Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(7): 070305    DOI: 10.1088/1674-1056/abf918
GENERAL Prev   Next  

Suppression of servo error uncertainty to 10-18 level using double integrator algorithm in ion optical clock

Jin-Bo Yuan(袁金波)1,2,3, Jian Cao(曹健)1,2,†, Kai-Feng Cui(崔凯枫)1,2, Dao-Xin Liu(刘道信)1,2,3, Yi Yuan(袁易)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,‡
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 Chinese Academy of Sciences, Beijing 100049, China
Abstract  A universal locking model for single ion optical clocks was built based on a simple integrator and a double integrator. Different integrator algorithm parameters have been analyzed in both numerical simulations and experiments. The frequency variation measured by the comparison of two optical clocks coincides well with the simulation results for different second integrator parameters. According to the experimental results, the sensitivity of the servo error influenced by laser frequency drift with the addition of a double integrator was suppressed by a factor of 107. In a week-long comparison of optical clocks, the relative uncertainty of the servo error is determined to be 1.9×10-18, which is meaningful for the systematic uncertainty of the transportable single 40Ca+ ion optical clock entering the 10-18 level.
Keywords:  optical clocks      frequency uncertainty      servo error      servo algorithm  
Received:  10 March 2021      Revised:  31 March 2021      Accepted manuscript online:  19 April 2021
PACS:  03.67.Ac (Quantum algorithms, protocols, and simulations)  
  03.67.Pp (Quantum error correction and other methods for protection against decoherence)  
  06.30.Ft (Time and frequency)  
Fund: Project supported by 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: 

Jin-Bo Yuan(袁金波), Jian Cao(曹健), Kai-Feng Cui(崔凯枫), Dao-Xin Liu(刘道信), Yi Yuan(袁易), Si-Jia Chao(晁思嘉), Hua-Lin Shu(舒华林), and Xue-Ren Huang(黄学人) Suppression of servo error uncertainty to 10-18 level using double integrator algorithm in ion optical clock 2021 Chin. Phys. B 30 070305

[1] Riehle F, Gill P, Arias F and Robertsson L 2018 Metrologia 55 188
[2] Oelker E, Hutson R B, Kennedy C J, Sonderhouse L, Bothwell T, Goban A, Kedar D, Sanner C, Robinson J M, Marti G E, et al. 2017 Nat. Photon. 13 714
[3] Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B and Leibrandt D R 2019 Phys. Rev. Lett. 123 033201
[4] Huntemann N, Sanner C, Lipphardt B, Tamm Chr and Peik E 2016 Phys. Rev. Lett. 116 063001
[5] McGrew W F, Zhang X, Fasano R J, Schäffer S A, Beloy K, Nicolodi D, Brown R C, Hinkley N, Milani G, Schioppo M, et al. 2018 Nature 564 87
[6] Lin Y G, Wang Q, Li Y, Meng F, Lin B K, Zang E J, Sun Z, Fang F, Li T C and Fang Z J 2015 Chin. Phys. Lett. 32 090601
[7] Kong D H, Wang Z H, Guo F, Zhang Q, Lu X T, Wang Y B and Chang H 2020 Chin. Phys. B 29 070602
[8] Sun Y X. Yao Y, Hao Y Q, Yu H F, Jiang Y Y and Ma L S 2020 Chin. Phys. Lett. 18 070201
[9] Mehlstäubler T E, Grosche G, Lisdat C, Schmidt P O and Denker H 2018 Rep. Prog. Phys. 81 064401
[10] Derevianko A and Pospelov M 2018 Nat. Phys. 10 933
[11] Arvanitaki A, Huang J and Van T K 2015 Phys. Rev. D 91 015015
[12] Safronova M S, Budker D, DeMille D, Kimball D F J, Derevianko A and Clark C W 2018 Rev. Mod. Phys. 90 025008
[13] Bernard J E, Marmet L and Madej A A 1998 Opt. Commun. 150 170
[14] Berkeland D J, Miller J D, Bergquist J C, Itano W M and Wineland D J 1998 Phys. Rev. Lett. 80 2089
[15] Leroux I D, Scharnhorst N, Hannig S, Kramer J, Pelzer L, Stepanova M and Schmidt P O 2017 Metrologia 54 307
[16] Zhang B L, Huang y, Zhang H Q, Hao Y M, Zeng M Y, Guan H and Gao K L 2020 Chin. Phys. B 29 074209
[17] Sauter T h, Neuhauser W, Blatt R and Toschek P E 1986 Phys. Rev. Lett. 57 1696
[18] Bergquist J C, Hulet R G, Itano W M and Wineland D J 1986 Phys. Rev. Lett. 57 1699
[19] Barwood G, Gao K, Gill P, Huang G L and Klein H A 2001 IEEE Trans. Instrum. Meas. 50 543
[20] Bernard J E, Madej A A, Marmet L, Whitford B G, Siemsen K J and Cundy S 1999 Phys. Rev. Lett. 82 3228
[21] Peik E, Schneider T and Tamm C 2005 J. Phys. B: At., Mol. Opt. Phys. 39 145
[22] Cao J, Zhang P, Shang J J, Cui K F, Yuan J B, Chao S J, Wang S M, Shu H L and Huang X R 2017 Appl. Phys. B: Lasers Opt. 123 1
[23] Wang S M, Cao J, Yuan J B, Liu D X, Shu H L and Huang X R 2020 Opt. Express 28 11852
[24] Margolis H S, Barwood G P, Huang G, Klein H A, Lea S N, Szymaniec K and Gill P 2004 Science 306 1355
[25] Black E D 2001 Am. J. Phys. 69 79
[26] Shang J J, Cao J, Cui K F, Wang S M, Zhang P, Yuan J B, Chao S J, Shu H L and Huang X R 2017 Opt. Commun. 382 410
[1] Study of optical clocks based on ultracold 171Yb atoms
Di Ai(艾迪), Hao Qiao(谯皓), Shuang Zhang(张爽), Li-Meng Luo(骆莉梦), Chang-Yue Sun(孙常越), Sheng Zhang(张胜), Cheng-Quan Peng(彭成权), Qi-Chao Qi(齐启超), Tao-Yun Jin(金涛韫), Min Zhou(周敏), Xin-Ye Xu(徐信业). Chin. Phys. B, 2020, 29(9): 090601.
[2] Progress on the 40Ca+ ion optical clock
Baolin Zhang(张宝林), Yao Huang(黄垚), Huaqing Zhang(张华青), Yanmei Hao(郝艳梅), Mengyan Zeng(曾孟彦), Hua Guan(管桦), Kelin Gao(高克林). Chin. Phys. B, 2020, 29(7): 074209.
[3] Experiments on trapping ytterbium atoms in optical lattices
Zhou Min, Chen Ning, Zhang Xiao-Hang, Huang Liang-Yu, Yao Mao-Fei, Tian Jie, Gao Qi, Jiang Hai-Ling, Tang Hai-Yao, Xu Xin-Ye. Chin. Phys. B, 2013, 22(10): 103701.
No Suggested Reading articles found!