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Chin. Phys. B, 2023, Vol. 32(1): 010601    DOI: 10.1088/1674-1056/ac6337
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Laboratory demonstration of geopotential measurement using transportable optical clocks

Dao-Xin Liu(刘道信)1,2,3, Jian Cao(曹健)1,2,†, Jin-Bo Yuan(袁金波)1,2, Kai-Feng Cui(崔凯枫)1,2, Yi Yuan(袁易)1,2,3, Ping Zhang(张平)1,2,3, Si-Jia Chao(晁思嘉)1,2, Hua-Lin Shu(舒华林)1,2, and Xue-Ren Huang(黄学人)1,2,4,‡
1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China;
2 Key Laboratory of Atomic Frequency Standards, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China;
3 University of the Chinese Academy of Sciences, Beijing 100049, China;
4 Wuhan Institute of Quantum Technology, Wuhan 430206, China
Abstract  We report an experimental demonstration of geopotential difference measurement using a pair of transportable $^{40}$Ca$^{+}$ optical clocks (TOC-729-1 and TOC-729-3) in the laboratory, each of them has an uncertainty of $1.3 \times 10^{-17}$ and an instability of $4.8 \times 10^{-15}/\sqrt{ \tau } $. Referenced to a stationary clock of TOC-729-1, the geopotential difference measurements are realized by moving TOC-729-3 to three different locations and the relevant altitude differences are measured with uncertainties at the level of 20 cm. After correcting the systematic shifts (including gravitational red shift), the two-clock frequency difference is measured to be $-0.7(2.2) \times 10^{-17}$, considering both the statistic $(1.0 \times 10^{-17})$ and the systematic $(1.9 \times 10^{-17})$ uncertainties. The frequency difference between these two clocks is within their respective uncertainties, verifying the reliability of transportable $^{40}$Ca$^{+}$ optical clocks at the low level of 10$^{-17}$.
Keywords:  geopotential difference measurement      transportable optical clock      repeatability evaluation of clocks  
Received:  26 January 2022      Revised:  29 March 2022      Accepted manuscript online:  01 April 2022
PACS:  06.30.Ft (Time and frequency)  
  37.10.Ty (Ion trapping)  
  37.10.Rs (Ion cooling)  
  04.20.-q (Classical general relativity)  
Fund: Project supported by the Basic Frontier Science Research Program of Chinese Academy of Sciences (Grant No. ZDBS-LY-DQC028), the National Key Research and Development Program of China (Grant No. 2017YFA0304404), and the National Natural Science Foundation of China (Grant No. 11674357).
Corresponding Authors:  Jian Cao, Xue-Ren Huang     E-mail:;

Cite this article: 

Dao-Xin Liu(刘道信), Jian Cao(曹健), Jin-Bo Yuan(袁金波), Kai-Feng Cui(崔凯枫), Yi Yuan(袁易),Ping Zhang(张平), Si-Jia Chao(晁思嘉), Hua-Lin Shu(舒华林), and Xue-Ren Huang(黄学人) Laboratory demonstration of geopotential measurement using transportable optical clocks 2023 Chin. Phys. B 32 010601

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