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The large electric dipole moment of the Rydberg atom allows for strong coupling with weak electric fields, and is widely used in electric field measurements because of its reproducibility, precision and stability. The combination of Rydberg atoms and electromagnetically induced transparency (EIT) technology has been used for detecting and characterizing radio-frequency (RF) electric fields. In this work, by selecting probe light (852 nm), dressed light (1470 nm), and coupled light (780 nm), the Rydberg state (49P3/2) of Cs atom is prepared by using a three-photon excitation scheme through using all-infrared light excitation of Rydberg atoms. We experimentally observe the EIT spectra of the Rydberg states decorated by radio-frequency electric fields, which optically detects Rydberg atoms. The effect of the amplitude and frequency of the RF electric field on the spectrum is explored in light of changes in the EIT spectrum. The results show that in the region of weak electric field, only the ac Stark energy shift and spectral broadening occur. As the electric field is further enhanced, the sideband phenomenon occurs in both the primary peak and secondary peak of the EIT. In the region of strong field, the Rydberg energy level produces a series of Floquet states with higher-order terms, as well as state shifting and mixing, resulting in asymmetry in the spectra of the EIT sideband peaks. The effect of frequency on the shielding effect of the Cs vapor cell is further discussed based on the shift of the main peak of the EIT. The demodulation of the electric field in a range of 50 Hz–1 kHz with a fidelity of 95% is achieved by modulating the low-frequency electric field to the RF electric field. The results can provide valuable references for spectral detection and traceable measurements of low-frequency electric fields. -
Keywords:
- Rydberg atoms /
- electromagnetically induced transparency spectroscopy /
- radio-frequency fields /
- ac Stark energy shift
[1] Gallagher T F 1994 Rydberg Atoms (Cambridge: Cambridge University Press
[2] Adams C S, Pritchard J D, Shaffer J P 2020 J. Phys. B: At. Mol. Opt. Phys. 53 012002
Google Scholar
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Google Scholar
[4] Yuan J, Yang W, Jing M, Zhang H, Jiao Y, Li W, Zhang L, Xiao L, Jia S 2023 Rep. Prog. Phys. 86 106001
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[5] Mohapatra A K, Jackson T R, Adams C S 2007 Phys. Rev. Lett. 98 113003
Google Scholar
[6] Sedlacek J A, Schwettmann A, Kübler H, Löw R, Pfau T, Shaffer J P 2012 Nat. Phys. 8 819
Google Scholar
[7] Kumar S, Fan H, Kübler H, Sheng J, Shaffer J P 2017 Sci. Rep. 7 42981
Google Scholar
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Google Scholar
[9] Gordon J A, Simons M T, Haddab A H, Holloway C L 2019 AIP Adv. 9 045030
Google Scholar
[10] Sedlacek J A, Schwettmann A, Kübler H, Shaffer J P 2013 Phys. Rev. Lett. 111 063001
Google Scholar
[11] Simons M T, Haddab A H, Gordon J A, Novotny D, Holloway C L 2019 IEEE Access 7 164975
Google Scholar
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Google Scholar
[13] Artusio-Glimpse A, Simons M T, Prajapati N, Holloway C L 2022 IEEE Microwave Mag. 23 44
Google Scholar
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Google Scholar
[15] Holloway C L, Simons M T, Kautz M D, Haddab A H, Gordon J A, Crowley T P 2018 Appl. Phys. Lett. 113 094101
Google Scholar
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Google Scholar
[17] Zhang L H, Liu Z K, Liu B, Zhang Z Y, Guo G C, Ding D S, Shi B S 2022 Phys. Rev. Appl. 18 014033
Google Scholar
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Google Scholar
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Google Scholar
[20] Shaffer J, Kübler H 2018 A Read-out Enhancement for Microwave Electric Field Sensing with Rydberg Atoms (Vol. 10674) (SPIE
[21] Ripka F, Amarloo H, Erskine J, Liu C, Ramirez-Serrano J, Keaveney J, Gillet G, Kübler H, Shaffer J 2021 Application-driven Problems in Rydberg Atom Electrometry (Vol. 11700) (SPIE
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Google Scholar
[23] Hu J, Li H, Song R, Bai J, Jiao Y, Zhao J, Jia S 2022 Appl. Phys. Lett. 121 014002
Google Scholar
[24] Carr C, Tanasittikosol M, Sargsyan A, Sarkisyan D, Adams C S, Weatherill K J 2012 Opt. Lett. 37 3858
Google Scholar
[25] Xu J H, Gozzini A, Mango F, Alzetta G, Bernheim R A 1996 Phys. Rev. A 54 3146
Google Scholar
[26] Pearman C P, Adams C S, Cox S G, Griffin P F, Smith D A, Hughes I G 2002 J. Phys. B: At. Mol. Opt. Phys. 35 5141
Google Scholar
[27] Robertson E J, Šibalić N, Potvliege R M, Jones M P A 2021 Comput. Phys. Commun. 261 107814
Google Scholar
[28] 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
[29] 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
[30] Daschner R, Ritter R, Kübler H, Frühauf N, Kurz E, Löw R, Pfau T 2012 Opt. Lett. 37 2271
Google Scholar
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Google Scholar
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Google Scholar
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图 1 (a) Cs原子阶梯型四能级示意图; (b) 实验装置示意图, 其中DM为二向色镜, PD为光电探测器
Figure 1. (a) Ladder-type four-level energy diagram of Cs atom; (b) schematic diagram of experimental apparatus, where DM is dichroic mirror, PD is photodiode detector.
图 2 不同强度的射频电场作用下Rydberg原子的EIT光谱 (a) E = 0 V/cm; (b) E = 25 V/cm; (c) E = 50 V/cm; (d) E = 100 V/cm; (e) E = 200 V/cm
Figure 2. EIT spectra of Rydberg atoms under different intensity RF electric fields: (a) E = 0 V/cm; (b) E = 25 V/cm; (c) E = 50 V/cm; (d) E = 100 V/cm; (e) E = 200 V/cm.
图 3 不同正弦射频电场情况下测量的EIT谱线随电场强度的变化 (a) ωRF = 30 MHz; (b) ωRF = 40 MHz; (c) ωRF = 50 MHz; (d) ωRF = 60 MHz
Figure 3. The variation of EIT spectral lines measured with the electric field intensity under different sinusoidal radio-frequency electric fields: (a) ωRF = 30 MHz; (b) ωRF = 40 MHz; (c) ωRF = 50 MHz; (d) ωRF = 60 MHz.
图 4 EIT主峰的能移与射频电场频率的关系
Figure 4. Relationship between frequency shift of EIT main peak and frequency of RF electric field.
图 5 不同频率电场作用下的EIT透射信号 (a) 50 Hz; (b) 100 Hz; (c) 500 Hz; (d) 1 kHz
Figure 5. EIT transmission signals under different frequency electric fields: (a) 50 Hz; (b) 100 Hz; (c) 500 Hz; (d) 1 kHz.
表 1 ARC软件包计算Cs原子直流极化率
Table 1. Theoretical calculation of dc polarizabilities for Cs by Alkali Rydberg Calculator Python package.
Cs原子直流极化率α/(Hz·V–2·m–2) Rydberg 态 49P1/2, |mj|=1/2 49P3/2, |mj|=1/2 49P3/2, |mj|=3/2 极化率 α: dc 74979.842 107095.687 89150.196 
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表 2 拟合正弦函数得到的振幅、频率等参数
Table 2. The parameters of amplitude and frequency are obtained by fitting the sinusoidal function.
拟合参数 频率 50 Hz 100 Hz 500 Hz 1000 Hz 振幅/V 0.0153 ± 0.0001 0.0182 ± 0.0001 0.0188 ± 0.0002 0.0173 ± 0.0001 频率/Hz 49.78 ± 0.09 100.18 ± 0.08 500.01 ± 0.09 1000.02 ± 0.07 R 2 (COD) 0.94356 0.95435 0.93143 0.9554
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[1] Gallagher T F 1994 Rydberg Atoms (Cambridge: Cambridge University Press
[2] Adams C S, Pritchard J D, Shaffer J P 2020 J. Phys. B: At. Mol. Opt. Phys. 53 012002
Google Scholar
[3] Liu B, Zhang L, Liu Z, Deng Z, Ding D, Shi B, Guo G 2023 Electromagn. Sci. 1 1
Google Scholar
[4] Yuan J, Yang W, Jing M, Zhang H, Jiao Y, Li W, Zhang L, Xiao L, Jia S 2023 Rep. Prog. Phys. 86 106001
Google Scholar
[5] Mohapatra A K, Jackson T R, Adams C S 2007 Phys. Rev. Lett. 98 113003
Google Scholar
[6] Sedlacek J A, Schwettmann A, Kübler H, Löw R, Pfau T, Shaffer J P 2012 Nat. Phys. 8 819
Google Scholar
[7] Kumar S, Fan H, Kübler H, Sheng J, Shaffer J P 2017 Sci. Rep. 7 42981
Google Scholar
[8] Tanasittikosol M, Pritchard J D, Maxwell D, Gauguet A, Weatherill K J, Potvliege R M, Adams C S 2011 J. Phys. B: At. Mol. Opt. Phys. 44 184020
Google Scholar
[9] Gordon J A, Simons M T, Haddab A H, Holloway C L 2019 AIP Adv. 9 045030
Google Scholar
[10] Sedlacek J A, Schwettmann A, Kübler H, Shaffer J P 2013 Phys. Rev. Lett. 111 063001
Google Scholar
[11] Simons M T, Haddab A H, Gordon J A, Novotny D, Holloway C L 2019 IEEE Access 7 164975
Google Scholar
[12] Jing M, Hu Y, Ma J, Zhang H, Zhang L, Xiao L, Jia S 2020 Nat. Phys. 16 911
Google Scholar
[13] Artusio-Glimpse A, Simons M T, Prajapati N, Holloway C L 2022 IEEE Microwave Mag. 23 44
Google Scholar
[14] Gordon J A, Holloway C L, Schwarzkopf A, Anderson D A, Miller S, Thaicharoen N, Raithel G 2014 Appl. Phys. Lett. 105 024104
Google Scholar
[15] Holloway C L, Simons M T, Kautz M D, Haddab A H, Gordon J A, Crowley T P 2018 Appl. Phys. Lett. 113 094101
Google Scholar
[16] Meyer D H, Kunz P D, Cox K C 2021 Phys. Rev. Appl. 15 014053
Google Scholar
[17] Zhang L H, Liu Z K, Liu B, Zhang Z Y, Guo G C, Ding D S, Shi B S 2022 Phys. Rev. Appl. 18 014033
Google Scholar
[18] Song Z, Liu H, Liu X, Zhang W, Zou H, Zhang J, Qu J 2019 Opt. Express 27 8848
Google Scholar
[19] Otto J S, Hunter M K, Kjærgaard N, Deb A B 2021 J. Appl. Phys. 129 154503
Google Scholar
[20] Shaffer J, Kübler H 2018 A Read-out Enhancement for Microwave Electric Field Sensing with Rydberg Atoms (Vol. 10674) (SPIE
[21] Ripka F, Amarloo H, Erskine J, Liu C, Ramirez-Serrano J, Keaveney J, Gillet G, Kübler H, Shaffer J 2021 Application-driven Problems in Rydberg Atom Electrometry (Vol. 11700) (SPIE
[22] Liu B, Zhang L H, Liu Z K, Zhang Z Y, Zhu Z H, Gao W, Guo G C, Ding D S, Shi B S 2022 Phys. Rev. Appl. 18 014045
Google Scholar
[23] Hu J, Li H, Song R, Bai J, Jiao Y, Zhao J, Jia S 2022 Appl. Phys. Lett. 121 014002
Google Scholar
[24] Carr C, Tanasittikosol M, Sargsyan A, Sarkisyan D, Adams C S, Weatherill K J 2012 Opt. Lett. 37 3858
Google Scholar
[25] Xu J H, Gozzini A, Mango F, Alzetta G, Bernheim R A 1996 Phys. Rev. A 54 3146
Google Scholar
[26] Pearman C P, Adams C S, Cox S G, Griffin P F, Smith D A, Hughes I G 2002 J. Phys. B: At. Mol. Opt. Phys. 35 5141
Google Scholar
[27] Robertson E J, Šibalić N, Potvliege R M, Jones M P A 2021 Comput. Phys. Commun. 261 107814
Google Scholar
[28] 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
[29] 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
[30] Daschner R, Ritter R, Kübler H, Frühauf N, Kurz E, Löw R, Pfau T 2012 Opt. Lett. 37 2271
Google Scholar
[31] Yoshida S, Reinhold C O, Burgdörfer J, Ye S, Dunning F B 2012 Phys. Rev. A 86 043415
Google Scholar
[32] Jau Y Y, Carter T 2020 Phys. Rev. Appl. 13 054034
Google Scholar
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