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在室温铯原子气室中利用探测光(852 nm)与耦合光(510 nm)构建的里德伯阶梯型结构, 实现了基于射频场缀饰的直流电场Floquet-电磁诱导透明(Floquet-electromagnetically induced transparency, Floquet-EIT)光谱, 并研究了直流电场下的Floquet-EIT光谱特性. 实验发现, 仅射频电场作用时, EIT光谱只呈现偶数阶边带, 而当射频场与直流电场同时作用时, 实验观测到Floquet-EIT的一阶边带信号. 随着直流电场强度增大, 一阶边带幅值逐渐升高. 然而, 当直流电场增大到一定强度时, 强电场会导致边带间相互串扰, 使边带幅值下降, 但增大射频频率可以延缓直流电场对一阶边带的串扰影响. 最后对比Floquet-EIT光谱的边带幅值与DC-Stark光谱的频率偏移在微弱直流电场下的相对标准偏差, 发现前者在微弱电场下的测量精确度明显优于后者. 本文工作为直流电场和低频电场的量子传感测量提供了新思路.
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关键词:
- 里德伯原子 /
- 电磁诱导透明 /
- Floquet-电磁诱导透明边带 /
- 射频调制
A Rydberg atom is a special type of atom characterized by a high principal quantum number. Electric field sensors based on Rydberg atoms have received widespread attention due to their high polarizability. However, there is currently little research on the use of Rydberg atoms for direct current (DC) or low-frequency electric fields, mainly due to the shielding effect of atomic vapor cells in low-frequency electric fields, which makes accurate measurement of the electric fields extremely challenging. In this paper, we construct a Rydberg ladder configuration by using probe laser at 852 nm and coupling laser at 510 nm in a room-temperature cesium vapor cell with integrated electrode plates, thereby enabling the realizing of a Floquet-EIT (electromagnetically induced transparency) spectrum dressed by a radio frequency (RF) field in the presence of a DC electric field. We further study the influence of DC electric field on spectral characteristic. Experimentally, it is observed that when only the RF electric field is applied, the EIT spectrum displays solely even-order sidebands. Furthermore, when both the RF field and the DC electric field are simultaneously present, the first-order sideband signal of the Floquet-EIT is observed. As the intensity of the DC electric field increases, the amplitude of the first-order sideband gradually increases. However, increasing the DC electric field to a sufficient magnitude induces sideband interference, which leads the sideband amplitudes to decrease. Furthermore, increasing the RF frequency can alleviate the interference effects induced by the DC electric field on the first-order sideband. Finally, comparing the relative standard deviation of the sideband amplitudes of the Floquet-EIT spectra with the frequency shifts of the DC-Stark spectra under weak DC electric fields, we find that the measurement accuracy of the former is significantly superior to that of the latter. This work makes use of a Cs atomic vapor cell with an integrated electrode to avoid shielding effects. By observing Floquet-EIT spectra, the response of the spectra to DC electric fields is investigated. This experiment provides novel insights into the quantum sensing measurements of DC and low-frequency electric fields. -
Keywords:
- Rydberg atoms /
- electromagnetically induced transparency /
- Floquet-electromagnetically induced transparency sideband /
- radio-frequency modulation
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 里德伯原子EIT能级示意图 (a)和实验装置图(b) OI, 光隔离器; ${\lambda {/ } 2}$, 半波片; PBS, 偏振分光棱镜; M, 852 nm高反镜; SG, 信号发生器; DM, 二向色镜; PD, 光电探测器; SP, 整形棱镜
Fig. 1. Schematic diagram of Rydberg EIT energy levels (a) and experimental setup diagram (b). OI, optical isolator; ${\lambda {/ } 2}$, half-wave plate; PBS, polarization beam splitter; M, 852 nm high reflectivity mirror; SG, signal Generator; DM, dichroic mirror; PD, photodiode; SP, shaping prism.
图 2 原子气室中内置极板间的电场模拟分布(a)和模拟电压云图(b)
Fig. 2. Simulated distribution of electric field between the built-in plates in the atomic cell (a) and simulated voltage cloud map (b).
图 3 基于DC-Stark效应的EIT光谱频移图 (a)不同DC电场强度下的EIT光谱; (b) DC电场强度和EIT光谱频移的关系
Fig. 3. EIT Spectral frequency shift based on DC Stark effect: (a) EIT spectra with different DC electric field intensity; (b) the relationship between DC electric field intensity and EIT spectral frequency shift.
图 4 在200 MHz下基于AC-Stark效应, 不同RF电场强度的EIT光谱 (a)Erf = 0 V/cm; (b) Erf = 1.8 V/cm; (c) Erf = 3.04 V/cm
Fig. 4. EIT spectra based on the AC-Stark effect at 200 MHz with different RF electric field intensity: (a) Erf = 0 V/cm; (b) Erf = 1.8 V/cm; (c) Erf = 3.04 V/cm.
图 5 Erf为2.58 V/cm的RF电场与DC电场同时作用产生的Floquet-EIT边带, 黑线和红线分别代表Edc为0.37 V/cm和0.74 V/cm的实验结果
Fig. 5. Floquet-EIT sidebands generated by the simultaneous action of RF electric field with Erf is 2.58 V/cm and DC. The black and red lines represent the experimental results with Edc values of 0.37 V/cm and 0.74 V/cm, respectively.
图 6 不同DC电场强度对一阶边带的影响 (a) DC电场强度与一阶边带幅值的对应关系; (b) DC电场强度与一阶边带FWHM的对应关系
Fig. 6. The effect of different DC electric fields on the first-order sidebands: (a) The correspondence between DC electric field intensity and first-order sideband amplitude; (b) the correspondence between DC electric field intensity and first-order sideband FWHM.
表 1 DC-Stark频移与Floquet-EIT边带幅值在不同DC电场下的相对标准偏差对比
Table 1. Comparison of the RSD of DC-Stark shift and Floquet-EIT sideband amplitude with different DC electric fields.
不同方法的RSD DC电场强度/(V·cm–1) 0.56 1.11 1.48 DC-Stark的频移/% 8.5 3.8 1.4 Floquet-EIT的
+1阶边带幅值/%0.9 1.7 0.8 
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[1] Prajapati N, Robinson A K, Berweger S, Simons M T, Artusio-Glimpse A B, Holloway C L 2021 Appl. Phys. Lett. 119 214001
Google Scholar
[2] Teale C, Sherman J, Kitching J 2022 AVS Quantum Sci. 4 024403
Google Scholar
[3] Liu X B, Jia F D, Zhang H Y, Mei J, Liang W C, Zhou F, Yu Y H, Liu Y, Zhang J, Xie F 2022 Chin. Phys. B 31 090703
Google Scholar
[4] Viteau M, Radogostowicz J, Bason M G, Malossi N, Ciampini D, Morsch O, Arimondo E 2011 Opt. Express 19 006007
Google Scholar
[5] Li L, Jiao Y C, Hu J L, Li H Q, Shi M, Zhao J M, Jia S T 2023 Opt. Express 31 29228
Google Scholar
[6] Holloway C L, Gordon J A, Jefferts S, Schwarzkopf A, Anderson D A, Miller S A 2014 IEEE Trans. Antennas Propag. 62 6169
Google Scholar
[7] Kai Y L, Hai T T, Shu Z Y, Chang J C, Xiao H L, Jie L, Xin D Z, Hui Y, Shi L Z 2020 Phys. Rev. A 101 053432
Google Scholar
[8] 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
[9] 王延正, 武博, 付云起, 安强 2025 激光与光电子学进展 62 0302001
Google Scholar
Wang Y Z, Wu B, Fu Y Q, An Q 2025 Laser Optoelectron. Prog. 62 0302001
Google Scholar
[10] Kumar S, Fan H, Kübler H, Jahangiri A J, Shaffer J P 2017 Opt. Express 25 8625
Google Scholar
[11] 吴逢川, 林沂, 武博, 付云起 2022 物理学报 71 207402
Google Scholar
Wu F C, Lin Y, Wu B, Fu Y Q 2022 Acta Phys. Sin. 71 207402
Google Scholar
[12] 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
[13] Hao J H, Jia F D, Cui Y, Wang Y H, Zhou F, Liu X B, Zhang J, Xie F, Bai J H, You J Q, Wang Y, Zhong Z P 2024 Chin. Phys. B 33 050702
Google Scholar
[14] 杨智伟, 焦月春, 韩小萱, 赵建明, 贾锁堂 2017 物理学报 66 093202
Google Scholar
Yang Z W, Jiao Y C, Han X X, Zhao J M, Jia S T 2017 Acta Phys. Sin. 66 093202
Google Scholar
[15] 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
Li W, Zhang C G, Zhang H, Jing M Y, Zhang L J 2021 Laser Optoelectron. Prog. 58 1702002
[16] Jau Y Y, Carter T 2020 Phys. Rev. Appl. 13 054034
Google Scholar
[17] Holloway C L, Prajapati N, Sherman J A, Rufenacht A, Artusio-Glimpse A B, Simons M T, Robinson A K, David S L M, Norrgard E B 2022 AVS Quantum Sci. 4 034401
Google Scholar
[18] Ouyang K, Shi Y S, Lei M W, Shi M 2023 Appl. Phys. Lett. 123 264001
Google Scholar
[19] Luo X B, Li L P, You L, Wu B 2014 New J. Phys. 16 013007
Google Scholar
[20] Rotunno A P, Berweger S, Prajapati N, Simons M T, Artusio-Glimpse A B, Holloway C L, Jayaseelan M, Potvliege R M, Adams C S 2023 J. Appl. Phys. 134 134501
Google Scholar
[21] Veit C, Epple G, Kübler H, Euser T G, Russell P S J, Löw R 2016 J. Phys. B 49 134005
Google Scholar
[22] 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
[23] Miller S A, Anderson D A, Raithel G 2016 New J. Phys. 18 053017
Google Scholar
[24] Song D N, Jiao Y C, Hu J L, Yin Y W, Li Z H, He Y H, Bai J X, Zhao J M, Jia S T 2024 Appl. Phys. Lett. 125 194001
Google Scholar
[25] Liu W X, Zhang L J, Wang T 2023 Chin. Phys. B 32 053203
Google Scholar
[26] Šibalić N, Pritchard J D, Weatherill K J, Adams C S 2017 Comput. Phys. Commun. 220 319
Google Scholar
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