Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields

Abstract We explore a class of quantum control operations based on a wide family of harmonic magnetic fields that vary softly in time. Depending on the magnetic field amplitudes taking part, these control operations can produce either squeezing or loop (orbit) effects, and even parametric resonances...

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Autor principal:	Jesús Fuentes
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2020
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/dd431d13f0414de4aa3f1e5f30f7d5e2
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spelling	oai:doaj.org-article:dd431d13f0414de4aa3f1e5f30f7d5e22021-12-02T13:58:12ZQuantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields10.1038/s41598-020-79309-82045-2322https://doaj.org/article/dd431d13f0414de4aa3f1e5f30f7d5e22020-12-01T00:00:00Zhttps://doi.org/10.1038/s41598-020-79309-8https://doaj.org/toc/2045-2322Abstract We explore a class of quantum control operations based on a wide family of harmonic magnetic fields that vary softly in time. Depending on the magnetic field amplitudes taking part, these control operations can produce either squeezing or loop (orbit) effects, and even parametric resonances, on the canonical variables. For these purposes we focus our attention on the evolution of observables whose dynamical picture is ascribed to a quadratic Hamiltonian that depends explicitly on time. In the first part of this work we survey such operations in terms of biharmonic magnetic fields. The dynamical analysis is simplified using a stability diagram in the amplitude space, where the points of each region will characterise a specific control operation. We discuss how the evolution loop effects are formed by fuzzy (non-commutative) trajectories that can be closed or open, in the latter case, even hiding some features that can be used to manipulate the operational time. In the second part, we generalise the case of biharmonic fields and translate the discussion to the case of polyharmonic fields. Using elementary properties of the Toeplitz matrices, we can derive exact solutions of the problem in a symmetric evolution interval, leading to the temporal profile of those magnetic fields suitable to achieve specific control operations. Some of the resulting fuzzy orbits can be destroyed by the influence of external forces, while others simply remain stable.Jesús FuentesNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 10, Iss 1, Pp 1-14 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Jesús Fuentes Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields
description	Abstract We explore a class of quantum control operations based on a wide family of harmonic magnetic fields that vary softly in time. Depending on the magnetic field amplitudes taking part, these control operations can produce either squeezing or loop (orbit) effects, and even parametric resonances, on the canonical variables. For these purposes we focus our attention on the evolution of observables whose dynamical picture is ascribed to a quadratic Hamiltonian that depends explicitly on time. In the first part of this work we survey such operations in terms of biharmonic magnetic fields. The dynamical analysis is simplified using a stability diagram in the amplitude space, where the points of each region will characterise a specific control operation. We discuss how the evolution loop effects are formed by fuzzy (non-commutative) trajectories that can be closed or open, in the latter case, even hiding some features that can be used to manipulate the operational time. In the second part, we generalise the case of biharmonic fields and translate the discussion to the case of polyharmonic fields. Using elementary properties of the Toeplitz matrices, we can derive exact solutions of the problem in a symmetric evolution interval, leading to the temporal profile of those magnetic fields suitable to achieve specific control operations. Some of the resulting fuzzy orbits can be destroyed by the influence of external forces, while others simply remain stable.
format	article
author	Jesús Fuentes
author_facet	Jesús Fuentes
author_sort	Jesús Fuentes
title	Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields
title_short	Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields
title_full	Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields
title_fullStr	Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields
title_full_unstemmed	Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields
title_sort	quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields
publisher	Nature Portfolio
publishDate	2020
url	https://doaj.org/article/dd431d13f0414de4aa3f1e5f30f7d5e2
work_keys_str_mv	AT jesusfuentes quantumcontroloperationswithfuzzyevolutiontrajectoriesbasedonpolyharmonicmagneticfields
_version_	1718392231410270208

Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields

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