Sensitivity of radio-frequency electric field sensor based on Rydberg Stark effect

Han Xiao-Xuan; Sun Guang-Zu; Hao Li-Ping; Bai Su-Ying; Jiao Yue-Chun

doi:10.7498/aps.73.20240162

Abstract

Rydberg atoms hold special attraction in electric applications due to their large transition electric dipole moments and huge polarization, which leads to a strong response of atom to electric fields. In radio-frequency (RF) fields, the Rydberg levels are AC Stark shift and splitting, which can realize the study of high-sensitivity electric field sensor of Rydberg atoms. In this work, we use the simpler Shirley’s time-independent Floquet Hamiltonian model to calculate the AC Stark energy spectrum of Cs Rydberg atoms. This model can reduce the basic Hamiltonian into such a Hamiltonian that includes only those Rydberg states that have direct dipole-allowed transitions with the target state, thereby significantly improving the speed of computation. The accuracy of the calculation is proved by fitting with the calculated frequency shift of DC Stark energy levels in the weak fields, and the polarizability of 60D_5/2 and 70D_5/2 Rydberg atomic states are obtained by fitting with the measured ion spectra of DC Stark Cs ultra-cold Rydberg atoms in magneto-optical trap. In addition, we calculate the AC Stark shift of Cs Rydberg atom $ \left| {60{{\text{D}}_{5/2}},{m_j} = 1/2} \right\rangle $ state in electric fields with different frequencies with ε = 100 mV/m. Rydberg atoms provide a structured spectrum of sensitivity to electric fields due to strong resonant interaction and off-resonant interaction with many dipole-allowed transitions to nearby Rydberg states. This kind of the frequency response structure is of significance to a broadband sensor. And we calculate the sensitivity and the scaling of the signal-to-noise ratio (SNR), β, varying with detuning from the $ \left| {60{{\text{D}}_{5/2}}} \right\rangle \to \left| {61{{\text{P}}_{3/2}}} \right\rangle $ transition. The value of β allows one to use the result for any Rydberg state sensor to determine the SNR for any Ε in a 1 s measurement. Therefrom, Rydberg sensor can preferentially detect many RF frequencies spreading across its carrier spectral range without modification while effectively rejecting large portions where the atom response is significantly weaker, and the signal depends primarily on the detuning of the RF field to the nearest resonance which does not convey the RF frequency directly.

Keywords:

Authors and contacts

1.
Department of Physics, Taiyuan Normal University, Jinzhong 030619, China
2.
Department of Materials and Chemical Engineering, Taiyuan University, Taiyuan 030032, China
3.
School of Physics and Information Engineering, Shanxi Normal University, Taiyuan 030031, China
4.
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China

Corresponding author: Jiao Yue-Chun, ycjiao@sxu.edu.cn

Funds: Project supported by the National Nature Science Foundation of China (Grant Nos. 12104337, 12204292, 12120101004), the Scientific and Technological Innovation Program of Higher Education Institutions in Shanxi, China (Grant Nos. 2021L438, 2022L268), and the Fundamental Research Program of Shanxi Province, China (Grant Nos. 202203021212018, 202203021212405).

FullText HTML : translate this paragraph

References

[1]	Fabre C, Gross M, Raimond J M, Haroche S 1983 J. Phys. B 16 L671 Google Scholar
[2]	Hansen W 1983 J. Phys. B. 16 933 Google Scholar
[3]	Feng Z G, Zhang H, Che J L, Zhang L J, Li C Y, Zhao J M, Jia S T 2011 Phys. Rev. A 83 042711 Google Scholar
[4]	Fabre C, Haroche S 1975 Opt. Commun. 15 254 Google Scholar
[5]	Shirley J H 1965 Phys. Rev. 138 B979 Google Scholar
[6]	Meyer D H, Castillo Z A, Cox K C, Kunz P D 2020 J. Phys. B 53 034001 Google Scholar
[7]	Jing M Y, Hu Y, Ma J, Zhang H, Zhang L J, Xiao L T, Jia S T 2020 Nat. Phys. 16 911 Google Scholar
[8]	Yang W G, Jing M Y, Zhang H, Zhang L J, Xiao L T, Jia S T 2023 Phys. Rev. Appl. 19 064021 Google Scholar
[9]	张临杰, 景明勇, 张好 2022 山西大学学报 45 712 Google Scholar Zhang L J, Jing M Y, Zhang H 2022 J. Shanxi Univ. 45 712 Google Scholar
[10]	Fan H, Kumar S, Sedlacek J, Kübler H, Karimkashi S, Shaffer J P 2015 J. Phys. B 48 202001 Google Scholar
[11]	Jiao Y C, Han X X, Yang Z W, Li J K, Raithel G, Zhao J M, Jia S T 2016 Phys. Rev. A 94 023832 Google Scholar
[12]	Jiao Y C, Hao L P, Han X X, Bai S Y, Raithel G, Zhao J M, Jia S T 2017 Phys. Rev. Appl. 8 014028 Google Scholar
[13]	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
[14]	Jia F D, Liu X B, Mei J, Yu Y H, Zhang H Y, Lin Z Q, Dong H Y, Zhang J, Xie F, Zhong Z P 2021 Phys. Rev. A 103 063113 Google Scholar
[15]	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
[16]	Hu J L, Jiao Y C, He Y H, Zhang H, Zhang L J, Zhao J M, Jia S T 2023 EPJ Quantum Tech. 10 51 Google Scholar
[17]	Sedlacek J A, Schwettmann A, Kübler H, Löw R, Pfau T, Shaffer J P 2012 Nat. Phys. 8 819 Google Scholar
[18]	Sedlacek J A, Schwettmann A, Kübler H, Shaffer J P 2013 Phys. Rev. Lett. 111 063001 Google Scholar
[19]	Simons M T, Haddab A H, Gordon J A, Holloway C L 2019 Appl. Phys. Lett. 114 114101 Google Scholar
[20]	Liu Z K, Zhang L H, Liu B, Zhang Z Y, Guo G C, Ding D S, Shi B S 2022 Nat. Commun. 13 1997 Google Scholar
[21]	Zhou F, Jia F D, Liu X B, Yu Y H, Mei J, Zhang J, Xie F, Zhong Z P 2023 J. Phys. B 56 025501 Google Scholar
[22]	Cui Y, Jia F D, Hao J H, Wang Y H, Zhou F, Liu X B, Yu Y H, Mei J, Bai J H, Bao Y Y, Hu D, Wang Y, Liu Y, Zhang J, Xie F, Zhong Z P 2023 Phys. Rev. A 107 043102 Google Scholar
[23]	Li X H, Cui Y, Hao J H, Zhou F, Wang Y X, Jia F D, Zhang J, Xie F, Zhong Z P 2023 Opt. Express 31 38165 Google Scholar
[24]	杨凯, 安强, 姚佳伟, 毛瑞棋, 林沂, 刘燚, 付云起 2022 光学学报 42 1528002 Google Scholar Yang K, An Q, Yao J W, Mao R Q, Lin Y, Liu Y, Fu Y Q 2022 Acta Opt. Sin. 42 1528002 Google Scholar
[25]	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
[26]	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
[27]	Khadjavi A, Lurio A, Happer W 1968 Phys. Rev. 167 128 Google Scholar
[28]	Zimmerman M L, Littman M G, Kash M M, Kleppner D 1979 Phys. Rev. A 20 2251 Google Scholar
[29]	Bason M G, Tanasittikosol M, Sargsyan A, Mohapatra A K, Sarkisyan D, Potvliege R M, Adams C S 2010 New J. Phys. 12 065015 Google Scholar
[30]	Jau Y Y, Carter T 2020 Phys. Rev. Appl. 13 054034 Google Scholar
[31]	Mohapatra A K, Bason M G, Butscher B, Weatherill K J, Adams C S 2008 Nat. Phys. 4 890 Google Scholar
[32]	Wade C G, Šibalić N, Melo N R, Kondo J M, Adams C S, Weatherill K J 2017 Nat. Photon. 11 40 Google Scholar

Cited By

图 1 理论计算 Cs 原子(a) $ \left| {60{{\text{D}}_{5/2}}, {m_j} = 5/2} \right\rangle $和(b) $ \left| {70{{\text{D}}_{5/2}}, {m_j} = 5/2} \right\rangle $态的Stark能谱, 红色虚线为AC Stark能谱, 黑色实线为校准后的DC Stark能谱

Figure 1. Calculated Stark spectra for Cs Rydberg atom of (a) $ \left| {60{{\text{D}}_{5/2}}, {m_j} = 5/2} \right\rangle $ and (b) $ \left| {70{{\text{D}}_{5/2}}, {m_j} = 5/2} \right\rangle $ state. The red dotted line is the AC Stark spectrum, and the black solid line is the Stark map in a DC electric field on a field axis scaled such that the rms fields.

DownLoad: Full-Size Img PowerPoint

图 2 实验测的x方向70D_5/2里德伯原子 Stark 谱, 黑、红和绿色点线分别为理论计算的m_j = 1/2, 3/2和5/2的Stark 谱

Figure 2. Measurements of the Stark spectrum for 70D_5/2 Rydberg atom in the x-direction, and the black, red, and green dotted lines show the calculation Stark spectra of m_j = 1/2, 3/2, and 5/2, respectively.

DownLoad: Full-Size Img PowerPoint

图 3 Cs里德伯原子60D_5/2态在 ε = 100 mV/m不同频率射频场中的AC Stark频移, 其中临近的共振态用黑色虚线标定

Figure 3. AC Stark shifts of the 60D_5/2 state in RF field with ε = 100 mV/m. The adjacent resonant state is labeled with a black dashed line.

DownLoad: Full-Size Img PowerPoint

图 4 在低频DC场中, 测量时间t = 1 s, 原子数N = 10³ (10⁴, 10⁵, 10⁶)的$ \left| {60{{\text{D}}_{5/2}}, {m_j} = 1/2} \right\rangle $Cs里德伯原子的最小可检测场与射频频率的关系

Figure 4. In a quasi-DC field, the minimum detectable field in a 1 s measurement vs. RF frequency using a $ \left| {60{{\text{D}}_{5/2}}, {m_j} = 1/2} \right\rangle $ target state with N = 10³ (10⁴, 10⁵, 10⁶) Cs Rydberg atoms.

DownLoad: Full-Size Img PowerPoint

图 5 测量时间为1 s的最小可检测场和信噪比缩放因子β (红色实线)与$ \left| {60{{\text{D}}_{5/2}}} \right\rangle \to \left| {61{{\text{P}}_{3/2}}} \right\rangle $射频共振失谐量的关系, 其中三角形、正方形和五边形分别对应β = 1, 1—2和 2

Figure 5. The minimum detectable field in a 1 s measurement and the scaling of the SNR (red solid), β, versus detuning of RF transition from the $ \left| {60{{\text{D}}_{5/2}}} \right\rangle \to $$ \left| {61{{\text{P}}_{3/2}}} \right\rangle $. The triangle, square, and pentagon symbols match correspond to β = 1, 2 or somewhere in between, respectively.

DownLoad: Full-Size Img PowerPoint

表 1 实验测量极化率与计算60D_5/2和70D_5/2态极化率的比较

Table 1. Comparisons of the measurement and calculation of the polarizability for 60D_5/2 and 70D_5/2 Rydberg atom.

状态	极化率实验值/ (MHz·cm²/V²)	极化率理论值/ (MHz·cm²/V²)
$ 60{{\text{D}}_{5/2, 1/2}} $	–5007.11	–4984.80
$ 60{{\text{D}}_{5/2, 3/2}} $	–3620.61	–3633.78
$ 60{{\text{D}}_{5/2, 5/2}} $	281.19	280.93
$ 70{{\text{D}}_{5/2, 1/2}} $	–15455.87	–15432.29
$ 70{{\text{D}}_{5/2, 3/2}} $	–11160.68	–11171.34
$ 70{{\text{D}}_{5/2, 5/2}} $	835.18	833.77

DownLoad: CSV

[1]	Fabre C, Gross M, Raimond J M, Haroche S 1983 J. Phys. B 16 L671 Google Scholar
[2]	Hansen W 1983 J. Phys. B. 16 933 Google Scholar
[3]	Feng Z G, Zhang H, Che J L, Zhang L J, Li C Y, Zhao J M, Jia S T 2011 Phys. Rev. A 83 042711 Google Scholar
[4]	Fabre C, Haroche S 1975 Opt. Commun. 15 254 Google Scholar
[5]	Shirley J H 1965 Phys. Rev. 138 B979 Google Scholar
[6]	Meyer D H, Castillo Z A, Cox K C, Kunz P D 2020 J. Phys. B 53 034001 Google Scholar
[7]	Jing M Y, Hu Y, Ma J, Zhang H, Zhang L J, Xiao L T, Jia S T 2020 Nat. Phys. 16 911 Google Scholar
[8]	Yang W G, Jing M Y, Zhang H, Zhang L J, Xiao L T, Jia S T 2023 Phys. Rev. Appl. 19 064021 Google Scholar
[9]	张临杰, 景明勇, 张好 2022 山西大学学报 45 712 Google Scholar Zhang L J, Jing M Y, Zhang H 2022 J. Shanxi Univ. 45 712 Google Scholar
[10]	Fan H, Kumar S, Sedlacek J, Kübler H, Karimkashi S, Shaffer J P 2015 J. Phys. B 48 202001 Google Scholar
[11]	Jiao Y C, Han X X, Yang Z W, Li J K, Raithel G, Zhao J M, Jia S T 2016 Phys. Rev. A 94 023832 Google Scholar
[12]	Jiao Y C, Hao L P, Han X X, Bai S Y, Raithel G, Zhao J M, Jia S T 2017 Phys. Rev. Appl. 8 014028 Google Scholar
[13]	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
[14]	Jia F D, Liu X B, Mei J, Yu Y H, Zhang H Y, Lin Z Q, Dong H Y, Zhang J, Xie F, Zhong Z P 2021 Phys. Rev. A 103 063113 Google Scholar
[15]	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
[16]	Hu J L, Jiao Y C, He Y H, Zhang H, Zhang L J, Zhao J M, Jia S T 2023 EPJ Quantum Tech. 10 51 Google Scholar
[17]	Sedlacek J A, Schwettmann A, Kübler H, Löw R, Pfau T, Shaffer J P 2012 Nat. Phys. 8 819 Google Scholar
[18]	Sedlacek J A, Schwettmann A, Kübler H, Shaffer J P 2013 Phys. Rev. Lett. 111 063001 Google Scholar
[19]	Simons M T, Haddab A H, Gordon J A, Holloway C L 2019 Appl. Phys. Lett. 114 114101 Google Scholar
[20]	Liu Z K, Zhang L H, Liu B, Zhang Z Y, Guo G C, Ding D S, Shi B S 2022 Nat. Commun. 13 1997 Google Scholar
[21]	Zhou F, Jia F D, Liu X B, Yu Y H, Mei J, Zhang J, Xie F, Zhong Z P 2023 J. Phys. B 56 025501 Google Scholar
[22]	Cui Y, Jia F D, Hao J H, Wang Y H, Zhou F, Liu X B, Yu Y H, Mei J, Bai J H, Bao Y Y, Hu D, Wang Y, Liu Y, Zhang J, Xie F, Zhong Z P 2023 Phys. Rev. A 107 043102 Google Scholar
[23]	Li X H, Cui Y, Hao J H, Zhou F, Wang Y X, Jia F D, Zhang J, Xie F, Zhong Z P 2023 Opt. Express 31 38165 Google Scholar
[24]	杨凯, 安强, 姚佳伟, 毛瑞棋, 林沂, 刘燚, 付云起 2022 光学学报 42 1528002 Google Scholar Yang K, An Q, Yao J W, Mao R Q, Lin Y, Liu Y, Fu Y Q 2022 Acta Opt. Sin. 42 1528002 Google Scholar
[25]	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
[26]	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
[27]	Khadjavi A, Lurio A, Happer W 1968 Phys. Rev. 167 128 Google Scholar
[28]	Zimmerman M L, Littman M G, Kash M M, Kleppner D 1979 Phys. Rev. A 20 2251 Google Scholar
[29]	Bason M G, Tanasittikosol M, Sargsyan A, Mohapatra A K, Sarkisyan D, Potvliege R M, Adams C S 2010 New J. Phys. 12 065015 Google Scholar
[30]	Jau Y Y, Carter T 2020 Phys. Rev. Appl. 13 054034 Google Scholar
[31]	Mohapatra A K, Bason M G, Butscher B, Weatherill K J, Adams C S 2008 Nat. Phys. 4 890 Google Scholar
[32]	Wade C G, Šibalić N, Melo N R, Kondo J M, Adams C S, Weatherill K J 2017 Nat. Photon. 11 40 Google Scholar

[1]	Liu Zhi-Hui, Liu Xiao-Na, He Jun, Liu Yao, Su Nan, Cai Ting, Du Yi-Jie, Wang Jie-Ying, Pei Dong-Liang, Wang Jun-Min. Tune-out wavelengths of Rydberg atoms. Acta Physica Sinica, 2024, 73(13): 130701. doi: 10.7498/aps.73.20240397
[2]	Wang Xin, Ren Fei-Fan, Han Song, Han Hai-Yan, Yan Dong. Perfect optomechanically induced transparency and slow light in an Rydberg atom-assisted optomechanical system. Acta Physica Sinica, 2023, 72(9): 094203. doi: 10.7498/aps.72.20222264
[3]	Fu Jing, Cai Yu-Long, Li Yu-Dong, Feng Jie, Wen Lin, Zhou Dong, Guo Qi. Single event transient effect of frontside and backside illumination image sensors under proton irradiation. Acta Physica Sinica, 2022, 71(5): 054206. doi: 10.7498/aps.71.20211838
[4]	Wang Kun, Duan Gao-Yan, Lang Pei-Lin, Zhao Yu-Fang, Liu Jian-Bin, Song Gang. Biosensor based on plasmonic Mach-Zehnder interferometer with metallic gratings. Acta Physica Sinica, 2022, 71(1): 017301. doi: 10.7498/aps.71.20211420
[5]	. Biosensor based on plasmonic Mach-Zehnder interferometer with metallic gratings. Acta Physica Sinica, 2021, (): . doi: 10.7498/aps.70.20211420
[6]	Wu Jian, Han Wen, Cheng Zhen-Zhen, Yang Bin, Sun Li-Li, Wang Di, Zhu Cheng-Peng, Zhang Yong, Geng Ming-Xin, Jing Yan. Structure optimization of carbon nanotube ionization sensor based on fluid model. Acta Physica Sinica, 2021, 70(9): 090701. doi: 10.7498/aps.70.20201828
[7]	Zhao Jia-Dong, Zhang Hao, Yang Wen-Guang, Zhao Jing-Hua, Jing Ming-Yong, Zhang Lin-Jie. Deceleration of optical pulses based on electromagnetically induced transparency of Rydberg atoms. Acta Physica Sinica, 2021, 70(10): 103201. doi: 10.7498/aps.70.20210102
[8]	Chao Xing-Bing, Pan Lu-Ping, Wang Zi-Sheng, Yang Feng-Tao, Ding Jian-Ping. Influence of pixelation effect of image sensor on resolution of Fresnel incoherent correlation holography. Acta Physica Sinica, 2019, 68(6): 064203. doi: 10.7498/aps.68.20181844
[9]	Yang Yi, Xu Ben, Liu Ya-Ming, Li Ping, Wang Dong-Ning, Zhao Chun-Liu. Sensitivity-enhanced temperature sensor with fiber optic Fabry-Perot interferometer based on vernier effect. Acta Physica Sinica, 2017, 66(9): 094205. doi: 10.7498/aps.66.094205
[10]	Cao Jiang-Wei, Wang Rui, Wang Ying, Bai Jian-Min, Wei Fu-Lin. Measurement and study of low-frequency noise in TMR magnetic field sensor. Acta Physica Sinica, 2016, 65(5): 057501. doi: 10.7498/aps.65.057501
[11]	Hao Xiao-Chen, Yao Ning, Ru Xiao-Yue, Liu Wei-Jing, Xin Min-Jie. Channel allocation game algorithm based on lifetime model in wireless sensor network. Acta Physica Sinica, 2015, 64(14): 140101. doi: 10.7498/aps.64.140101
[12]	Liu Hao-Ran, Yin Wen-Xiao, Dong Ming-Ru, Liu Bin. Study on the scale-free topology model with strong intrusion-tolerance ability in wireless sensor networks. Acta Physica Sinica, 2014, 63(9): 090503. doi: 10.7498/aps.63.090503
[13]	Liu Bin, Dong Ming-Ru, Liu Hao-Ran, Yin Rong-Rong, Han Li. A scale-free fault tolerant topology model in wireless sensor network for toleration of comprehensive fault. Acta Physica Sinica, 2014, 63(17): 170506. doi: 10.7498/aps.63.170506
[14]	Zeng Zhi-Wen, Liu Hai-Tao, Zhang Si-Wen. Design of extraordinary-optical-transimission refractive-index sensor of subwavelength metallic slit array based on a Fabry-Perot model. Acta Physica Sinica, 2012, 61(20): 200701. doi: 10.7498/aps.61.200701
[15]	Li Chang-Yong, Zhang Lin-Jie, Zhao Jian-Ming, Jia Suo-Tang. Measurement and theoretical calculation for Stark energy and electric dipole moment of Cs Rydberg state. Acta Physica Sinica, 2012, 61(16): 163202. doi: 10.7498/aps.61.163202
[16]	Wang Ya-Qi, Yang Xiao-Yuan. Study on a model of topology evolution of wireless sensor networks among cluster heads and its immunization. Acta Physica Sinica, 2012, 61(9): 090202. doi: 10.7498/aps.61.090202
[17]	Li Yong-Fang, Zhang Xiang-Yang, Sun Jian-Feng, Wang Yong-Fang. . Acta Physica Sinica, 2002, 51(4): 782-788. doi: 10.7498/aps.51.782
[18]	XING AI-TANG, HUANG XIANG-YOU, DONG TAI-QIAN. AC-STARK SHIFT OF LEVEL IN TWO-LEVEL ATOM UNDER THE INTERACTION OF MONO-MODE QUANTIZED FIELD. Acta Physica Sinica, 2000, 49(11): 2146-2150. doi: 10.7498/aps.49.2146
[19]	Fang Da-Wei, Dao Chang-Jian, Li Jing, Wang Yun-Xian, Chu Xiao-Feng, Xu Yun-Fei, Zhang Shen. . Acta Physica Sinica, 1995, 44(3): 365-374. doi: 10.7498/aps.44.365
[20]	DING GUANG-LIANG, LIU BING-MO, WANG JIA-MIN, GONG SHUN-SHENG. EXPERIMENTAL STUDY OF RELATIONS BETWEEN ｜ml｜ AND FIELD STARK IONIZATION THRESHOLD IN RYDBERG Cs ATOMS. Acta Physica Sinica, 1994, 43(11): 1754-1758. doi: 10.7498/aps.43.1754

Catalog

Vol. 73, Issue 9 - 2024-05-05

Metrics

Abstract views: 1001
PDF Downloads: 77
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板