Regulation of Stark effect in Rydberg atoms by AC and DC electric fields and measurement of power-frequency strong fields

XIAO Dongping; CHEN Ling; YAN Sheng; WANG Hao; XU Xianli; PAN Feng; WEN Dongyang; ZHANG Huaiqing

doi:10.7498/aps.74.20250677

Abstract

The Stark effect in Rydberg atoms exhibits remarkable sensitivity to external electric fields, thus forming the fundamental basis for precision electric field measurements. This study systematically and comprehensively investigates the regulatory effects of DC and AC electric fields on cesium Rydberg atoms, both experimentally and theoretically. Utilizing a two-photon three-level system, we generate 28D_5/2 Rydberg states and establish electromagnetically induced transparency (EIT) as the macroscopic observable. Our experimental results demonstrate distinct Stark splitting patterns under DC fields, revealing three fine-structure states each with polarization-dependent frequency shift, they being the negative polarizability states (m_j = 1/2, 3/2) exhibiting rightward shifts, and the positive polarizability state (m_j = 5/2) showing leftward displacement. For power-frequency AC fields (50 Hz), we observe characteristic double-frequency modulation of the EIT-Stark spectra, with measurement limitations emerging at field strengths above 24 V/cm due to laser scanning range constraints. To overcome this limitation, we develop an innovative DC field regulated measurement scheme, establishing a dynamic model for the combined AC/DC field interaction with Rydberg atoms. The model successfully derives demodulation expressions for extracting both DC and AC field components from the composite spectral shifts. Experimental validation shows that applying an 8 V/cm DC bias field can extend the measurable AC field range to 32 V/cm, achieving a 33.3% improvement over direct measurement methods within a 1 GHz laser scanning range, while maintaining exceptional accuracy with demodulation errors below 0.8% across all tested configurations. The detailed error analysis reveals that the measurement precision improves with the increase of field strength, with a standard deviation of σ = 0.2196%, demonstrating the robustness of our approach. Compared with existing techniques, this DC-field regulation method effectively addresses the critical challenge of limited laser scanning range in strong-field measurements, while preserving the quantum advantages of Rydberg atom sensors. The research provides both theoretical foundations and practical solutions for measuring power-frequency strong electric fields in power systems, with potential applications extending to other low-frequency strong-field measurement scenarios. Future work will focus on enhancing measurement stability in extreme field conditions, improving accuracy, and further expanding the operational range of this quantum sensing technology.

Keywords:

Rydberg atom /
Stark effect /
electromagnetically induced transparency effect /
power-frequency strong field measurements

Authors and contacts

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 National Natural Science Foundation of China (Grant No. 52477001) .

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References

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[2]	Han Z F, Xue F, Hu J, He J L 2021 IEEE Ind. Electron. Mag. 15 35 Google Scholar
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[23]	Song H T, Xiao Y, Hu S S, Xiao D P, Wang B S, Shi Z X, Zhang H Q 2024 IET Energy Syst. Integr. 6 174 Google Scholar
[24]	Urbańczyk T, Kędziorski A, Krośnicki M, Koperski J 2024 Molecules 29 4657 Google Scholar
[25]	Gatzke M, Veale J R, Swindell W R, Gallagher T F 1996 Phys. Rev. A 54 2492.Google Scholar
[26]	Lihachev G, Riemensberger J, Weng W, Liu J, Tian H, Siddharth A, Snigirev V, Shadymov V, Voloshin A, Wang R N, He J, Bhave S A, Kippenberg T J 2022 Nat. Commun. 13 3522 Google Scholar
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Cited By

图 1 里德伯原子电场量子传感器的实验装置示意图　(a) 铯里德伯原子三能级结构和跃迁过程示意图; (b) 实验装置的布局示意图

Figure 1. Experimental setup of a Rydberg atom electric field quantum sensor: (a) Schematic diagram of the three-level structure and transition process of a cesium Rydberg atom; (b) experimental apparatus layout diagram.

DownLoad: Full-Size Img PowerPoint

图 2 直流电场作用下的EIT光谱

Figure 2. EIT spectra under the action of a DC electric field.

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图 3 不同电场作用下的各里德伯态光谱频移量Δ_Stark随时间变化轨迹　(a)—(d) 不同工频交流场强作用的结果; (e)—(i) 直流调控不同工频交流场强作用的结果

Figure 3. Trajectories of the spectral frequency shifts Δ_Stark of each Rydberg state with time under the action of different electric fields: (a)–(d) The results of the action of different industrial frequency AC field strengths; (e)–(i) the results of the action of different industrial frequency AC field strengths of DC modulation

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图 4 28D_5/2(m_j = 1/2)里德伯态在不同交直流调制电场下, EIT-Stark光谱频移量随ωt的变化　(a) E_DC = 4 V/cm, E_AC = 28 V/cm; (b) E_DC = 6 V/cm, E_AC = 28 V/cm; (c) E_DC = 8 V/cm, E_AC = 28 V/cm

Figure 4. Relationship between the frequency shift of the EIT-Stark spectral spectrum and ωt in the 28D_5/2(m_j = 1/2) Rydberg state under different AC/DC electric fields: (a) E_DC = 4 V/cm, E_AC = 28 V/cm; (b) E_DC = 6 V/cm, E_AC = 28 V/cm; (c) E_DC = 8 V/cm, E_AC = 28 V/cm

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图 5 不同直流场调控下交流场强测量值及准确性分析

Figure 5. Measured values and accuracy analysis of AC field strength under different DC field controls.

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表 1 28D_5/2精细能级态极化率α (MHz·cm²/V²)

Table 1. Polarizability of 28D_5/2 fine energy states α (MHz·cm²/V²).

m_j 理论计算结果实验拟合结果

1/2 –16.34966 –16.17472

3/2 –11.81798 –11.51648

5/2 1.22474 1.09556

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map

[1]	Peng J, Jia S H, Bian J M, Zhang S, Liu J B, Zhou X 2019 Sensors 19 2860 Google Scholar
[2]	Han Z F, Xue F, Hu J, He J L 2021 IEEE Ind. Electron. Mag. 15 35 Google Scholar
[3]	韩小萱, 孙光祖, 郝丽萍, 白素英, 焦月春 2024 73 093202 Google Scholar Han X X, Sun G Z, Hao L P, Bai S Y, Jiao Y C 2024 Acta Phys. Sin. 73 093202 Google Scholar
[4]	Liu Q, Chen J Z, Wang H, Zhang J, Ruan W M, Wu G Z, Zheng S Y, Luo J T, Song Z F 2024 Chin. Phys. B 33 054203 Google Scholar
[5]	张学超, 乔佳慧, 刘瑶, 苏楠, 刘智慧, 蔡婷, 何军, 赵延霆, 王军民 2024 73 070201 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 070201 Google Scholar
[6]	Facon A, Dietsche E K, Grosso D, Haroche S, Raimond J M, Brune M, Gleyzes S 2016 Nature 535 262 Google Scholar
[7]	Duspayev A, Cardman R, Anderson D A, Raithel G 2024 Phys. Rev. Res. 6 023138 Google Scholar
[8]	Li C Y, Zhang L J, Zhao J M, Jia S T 2012 Acta Phys. Sin. 61 163202 [李昌勇, 张临杰, 赵建明, 贾锁堂 2012 61 163202]Google Scholar Li C Y, Zhang L J, Zhao J M, Jia S T 2012 Acta Phys. Sin. 61 163202 Google Scholar
[9]	黄巍, 梁振涛, 杜炎雄, 颜辉, 朱诗亮 2015 64 160702 Google Scholar Huang W, Liang Z T, Du Y X, Yan H, Zhu S L 2015 Acta Phys. Sin. 64 160702 Google Scholar
[10]	Liao K Y, Tu H T, Yang S Z, Chen C J, Liu X H, Liang J, Zhang X D, Yan H, Zhu S L 2020 Phys. Rev. A 101 053432 Google Scholar
[11]	Liu X B, Jia F D, Zhang H Y, Mei J Yu Y H, Liang W C, Zhang J, Xie F, Zhong Z P 2021 AIP Adv. 11 085127 Google Scholar
[12]	Jia F D, Liu X B, Mei J, Yu Y H, Zhang H Y, Lin Z Q, Dong H Y, Zhang J, Xie F 2021 Phys. Rev. A 103 063113 Google Scholar
[13]	周飞, 贾凤东, 刘修彬, 张剑, 谢锋, 钟志萍 2023 72 045204 Google Scholar Zhou F, Jia F D, Liu X B, Zhang J, Xie F, Zhong Z P 2023 Acta Phys. Sin. 72 045204 Google Scholar
[14]	Holloway C L, Prajapati N, Artusio-Glimpse A B, Berweger S, Simons M T, Kasahara Y, Alù A, Ziolkowski R W 2022 Appl. Phys. Lett. 120 204001 Google Scholar
[15]	Wang Y X, Liu Y Q, Zhang Q Y, Gong P W, Xie W, Wu Z N, Jia F D, Zhong Z P 2024 AIP Adv. 14 105137 Google Scholar
[16]	Weller D 2019 Thermal Rydberg Spectroscopy and Plasma (Munich: Verlag Dr. Hut) p68
[17]	Anderson D A, Schwarzkopf A, Miller S A, Thaicharoen N, Raithel G, Gordon J A, Holloway C L 2014 Phys. Rev. A 90 043419 Google Scholar
[18]	Anderson D A, Miller S A, Raithel G, Gordon J A, Butler M L, Holloway C L 2016 Phys. Rev. Appl. 5 034003 Google Scholar
[19]	Song H T, Hu S S, Ding C, Xiao Y, Wang B S, Zhang Y 2023 Proceedings of the 2023 8th Asia Conference on Power and Electrical Engineering (ACPEE 2023) Tianjin, China, April 14–16, 2023 p1638
[20]	丁超, 胡珊珊, 邓松, 宋宏天, 张英, 王保帅, 阎晟, 肖冬萍, 张淮清 2025 74 043201 Google Scholar Ding C, Hu S S, Deng S, Song H T, Zhang Y, Wang B S, Yan S, Xiao D P, Zhang H Q 2025 Acta Phys. Sin. 74 043201 Google Scholar
[21]	焦月春 2017 博士论文 (山西: 山西大学) Jiao Y C 2017 Ph. D. Dissertation (Shanxi: Shanxi University
[22]	Xiao D P, Shi Z X, Chen L, Yan S, Xu L X, Zhang H Q 2024 Front. Phys. 12 1405149 Google Scholar
[23]	Song H T, Xiao Y, Hu S S, Xiao D P, Wang B S, Shi Z X, Zhang H Q 2024 IET Energy Syst. Integr. 6 174 Google Scholar
[24]	Urbańczyk T, Kędziorski A, Krośnicki M, Koperski J 2024 Molecules 29 4657 Google Scholar
[25]	Gatzke M, Veale J R, Swindell W R, Gallagher T F 1996 Phys. Rev. A 54 2492.Google Scholar
[26]	Lihachev G, Riemensberger J, Weng W, Liu J, Tian H, Siddharth A, Snigirev V, Shadymov V, Voloshin A, Wang R N, He J, Bhave S A, Kippenberg T J 2022 Nat. Commun. 13 3522 Google Scholar
[27]	董慧杰, 王新宇, 李昌勇, 贾锁堂 2015 64 093201 Google Scholar Dong H J, Wang X Y, Li C Y, Jia S T 2015 Acta Phys. Sin. 64 093201 Google Scholar
[28]	李伟, 张淳刚, 张好, 景明勇, 张临杰 2021 激光与光电子学进展 58 144 Google Scholar Li W, Zhang C G, Zhang H, Jing M Y, Zhang L J 2021 Acta Laser Optoelectron. Prog. 58 144 Google Scholar
[29]	崔帅威, 彭文鑫, 李松浓, 蒋源, 姬中华, 赵延霆 2023 高电压技术 49 644 Google Scholar Cui S W, Peng W X, Li S N, Jiang Y, Ji Z H, Zhao Y T 2023 High Volt. Eng. 49 644 Google Scholar
[30]	Harmin D A 1982 Phys. Rev. A 26 2656 Google Scholar
[31]	Cardman R, MacLennan J L, Anderson S E, Raithel G 2021 New J. Phys. 23 063074 Google Scholar

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