Rydberg atom electric field based quantum measurement method and polarization influence analysis

DING Chao; HU Shanshan; DENG Song; SONG Hongtian; ZHANG Ying; WANG Baoshuai; YAN Sheng; XIAO Dongping; ZHANG Huaiqing

doi:10.7498/aps.74.20241362

Abstract

The interaction between an electric field and the energy levels of Rydberg states results in the Stark effect, which can be used for quantum detection by measuring the frequency shift in electromagnetically induced transparency (EIT) spectra. By using the functional relationship between the frequency shift and the electric field, it is possible to measure the electric field in question. However, the mismatch between the probe laser and the polarization direction of the coupled laser leads to errors in the measurement of the frequency shift, affecting the accurate measurement of the electric field. In this work, the Schrödinger equation is solved by perturbation method to derive the functional relationship between the energy offset and the electric field strength. Then, the functional relationship between the energy offset and the electric field strength is brought into the solution of the density matrix equation, and the influences of the polarization direction of the detected light and coupled light on the EIT-Stark mathematical model are analyzed. Then an internal electrode method is used to prevent shielding effects caused by alkali metal atoms adhering to the surface of the atomic vapor cell, thereby enabling the application of the electric field. The calibration of the Rydberg state polarisation rate is achieved by using a standard source and measuring the frequency shift of the EIT spectrum. Finally, the effects of polarisation mismatch on the measurement results of EIT spectrum and the electric field are verified by modulating the laser polarization direction. The experimental data show that when the polarization directions of the probe laser and coupled laser are parallel to each other, it is the most matched polarization direction for the lasers, the peak value of the EIT spectrum is the largest, and the maximum relative error of the electric field measurement is 1.67%. When the angle between the polarisation directions of the probe light and the coupled light laser is 45°, the laser polarisation mismatch is the most severe, the EIT spectral peak is the lowest and the maximum relative error of the electric field measurement is 10.24%.

Keywords:

electric field measurement /
Rydberg atom /
electromagnetically induced transparency /
direction of laser polarisation

Authors and contacts

1.
Electric Power Research Institute of Guizhou Power Grid Co. Ltd., Guiyang 550001, China
2.
CSG Electric Power Research Institute, Guangzhou 510700, China
3.
Guangdong Provincial Key Laboratory of Intelligent Measurement and Advanced Metering of Power Grid, Guangzhou 510700, China
4.
National Key Laboratory of Power Transmission Equipment Technology, School of Electrical Engineering, Chongqing University, Chongqing 400044, China

Corresponding author: XIAO Dongping, xiaodongping@cqu.edu.cn

Funds: Project supported by the Funding Program of China Southern Power Grid Guizhou Power Grid Co., Ltd. (Grant Nos. GZKJXM20222158, GZKJXM20222147, GZKJXM20222200) and the Science and Technology Plan Program of Guangdong Province, China (Grant No. 2021B1212050014).

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References

[1]	Holloway C L, Prajapati N, Simons M T, Artusio-Glimpse A 2022 IEEE Microw. Mag. 23 44 Google Scholar
[2]	张学超, 乔佳慧, 刘瑶, 苏楠, 刘智慧, 蔡婷, 何军, 赵延霆, 王军民 2024 物理学报 73 073201 Google Scholar Zhang X C, Qiao J H, Liu Y, Su N, Liu Z H, Cai T, He J, Zhao Y T, Wang J M 2024 Acta Phys. Sin. 73 073201 Google Scholar
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Cited By

图 1 测量系统能级结构

Figure 1. Measurement system energy level structure.

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图 2 试验装置结构图

Figure 2. Structure of the test device.

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图 3 饱和光谱法稳频结构图

Figure 3. Structural diagram of frequency stabilisation by saturation spectroscopy.

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图 4 饱和光谱法锁频原理图　(a) 饱和光谱图; (b) 精细能级结构; (c) 饱和光谱及其鉴频曲线

Figure 4. Schematic diagram of frequency locking by saturation spectroscopy: (a) Saturation spectrum; (b) fine structure levels; (c) saturation spectrum and its frequency discrimination curve.

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图 5 AOM结构图

Figure 5. AOM structure diagram.

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图 6 内置极板原子蒸气室结构图

Figure 6. Atomic vapour chamber structure.

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图 7 加载标准源的EIT光谱变化

Figure 7. EIT spectral variation of loaded standard sources.

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图 8 激光偏振方向调控装置

Figure 8. Laser polarisation direction control device.

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图 9 EIT光谱峰值随双光子偏振夹角增加变化曲线

Figure 9. Variation curve of EIT spectral peak with increasing two-photon polarisation pinch angle.

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图 10 考虑精细能级下的能级图

Figure 10. Consider energy level diagrams at fine energy levels

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图 11 激光偏振方向对EIT光谱的影响　(a)探测光和耦合光偏振方向平行; (b) 探测光和耦合光偏振方向夹角20°; (c) 探测光和耦合光偏振方向夹角45°; (d) 探测光和耦合光偏振方向垂直

Figure 11. Effect of laser polarisation direction on EIT spectra: (a) Polarization directions of the probe light and coupling light are parallel; (b) the polarization directions of the probe light and coupling light form an angle of 20°; (c) the polarization directions of the probe light and coupling light form an angle of 45°; (d) the polarization directions of the probe light and coupling light are perpendicular.

DownLoad: Full-Size Img PowerPoint

图 12 D态原子轨道

Figure 12. D-state atomic orbitals.

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图 13 测量结果　(a)探测光和耦合光偏振方向平行; (b)探测光和耦合光偏振方向夹角22.5°; (c)探测光和耦合光偏振方向夹角45°

Figure 13. Measurement results: (a) Parallelism between the direction of polarisation of the probe and coupled laser; (b) 22.5° angle between the direction of polarisation of the probe and coupled laser; (c) 45° angle between the direction of polarisation of the probe and coupled laser.

DownLoad: Full-Size Img PowerPoint

[1]	Holloway C L, Prajapati N, Simons M T, Artusio-Glimpse A 2022 IEEE Microw. Mag. 23 44 Google Scholar
[2]	张学超, 乔佳慧, 刘瑶, 苏楠, 刘智慧, 蔡婷, 何军, 赵延霆, 王军民 2024 物理学报 73 073201 Google Scholar Zhang X C, Qiao J H, Liu Y, Su N, Liu Z H, Cai T, He J, Zhao Y T, Wang J M 2024 Acta Phys. Sin. 73 073201 Google Scholar
[3]	夏刚, 张亚鹏, 汤婧雯, 李春燕, 吴春旺, 张杰, 周艳丽 2024 物理学报 73 104203 Google Scholar Xia G, Zhang Y P, Tang J W, Li C Y, Wu C W, Zhang J, Zhou Y L 2024 Acta Phys. Sin. 73 104203 Google Scholar
[4]	Hao L, Xue Y, Fan J, Bai J, Jiao Y, Zhao J 2020 Chin. Phys. B 29 033201 Google Scholar
[5]	张淳刚, 李伟, 张好, 景明勇, 张临杰 2021 光子学报 50 0602001 Google Scholar Zhang C G, Li W, Zhang H, Jing M Y, Zhang L J 2021 Acta Photon. Sin. 50 0602001 Google Scholar
[6]	李伟, 张淳刚, 张好, 景明勇, 张临杰 2021 激光与光电子学进展 58 1702002 Google Scholar Li W, Zhang C G, Zhang H, Jing M Y, Zhang L J 2021 Laser Optoelectron. Prog. 58 1702002 Google Scholar
[7]	Hu J L, Li H Q, Song R, Bai J X, Jiao Y C, Zhao J M, Jia S T 2022 Appl. Phys. Lett. 121 014002 Google Scholar
[8]	Gordon J A, Simons M T, Haddab A H, Holloway C L 2019 AIP Adv. 9 045030 Google Scholar
[9]	Amy K R, Nikunjkumar P, Senic D 2021 Appl. Phys. Lett. 118 114001 Google Scholar
[10]	阮伟民, 张映昀, 冯志刚, 周亚东, 宋振飞, 屈继峰 2024 计量学报 45 97 Google Scholar Ruan W M, Zhang Y Y, Feng Z G, Zhou Y D, Song Z F, Qu J F 2024 Acta Metrol. Sin. 45 97 Google Scholar
[11]	张映昀, 阮伟民, 冯志刚, 屈继峰, 宋振飞 2023 计量学报 44 1438 Google Scholar Zhang Y Y, Ruan W M, Feng Z G, Qu J F, Song Z F 2023 Acta Metrologica Sinca 44 1438 Google Scholar
[12]	李可, 田建飞, 张好, 景明勇, 张临杰 2023 光子学报 52 0902001 Google Scholar Li K, Tian J F, Zhang H, Jing M Y, Zhang L J 2023 Acta Photon. Sin. 52 0902001 Google Scholar
[13]	刘修彬, 贾凤东, 周飞, 俞永宏, 张剑, 谢锋, 钟志萍 2023 宇航计测技术 43 5 Google Scholar Liu X B, Jia F D, Zhou F, Yu Y Y, Zhang J, Xie F, Zhong Z P 2023 J. Astron. Metrol. Measurem. 43 5 Google Scholar
[14]	Cai M H, Xu Z S, You S H, Liu H P 2022 Photonics 9 250 Google Scholar
[15]	蔡德成, 胡星, 吴海洋, 吕健双 2023 电力大数据 26 90 Google Scholar Cai D C, Hu X, Wu H Y, Lü J S 2023 Power Syst. Big Data 26 90 Google Scholar
[16]	张缘圆, 辛明勇, 冯起辉, 祝健杨 2023 电力大数据 26 69 Google Scholar Zhang Y Y, Xin M Y, Feng Q H, Zhu J Y 2023 Power Syst. Big Data 26 69 Google Scholar
[17]	Liu W, Zhang L, Wang T 2023 Chin. Phys. B 32 053203 Google Scholar
[18]	Zhao S S, Gao W, Cheng H, You L, Liu H P 2018 Phys. Rev. Lett. 120 063203 Google Scholar
[19]	韩玉龙, 刘邦, 张侃, 孙金芳, 孙辉, 丁冬生 2024 物理学报 73 113201 Google Scholar Han Y L, Liu B, Zhang K, Sun J F, Sun H, Ding D S 2024 Acta Phys. Sin. 73 113201 Google Scholar
[20]	阎晟, 肖冬萍, 石筑鑫, 张淮清, 刘卫华 2024 电工技术学报 39 2953 Google Scholar Yan S, Xiao D P, Shi Z X, Zhang H Q, Liu W H 2024 Transactions of China Electrotechnical Society 39 2953 Google Scholar
[21]	王延正, 武博, 付运起, 安强 2025 激光与光电子学进展 62 0302001 Wang Y Z, Wu B, Fu Y Q, An Q 2025 Laser Optoelectron. Prog. 62 0302001
[22]	Noah S, Andrew P R, Alexandra B A, Nikunjkumar P, Samuel B, Dangka S, Matthew T S, Christopher L H 2024 Phys. Rev. A 109 L021702 Google Scholar
[23]	Sedlacek J A, Schwettmann A, Kubler H, Shaffer J P 2013 Phys. Rev. Lett. 111 063001 Google Scholar
[24]	Bao S X, Zhang H, Zhou J, Zhang L J, Zhao J M, Xiao L T, Jia S T 2016 Phys. Rev. A 94 043822 Google Scholar

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