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

Abstract 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 fundament...

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Autores principales:	L. Van Damme, D. Leiner, P. Mardešić, S. J. Glaser, D. Sugny
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/3575380794d14893a266205b0864248d
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spelling	oai:doaj.org-article:3575380794d14893a266205b0864248d2021-12-02T16:05:59ZLinking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond10.1038/s41598-017-04174-x2045-2322https://doaj.org/article/3575380794d14893a266205b0864248d2017-06-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-04174-xhttps://doaj.org/toc/2045-2322Abstract 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.L. Van DammeD. LeinerP. MardešićS. J. GlaserD. SugnyNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-8 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q L. Van Damme D. Leiner P. Mardešić S. J. Glaser D. Sugny Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond
description	Abstract 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.
format	article
author	L. Van Damme D. Leiner P. Mardešić S. J. Glaser D. Sugny
author_facet	L. Van Damme D. Leiner P. Mardešić S. J. Glaser D. Sugny
author_sort	L. Van Damme
title	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_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_sort	linking the rotation of a rigid body to the schrödinger equation: the quantum tennis racket effect and beyond
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/3575380794d14893a266205b0864248d
work_keys_str_mv	AT lvandamme linkingtherotationofarigidbodytotheschrodingerequationthequantumtennisracketeffectandbeyond AT dleiner linkingtherotationofarigidbodytotheschrodingerequationthequantumtennisracketeffectandbeyond AT pmardesic linkingtherotationofarigidbodytotheschrodingerequationthequantumtennisracketeffectandbeyond AT sjglaser linkingtherotationofarigidbodytotheschrodingerequationthequantumtennisracketeffectandbeyond AT dsugny linkingtherotationofarigidbodytotheschrodingerequationthequantumtennisracketeffectandbeyond
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Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond

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