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为进一步提高真空量值的复现性和准确性, 最新研究采用量子技术实现对真空量值的测量与表征. 该方法利用Fabry-Perot谐振腔实现腔内气体折射率的精密测量, 并反演出气体密度, 进而获得对应的真空量值, 其中气体折射率的测量是影响真空量值准确性的关键. 本文基于第一性原理, 利用从头计算理论计算了在已知压力和温度条件下的氦气折射率, 给出腔内气体压力与折射率关系的表达式, 并利用基于Fabry-Perot激光谐振腔的真空测量装置, 通过双腔谐振激光拍频精确测量了充气前后谐振激光频率的变化, 测出了氦气折射率, 并分析了测量不确定度. 将理论计算值与实验测量值进行了对比分析, 得出了制约准确度提高的主要因素, 并提出了修正方法.
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关键词:
- 真空计量 /
- Fabry-Perot谐振腔 /
- 气体折射率 /
- 氦气渗透率
In the face of the historical change of international measurement system, the classical physics based physical standard corresponding to many measurement parameters develops toward "natural standard", namely quantum standard. In order to further improve the reproducibility and accuracy of vacuum value, the latest research uses quantum technology to realize the measurement and characterization of vacuum value. In this method, Fabry- Perot cavity is used to accurately measure the refractive index of the gas. The density can be calculated by the refractive index and inversed to obtain the corresponding vacuum value. The measurement of the gas refractive index is the key to the accuracy of the vacuum value. The macroscopic permittivity of nonpolar gases is related to the microscopic polarization parameters of atoms through quantum dynamics. In recent years, with the rapid development of ab initio theory and methods on the electromagnetic and thermodynamic properties of monatomic molecules, the calculation accuracy of relevant parameters was constantly improved, which can further reduce the measurement uncertainty of the above methods. In this paper, the theoretical value of helium refractive index is calculated accurately based on the first principle with known pressure and temperature. The relationship between gas pressure and refractive index is obtained, and the relative uncertainty of the theoretical value of refractive index is 6.27 × 10–12. Then, the refractive index of helium in a range of 102–105 Pa is measured by the vacuum measuring device which is based on Fabry-Perot cavity, and the uncertainty of measurement is 9.59 × 10–8. Finally, the discrepancy between the theoretical and measured values of helium refractive index is compared and analyzed. It can be concluded that the the uncertainty of helium refractive index measurement originates from the deformation of the cavity caused by helium permeation. Therefore, solving the problem of helium permeation is the key to establishing a new vacuum standard. In this paper, the change of cavity length caused by helium penetration in the cavity is corrected. The refractive index coefficient is corrected at various pressure points in a vacuum range of 103–105 Pa, and its pressure-dependent expression is obtained The variation of cavity length caused by gas pressure is further quantified. The relationship between the change of cavity caused by gas pressure and that caused by the refractive index is obtained. The correction parameter of cavity length is calculated to be 3.12 × 10–2. In the future experiment of helium refractive index measurement by means of Fabry-Perot cavity, the refractive index correction coefficient at each pressure point given in this paper can be used to correct the refractive index measurement results, thereby eliminating the influence of helium penetration on the refractive index measurement, and obtaining the gas pressure with high accuracy.-
Keywords:
- vacuum metrology /
- Fabry-Perot cavity /
- refractive index of gas /
- helium permeability
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图 1 基于F-P激光谐振腔的真空测量装置结构图 (a)部分为光路图;(b)部分为气路图 (1. 激光器; 2. 分束光纤; 3. 激光准直器; 4. 1/2波片; 5. 格兰棱镜; 6.透镜组; 7.电光调制器; 8. 光隔离器; 9. 偏振分光棱镜; 10. 1/4波片; 11. 高反镜; 12. 透镜; 13. 光电放大探测器; 14. PDH锁频装置; 15. 光电探测器; 16. 频率计; 17. 检测腔; 18. 参考腔; 19. 电容薄膜真空计; 20. 气瓶; 21. 冷阱; 22. 离子泵; 23. 电离规; 24. 分子泵; 25. 机械泵. 红色实线为光路; 黑色实线为光纤; 黑色虚线表示反馈作用; 蓝色实线为气路.)
Fig. 1. Structure diagram of vacuum measuring device based on F-P cavity.
图 2 (a)102−103 Pa范围内折射率理论值与测量值对比图; (b) 103−105 Pa范围内折射率理论值与测量值对比图; (c) 102−105 Pa范围内折射率理论值与测量值总对比图
Fig. 2. (a) Comparison between theoretical and measured values of refractive index in the range of 102−103 Pa; (b) comparison between theoretical and measured values of refractive index in the range of 103−104 Pa; (c) total comparison between theoretical and measured values of refractive index in the range of 102−105 Pa.
表 1 He极化率的展开系数(原子单位制)[17]
Table 1. Cofficients in the expansion of the polarizability of Helium.
系数 值 A0 1.3837295330(1) A2 3.2036661813(3) × 105 A4 8.803569264(2) × 1010 A6 2.6219915496(7) × 1016 
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表 2 折射率计算结果
Table 2. Calculation results of refractive index.
序号 真空度 p/Pa 折射率 n – 1 序号 真空度 p/Pa 折射率 n – 1 1 101 3.17726 × 10–8 13 4015 1.25716 × 10–6 2 201 6.29408 × 10–8 14 7031 2.20149 × 10–6 3 301 9.42498 × 10–8 15 10036 3.14235 × 10–6 4 402 1.25916 × 10–7 16 20086 6.28879 × 10–6 5 500 1.56736 × 10–7 17 30252 9.47123 × 10–6 6 601 1.88312 × 10–7 18 40070 1.25445 × 10–5 7 701 2.19523 × 10–7 19 50035 1.56690 × 10–5 8 804 2.51819 × 10–7 20 60098 1.88127 × 10–5 9 901 2.82417 × 10–7 21 70122 2.19495 × 10–5 10 1075 3.36856 × 10–7 22 80111 2.50751 × 10–5 11 2020 6.32721 × 10–7 23 90131 2.82100 × 10–5 12 3012 9.43113 × 10–7 24 100166 3.13494 × 10–5
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表 3 折射率测量结果
Table 3. Text results of refractive index.
序号 真空度 p/Pa 折射率n – 1 序号 真空度 p/Pa 折射率n – 1 1 101 3.93406 × 10–8 13 4015 1.23185 × 10–6 2 201 7.02328 × 10–8 14 7031 1.69882 × 10–6 3 301 1.01155 × 10–7 15 10036 2.53943 × 10–6 4 402 1.32115 × 10–7 16 20086 5.48760 × 10–6 5 500 1.61436 × 10–7 17 30252 8.46879 × 10–6 6 601 1.92653 × 10–7 18 40070 1.13490 × 10–5 7 701 2.24327 × 10–7 19 50035 1.42741 × 10–5 8 804 2.56659 × 10–7 20 60098 1.72200 × 10–5 9 901 2.87352 × 10–7 21 70122 2.01575 × 10–5 10 1075 3.32603 × 10–7 22 80111 2.30841 × 10–5 11 2020 6.27737 × 10–7 23 90131 2.61473 × 10–5 12 3012 9.38649 × 10–7 24 100166 2.89609 × 10–5
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表 4 折射率修正系数
Table 4. Refractive index correction coefficient.
序号 真空度 p/Pa 修正系数 φ(p) 序号 真空度 p/Pa 修正系数 φ(p) 1 1075 4.25267 × 10–9 13 40070 1.19548 × 10–6 2 2020 4.98394 × 10–9 14 50053 1.39494 × 10–6 3 3012 4.46381 × 10–9 15 60098 1.59267 × 10–6 4 4015 2.53114 × 10–8 16 70122 1.79205 × 10–6 5 7031 5.02669 × 10–7 17 80111 1.99100 × 10–6 6 10036 6.02924 × 10–7 18 90131 2.06270 × 10–6 7 20086 8.01189 × 10–7 19 100166 2.38851 × 10–6 8 30252 1.00244 × 10–6
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[1] Gibney E 2017 Nature 550 312
Google Scholar
[2] 李得天, 成永军, 习振华 2018 宇航计测技术 38 1
Google Scholar
Li D T, Cheng Y J, Xi Z H 2018 Journal of Astronautic Metrology and Measurement 38 1
Google Scholar
[3] Egan P F, Stone J A, Scherschligt J K, Harvey A H 2019 J. Vac. Sci. Technol. A 37 031603
Google Scholar
[4] Silander I, Hausmaninger T, Zelan M, Axner O 2018 J. Vac. Sci. Technol. A 36 03E105
[5] Egan P F, Stone J A 2011 Appl. Opt. 50 3076
Google Scholar
[6] Hendricks J H, Ricker J E, Stone J A, Egan P F, Scace G E, Strouse G F, Olson D A, Gerty D 2015 XXI IMEKO World Congress “Measurement in Research and Industry” Prague, Czech Republic, August 30–September 4, 2015 p1636
[7] Egan P, Stone J, Ricker J, Hendricks J 2016 2016 Conference on Precision Electromagnetic Measurements Ottawa, Canada, July 10–15, 2016 p1
[8] Zelan M, Silander I, Hausmaninger T, Axner O 2017 arXiv: 1704.01185
[9] Takei Y, Arai K, Yoshida H 2020 Measurement 151 107090
Google Scholar
[10] Axner O, Silander I, Hansmaninger T, Zelan M 2017 arXiv: 1704.01187
[11] 贾文杰, 习振华, 范栋, 董猛, 吴成耀, 成永军 2020 光学学报 40 2212005
Google Scholar
Jia W J, Xi Z H, Fan D, Dong M, Wu C Y, Cheng Y J 2020 Acta Opt. Sin. 40 2212005
Google Scholar
[12] 许玉蓉, 刘洋洋, 王进, 孙羽, 习振华, 李得天, 胡水明 2020 69 15
Xu Y R, Liu Y Y, Wang J, Sun Y, Xi Z H, Li D T, Hu S M 2020 Acta Phys. Sin. 69 15
[13] Bhatia A K, Drachman R J 1998 Phys. Rev. A. 58 4470
Google Scholar
[14] Hurly J J, Moldover M R 2000 Res. Natl. Inst. Stand. Technol. 105 667
Google Scholar
[15] Koch H, Hättig C, Larsen H, Olsen J, Jorgensen P, Fernandez B, Rizzo A 1999 J. Chem. Phys. 111 10108
Google Scholar
[16] Łach G, Jeziorski B, Szalewicz K 2004 Phys. Rev. Lett. 92 233001
Google Scholar
[17] Puchalski M, Piszczatowski K, Komasa J, Jeziorski B, Szalewicz K 2016 Phys. Rev. A 93 032515
Google Scholar
[18] Cencek W, Drzybytek M, Komasa J, Mehl J B, Jeziorski B 2012 J. Chem. Phys. 136 224303
Google Scholar
[19] Bich E, Hellmann R, Vogel E 2007 Mol. Phys. 105 3035
Google Scholar
[20] Rizzo K A, Hättig C, Fernández B, Koch H 2002 J. Chem. Phys. 117 2609
Google Scholar
[21] Bruch L W, Weinhold F 2002 J. Chem. Phys. 117 3243
Google Scholar
[22] Mohr P J, Newell D B, Taylor B N, Tiesinga E 2018 Metrologia 55 125
Google Scholar
[23] Acdiaj S, Yang Y C, Jousten K, Rubin T 2018 J. Chem. Phys. 148 116101
Google Scholar
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