class under consideration can be either uncontrollable or controllable.
Funding agency Grant number
Russian Science Foundation 22-11-00330
This work was supported by the Russian Science Foundation under grant no. 22-11-00330, https://rscf.ru/en/project/22-11-00330/.
Received: July 13, 2022
Revised: October 6, 2022
Accepted: January 9, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 321, Pages 222–235
DOI: https://doi.org/10.1134/S0081543823020165
Bibliographic databases:
Document Type: Article
UDC: 530.145+517.97
Language: Russian
Citation: Anastasia A. Myachkova, Alexander N. Pechen, “Some Controllable and Uncontrollable Degenerate Four-Level Quantum Systems”, Optimal Control and Dynamical Systems, Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze, Trudy Mat. Inst. Steklova, 321, Steklov Math. Inst., Moscow, 2023, 237–251; Proc. Steklov Inst. Math., 321 (2023), 222–235
Citation in format AMSBIB
\Bibitem{MyaPec23}
\by Anastasia~A.~Myachkova, Alexander~N.~Pechen
\paper Some Controllable and Uncontrollable Degenerate Four-Level Quantum Systems
\inbook Optimal Control and Dynamical Systems
\bookinfo Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 321
\pages 237--251
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4321}
\crossref{https://doi.org/10.4213/tm4321}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 321
\pages 222--235
\crossref{https://doi.org/10.1134/S0081543823020165}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85161441194}
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  • https://doi.org/10.4213/tm4321
  • https://www.mathnet.ru/eng/tm/v321/p237
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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