Evaluation of systematic uncertainty for transportable <sup>87</sup>Sr optical lattice clock

Kong De-Huan; Guo Feng; Li Ting; Lu Xiao-Tong; Wang Ye-Bing; Chang Hong

doi:10.7498/aps.70.20201204

Abstract

Transportable optical clocks have broad applications in scientific research and engineering. Accurate evaluation of systematic uncertainty for the transportable ⁸⁷Sr optical lattice clock is a prerequisite for the practical realization of the optical clock. Four main frequency shifts of the ⁸⁷Sr optical lattice clock are measured, i.e. blackbody-radiation (BBR) shift, collision shift, lattice alternating current (AC) Stark shift, and second-order Zeeman shift. Firstly, by measuring the temperature distribution on the surface of the magneto-optical trap cavity and analyzing the influence of different heat sources on atomic cloud, the BBR shift correction is measured to be 50.4 × 10^–16 Hz with an uncertainty of 5.1 × 10^–17. Secondly, the time-interleaved self-comparison method is used under high and low atom density condition to evaluate the collision shift of the system. The correction of collision shift is 4.7 × 10^–16 with an uncertainty of 5.6 × 10^–17. Thirdly, the lattice AC Stark shift is evaluated by the time-interleaved self-comparison method. By measuring the dependence of the lattice AC Stark shift on the wavelength of the lattice light, the magic wavelength is measured to be 368554393(78) MHz. As a result, the lattice AC Stark shift correction is 3.0 × 10^–16 with an uncertainty of 2.2 × 10^–16. Finally, using the time-interleaved self-comparison technology, the second-order Zeeman frequency shift is evaluated by measuring the fluctuation of the difference in center frequency between the ${m_{\text{F}}} = + {9 / 2} \to {m_{\text{F}}} = + {9 / 2}$ polarization spectrum and ${m_{\text{F}}} = - {9 / 2} \to {m_{\text{F}}} = - {9 / 2}$ polarization spectrum. The correction of second-order Zeeman shift is calculated to be 0.7 × 10^–16, and corresponding uncertainty is 0.2 × 10^–17. Experimental results indicate that the frequency shift correction due to the blackbody radiation is the largest, while the uncertainty caused by the lattice AC Stark effect is the largest in the evaluated shifts. The systematic shift is 58.8 × 10^–16, the total uncertainty is 2.3 × 10^–16. In the next work, the magneto-optical trap cavity will be placed in a blackbody-radiation cavity to reduce the blackbody-radiation shift. The uncertainty of the collision shift will be reduced by increasing the beam waist of the lattice and reducing the potential well depth of the lattice, which will reduce the density of atoms. What is more, the light source for the optical lattice after spectral filtering will be measured by an optical frequency comb locked to the hydrogen clock signal to reduce the uncertainty of the lattice AC Stark frequency shift. The systematic uncertainty is expected to be on the order of 10^–17. The evaluation of the systematic uncertainty for the transportable ⁸⁷Sr optical lattice clock lays the foundation for the practical application.

Keywords:

transportable ⁸⁷Sr optical lattice clock /
systematic shift /
uncertainty /
time-interleaved self-comparison method

Authors and contacts

1.
CAS Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Xi’an 710600, China
2.
School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: Wang Ye-Bing, wangyebing@ntsc.ac.cn ; Chang Hong, changhong@ntsc.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61775220, 11803042), the Key Research Project of Frontier Science of the Chinese Academy of Sciences (Grant No. QYZBD-SSW-JSC004), and the Youth Innovation Promotion Association CAS (Grant No. 2019400)

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References

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[19]	Chou C W, Hume D B, Rosenband T, Wineland D J 2010 Science 329 1630 Google Scholar
[20]	Lopez O, Haboucha A, Chanteau B, Chardonnet Ch, Amy-Klein A, Santarelli G 2012 Opt. Express 20 23518 Google Scholar
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[34]	Bureau International des Poids et Mesures (BIPM) Consultative Committee for Time and Frequency (CCTF) Report of the 21st Meeting (June 8-9, 2017) to the International Committee for Weights and Measures https://www.bipm.org/utils/common/pdf/CC/CCTF/CCTF21.pdf
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[36]	卢晓同, 李婷, 孔德欢, 王叶兵, 常宏 2019 物理学报 68 233401 Google Scholar Lu X T, Li T, Kong D H, Wang Y B, Chang H 2019 Acta Phys. Sin. 68 233401 Google Scholar
[37]	Katori H, Takamoto M, Pal’chikov V G, Ovsiannikov V D 2003 Phys. Rev. Lett. 91 173005 Google Scholar
[38]	林弋戈, 方占军 2018 物理学报 67 160604 Google Scholar Lin Y G, Fang Z J 2018 Acta Phys. Sin. 67 160604 Google Scholar
[39]	Westergaard P G, Lodewyck J, Lorini L, Lecallier A, Burt E A, Zawada M, Millo J, Lemonde P 2011 Phys. Rev. Lett. 106 210801 Google Scholar
[40]	Bloom B J, Nicholson T L, William J R, Campbell S L, Bishof M, Zhang X, Zhang W, Bromley S L 2014 Nature 506 71 Google Scholar
[41]	Bailard X, Fouché M, Targat R L, Westergaard P G, Lecallier A, Coq Y L, Rovera G D, Bize S, Lemonde P 2007 Opt. Lett. 32 1812 Google Scholar
[42]	Bothwell T, Kedar D, Oelker E, Robinson J M, Bromley S L, L Tew W L, Ye J, Kennedy C J 2019 Metrologia 56 065004 Google Scholar

Cited By

图 1 可搬运⁸⁷Sr光晶格钟的物理系统(PMT, 光电倍增管; EMCCD, 电子倍增电荷耦合相机)

Figure 1. Physical system of the transportable strontium optical lattice clock (PMT, photo-multiplier tube; EMCCD, electron-multiplying charge coupled device)

DownLoad: Full-Size Img PowerPoint

图 2 磁光阱腔体上测量点的分布示意图

Figure 2. Distribution of the temperature points on the magneto-optical trap cavity.

DownLoad: Full-Size Img PowerPoint

图 3 磁光阱腔体各测温点的温度波动

Figure 3. Temperature fluctuations at the temperature points on the magneto-optical trap cavity

DownLoad: Full-Size Img PowerPoint

图 4 碰撞频移的测试结果

Figure 4. Measurement for the collision shift

DownLoad: Full-Size Img PowerPoint

图 5 单次高低原子密度自比对的阿伦偏差

Figure 5. The Allan deviation obtained by the time-interleaved self-comparison method between high and low atomic density

DownLoad: Full-Size Img PowerPoint

图 6 晶格光频移系数随晶格光频率的变化

Figure 6. Clock sensitivity to lattice wavelength.

DownLoad: Full-Size Img PowerPoint

图 7 钟跃迁极化峰间距的测量结果

Figure 7. Frequency gap between two different spin-polarized peaks.

DownLoad: Full-Size Img PowerPoint

表 1 可搬运⁸⁷Sr光晶格钟的系统不确定度评估

Table 1. Uncertainty budget for the transportable strontium optical lattice clock.

频移项相对频移修正/10^–16 相对不确定度/10^–17

黑体辐射 50.4 5.1
碰撞 4.7 5.6
晶格光交流斯塔克 3.0 22.1
二阶塞曼 0.7 0.2
钟激光交流斯塔克 0 1.0
线牵引 0 1.0
总和 58.8 23.4

DownLoad: CSV

[1]	Ludlow A D, Boyd M M, Ye J, Peik E, Schimidt P O 2015 Rev. Mod. Phys. 87 637 Google Scholar
[2]	Rosenband T, Hume D B, Schmidt P O, Schmidt P O, Chou C W, Brusch A, Lorini L, Oskay W H, Drullinger R E, Fortier T M, Stalnaker J E, Diddams S A, Swann W C, Newbury N R, Itano W M, Wineland D J, Bergquist J C 2008 Science 319 1808 Google Scholar
[3]	Diddams S A 2001 Science 293 825 Google Scholar
[4]	Dube P, Madej A A, Zhou Z C, Bernard J E 2013 Phys. Rev. A 87 023806 Google Scholar
[5]	Nicholson T L, Campbell S L, Hutson R B, Marti G E, Bloom B G, MacNally R L, Zhang W, Barrett M D, Safronova M S, Strouse G F, Tew W L, Ye J 2015 Nat. Commun. 6 6896 Google Scholar
[6]	Campbell S L, Hutson R B, Marti G E, Goban A, Darkwah O N, MacNally R L, Souderhouse L, Robinson J M, Zhang W, Bloom B G, Ye J 2017 Science 358 90 Google Scholar
[7]	Poli N, Schioppo M, Vogt S, Falke S, Sterr U, Lisdat C, Tino G M 2014 Appl. Phys. B 117 1107 Google Scholar
[8]	Lin Y G, Wang Q, Li Y, Meng F, Lin B K, Zang E J, Sun Z, Fang F, Li T C, Fang Z J 2015 Chin. Phys. Lett. 32 090601 Google Scholar
[9]	Ohmae N, Sakama S, Katori H 2019 Electr. Commun. JPN 102 43 Google Scholar
[10]	Liu H, Zhang X, Jiang K L, Wang J Q, Zhou Q, Xiong Z X, He L X, Lü B L 2017 Chin. Phys. Lett. 34 020601 Google Scholar
[11]	周敏, 徐信业 2016 物理 45 431 Google Scholar Zhou M, Xu X Y 2016 Physics 45 431 Google Scholar
[12]	管桦, 黄垚, 李承斌, 高克林 2018 物理学报 67 164202 Google Scholar Guan H, Huang Y, Li C B, Gao K L 2018 Acta Phys. Sin. 67 164202 Google Scholar
[13]	Huang Y, Guan H, Zeng M, Tang L, Gao K 2019 Phys. Rev. A 99 011401 Google Scholar
[14]	Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B, Leibrandt D R 2019 Phys. Rev. Lett. 123 033201 Google Scholar
[15]	Oelker E, Hutson R B, Kennedy C J, Sonderhouse L, Bothwell T, Goban A, Kedar D, Sanner C, Robinson J M, Marti G E, Matei D G, Legero T, Giunta M, Holzwarth R, Riehle F, Sterr U, Ye J 2019 Nat. Photon. 13 714 Google Scholar
[16]	Paul S, Swanson T B, Hanssen J, Taylor J 2017 Metrologia 54 247 Google Scholar
[17]	Derevianko A, Pospelov M 2014 Nat. Phys. 10 933 Google Scholar
[18]	Kolkowitz S, Pikovski I, Langellier N, Lukin M D, Walsworth R L, Ye J 2016 Phys. Rev. D 94 124043 Google Scholar
[19]	Chou C W, Hume D B, Rosenband T, Wineland D J 2010 Science 329 1630 Google Scholar
[20]	Lopez O, Haboucha A, Chanteau B, Chardonnet Ch, Amy-Klein A, Santarelli G 2012 Opt. Express 20 23518 Google Scholar
[21]	Bercy A, Lopez O, Pottie P E, Amy-Klein A 2016 Appl. Phys. B 122 189 Google Scholar
[22]	Mcgrew W F, Zhang X, Fasano R J, Schäffer S A, Beloy K, Nicolodi D, Brown R C, Hinkley N, Milani G, Schioppo M, Yoon T H, Ludlow A D 2018 Nature 564 87 Google Scholar
[23]	Grotti J, Koller S, Vogt S, Häfner S, Sterr U, Lisdat C, Denker H, Voigt C, Timmen L, Rolland A, Fred N B, Margolis H S, Zampaolo M, Thoumany P, Pizzocaro M, Rauf B, Bregolin F, Tampellini A, Barbieri P, Zucco M, Costanzo G A, Clivati C, Levi F, Calonico D 2018 Nat. Phys. 14 437 Google Scholar
[24]	Shang H S, Zhang X G, Zhang S N, Pan D, Chen H J, Chen J B 2017 Opt. Express 25 30459 Google Scholar
[25]	Zhang S, Zhang X, Cui J, Jiang Z J, Shang H S, Zhu C W, Chang P Y, Zhang L, Tu J H, Chen J B 2017 Rev. Sci. Instrum. 88 103106 Google Scholar
[26]	Koller S B, Grotti J, Al-Masoudi A, Dörscher S, Häfner S, Sterr U, Lisdat C 2017 Phys. Rev. Lett. 118 073601 Google Scholar
[27]	Cao J, Zhang P, Shang J, Cui K, Yuan J, Chao S, Wang S, Shu H, Huang X 2017 Appl. Phys. B 123 112 Google Scholar
[28]	Takamoto M, Ushijima I, Ohmae N, Yahagi T, Kokado K, Shinkai H, Katori H 2020 Nat. Photon. 14 411 Google Scholar
[29]	Wang Y B, Yin M J, Ren J, Xu Q F, Lu B Q, Han J X, Guo Y, Chang H 2018 Chin. Phys. B 27 023701 Google Scholar
[30]	Kong D H, Wang Z H, Guo F, Zhang Q, Lu X T, Wang Y B, Chang H 2020 Chin. Phys. B 29 070602 Google Scholar
[31]	Middlemann T, Falkes S, Listat C, Sterr U 2012 Phys. Rev. Lett. 109 263004 Google Scholar
[32]	李婷, 卢晓同, 张强, 孔德欢, 王叶兵, 常宏 2019 物理学报 68 093701 Google Scholar Li T, Lu X T, Zhang Q, Kong D H, Wang Y B, Chang H 2019 Acta Phys. Sin. 68 093701 Google Scholar
[33]	Origlia S, Pramod M S, Schiller S, Singh Y, Bongs K, Schwarz R, Al-Masoudi A, Dörscher S, Häfner S, Sterr U, Lisdat C 2018 Phys. Rev. A 98 053443 Google Scholar
[34]	Bureau International des Poids et Mesures (BIPM) Consultative Committee for Time and Frequency (CCTF) Report of the 21st Meeting (June 8-9, 2017) to the International Committee for Weights and Measures https://www.bipm.org/utils/common/pdf/CC/CCTF/CCTF21.pdf
[35]	Lemke N D, von Stecher J, Sherman J A, Rey A M, Oates C W, Ludlow A D 2011 Phys. Rev. Lett. 107 103902 Google Scholar
[36]	卢晓同, 李婷, 孔德欢, 王叶兵, 常宏 2019 物理学报 68 233401 Google Scholar Lu X T, Li T, Kong D H, Wang Y B, Chang H 2019 Acta Phys. Sin. 68 233401 Google Scholar
[37]	Katori H, Takamoto M, Pal’chikov V G, Ovsiannikov V D 2003 Phys. Rev. Lett. 91 173005 Google Scholar
[38]	林弋戈, 方占军 2018 物理学报 67 160604 Google Scholar Lin Y G, Fang Z J 2018 Acta Phys. Sin. 67 160604 Google Scholar
[39]	Westergaard P G, Lodewyck J, Lorini L, Lecallier A, Burt E A, Zawada M, Millo J, Lemonde P 2011 Phys. Rev. Lett. 106 210801 Google Scholar
[40]	Bloom B J, Nicholson T L, William J R, Campbell S L, Bishof M, Zhang X, Zhang W, Bromley S L 2014 Nature 506 71 Google Scholar
[41]	Bailard X, Fouché M, Targat R L, Westergaard P G, Lecallier A, Coq Y L, Rovera G D, Bize S, Lemonde P 2007 Opt. Lett. 32 1812 Google Scholar
[42]	Bothwell T, Kedar D, Oelker E, Robinson J M, Bromley S L, L Tew W L, Ye J, Kennedy C J 2019 Metrologia 56 065004 Google Scholar

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Evaluation of systematic uncertainty for transportable ⁸⁷Sr optical lattice clock

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Corresponding author: Wang Ye-Bing, wangyebing@ntsc.ac.cn ; Chang Hong, changhong@ntsc.ac.cn

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频移项	相对频移修正/10^–16	相对不确定度/10^–17
黑体辐射	50.4	5.1
碰撞	4.7	5.6
晶格光交流斯塔克	3.0	22.1
二阶塞曼	0.7	0.2
钟激光交流斯塔克	0	1.0
线牵引	0	1.0
总和	58.8	23.4

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Evaluation of systematic uncertainty for transportable 87Sr optical lattice clock

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Corresponding author: Wang Ye-Bing, wangyebing@ntsc.ac.cn ; Chang Hong, changhong@ntsc.ac.cn

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Evaluation of systematic uncertainty for transportable ⁸⁷Sr optical lattice clock