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Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond

The design of efficient and robust pulse sequences is a fundamental requirement in quantum control. Numerical methods can be used for this purpose, but with relatively little insight into the control mechanism. Here, we show that the free rotation of a classical rigid body plays a fundamental role i...

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Autores principales: Damme, L. Van, Leiner, D., Mardešić, P., Glaser, S. J., Sugny, D.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5479806/
https://www.ncbi.nlm.nih.gov/pubmed/28638097
http://dx.doi.org/10.1038/s41598-017-04174-x
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author Damme, L. Van
Leiner, D.
Mardešić, P.
Glaser, S. J.
Sugny, D.
author_facet Damme, L. Van
Leiner, D.
Mardešić, P.
Glaser, S. J.
Sugny, D.
author_sort Damme, L. Van
collection PubMed
description The design of efficient and robust pulse sequences is a fundamental requirement in quantum control. Numerical methods can be used for this purpose, but with relatively little insight into the control mechanism. Here, we show that the free rotation of a classical rigid body plays a fundamental role in the control of two-level quantum systems by means of external electromagnetic pulses. For a state to state transfer, we derive a family of control fields depending upon two free parameters, which allow us to adjust the efficiency, the time and the robustness of the control process. As an illustrative example, we consider the quantum analog of the tennis racket effect, which is a geometric property of any classical rigid body. This effect is demonstrated experimentally for the control of a spin 1/2 particle by using techniques of Nuclear Magnetic Resonance. We also show that the dynamics of a rigid body can be used to implement one-qubit quantum gates. In particular, non-adiabatic geometric quantum phase gates can be realized based on the Montgomery phase of a rigid body. The robustness issue of the gates is discussed.
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spelling pubmed-54798062017-06-23 Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond Damme, L. Van Leiner, D. Mardešić, P. Glaser, S. J. Sugny, D. Sci Rep Article The design of efficient and robust pulse sequences is a fundamental requirement in quantum control. Numerical methods can be used for this purpose, but with relatively little insight into the control mechanism. Here, we show that the free rotation of a classical rigid body plays a fundamental role in the control of two-level quantum systems by means of external electromagnetic pulses. For a state to state transfer, we derive a family of control fields depending upon two free parameters, which allow us to adjust the efficiency, the time and the robustness of the control process. As an illustrative example, we consider the quantum analog of the tennis racket effect, which is a geometric property of any classical rigid body. This effect is demonstrated experimentally for the control of a spin 1/2 particle by using techniques of Nuclear Magnetic Resonance. We also show that the dynamics of a rigid body can be used to implement one-qubit quantum gates. In particular, non-adiabatic geometric quantum phase gates can be realized based on the Montgomery phase of a rigid body. The robustness issue of the gates is discussed. Nature Publishing Group UK 2017-06-21 /pmc/articles/PMC5479806/ /pubmed/28638097 http://dx.doi.org/10.1038/s41598-017-04174-x Text en © The Author(s) 2017 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Damme, L. Van
Leiner, D.
Mardešić, P.
Glaser, S. J.
Sugny, D.
Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond
title Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond
title_full Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond
title_fullStr Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond
title_full_unstemmed Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond
title_short Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond
title_sort linking the rotation of a rigid body to the schrödinger equation: the quantum tennis racket effect and beyond
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5479806/
https://www.ncbi.nlm.nih.gov/pubmed/28638097
http://dx.doi.org/10.1038/s41598-017-04174-x
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