Abstract:The quantum measurement of the electric field based on the electromagnetically induced transparency (EIT) effect of the Rydberg atom surpasses the limitations of traditional measuring methods in accuracy and sensitivity, offering self-calibration capability. Ideally, the electric fieldismeasured by stationary cold atoms. However, preparing cold atoms requires multi-lasersynergy and gradient magnetic field coils to reduce the atomtemperature, which needs complex experimental setups, precise operational techniques, and expensive equipment. Using hot atoms at room temperature is convenient in engineering applications. However, the atom’s thermal motion affects the relative velocity between atoms and lasers, resulting in the Doppler effect. Accordingly, frequency shifts and deformations in the EIT spectruminterfere with the coherent effect of the electric field. Mitigating the Doppler effectis essential to enhance the quantum measurement accuracy of theelectric field using hot Rydberg atoms. This paper proposes a method to correct the Doppler effect by adjusting the probe and coupling laserfrequencies. The density matrix equation is established based on the multiphot on interaction with atoms. By solving the equation and deriving the mathematical relationship among the absorption rate of the probe laser, the dispersion rate of the probe laser, and the frequency detuning of the coupled laser in the atomic system, an accurate description of the EIT effect is obtained. Then, the relationship between temperature and atomic motion is introduced to quantify the Doppler effect of atomic thermal motion, which convertsatomic thermal motion into the quantity of probe laser and coupled laser frequency detuning. The Doppler effect on the absorbance and dispersion of the atomic system is analyzed. Finally, the EIT spectrum is corrected by reverselyadjusting the input frequency parameters of lasers based on the calculated quantities. Simulations verify the effectiveness of the proposed method. The results show that the EIT absorption and dispersion curve line is asymmetric with the increase in temperature. Simultaneously, the deformation of the absorption curve reduces the depth of the absorption window and inhomogeneous broadening, leading to a frequency shift in the absorption spectrum. The proposed method corrects the anomalous trend of the dispersion and absorption spectra, eliminating the Doppler effect due to the atom’s thermal motion. The quantum measurement accuracy of the electric field is enhanced based on Rydberg atoms at room temperature, which promotes the engineering application process of quantum measurement.
阎晟, 肖冬萍, 石筑鑫, 张淮清, 刘卫华. 原子热运动对电场量子测量的影响及修正方法[J]. 电工技术学报, 2024, 39(10): 2953-2960.
Yan Sheng, Xiao Dongping, Shi Zhuxin, Zhang Huaiqing, Liu Weihua. Study on the Influence of Atomic Thermal Motion on Quantum Measurement of Electric Field and its Correction Method. Transactions of China Electrotechnical Society, 2024, 39(10): 2953-2960.
[1] 吴桂芳, 崔勇, 刘宏, 等. 基于差分进化算法的三维电场传感器解耦标定方法[J]. 电工技术学报, 2021, 36(19): 3993-4001. Wu Guifang, Cui Yong, Liu Hong, et al.Decoupling calibration method of 3D electric field sensor based on differential evolution algorithm[J]. Transactions of China Electrotechnical Society, 2021, 36(19): 3993-4001. [2] 杨圆, 高克利, 袁帅, 等. 典型电场下C4F7N/CO2/O2混合气体工频击穿特性研究[J]. 电工技术学报, 2022, 37(15): 3913-3922. Yang Yuan, Gao Keli, Yuan Shuai, et al.Research on the power frequency breakdown characteristics of C4F7N/CO2/O2 gas mixture under typical electric fields[J]. Transactions of China Electrotechnical Society, 2022, 37(15): 3913-3922. [3] 李国倡, 梁箫剑, 魏艳慧, 等. 配电电缆附件复合绝缘界面缺陷类型和位置对电场分布的影响研究[J]. 电工技术学报, 2022, 37(11): 2707-2715. Li Guochang, Liang Xiaojian, Wei Yanhui, et al.Influence of composite insulation interface defect types and position on electric field distribution of distribution cable accessories[J]. Transactions of China Electrotechnical Society, 2022, 37(11): 2707-2715. [4] 米彦, 葛欣, 刘露露, 等. 微秒脉冲电场强度对BNNSs取向程度和环氧树脂复合材料热导率的影响[J]. 电工技术学报, 2022, 37(6): 1533-1541. Mi Yan, Ge Xin, Liu Lulu, et al.Effect of microsecond pulsed electric field strength on the BNNSs orientation degree and the thermal con- ductivity of epoxy resin composites[J]. Transactions of China Electrotechnical Society, 2022, 37(6): 1533-1541. [5] 陈蔚, 黎卫国, 欣振宇, 等. GIL三支柱绝缘子电场仿真与表面电荷测量[J]. 高压电器, 2021, 57(11): 42-50. Chen Wei, Li Weiguo, Xin Zhenyu, et al.Electric field simulation and surface charge measurement of tri-post insulator in GIL[J]. High Voltage Apparatus, 2021, 57(11): 42-50. [6] 刘鹏, 吴泽华, 朱思佳, 等. 缺陷对交流1100kV GIL三支柱绝缘子电场分布影响的仿真[J]. 电工技术学报, 2022, 37(2): 469-478. Liu Peng, Wu Zehua, Zhu Sijia, et al.Simulation on electric field distribution of 1100kV AC tri-post insulator influenced by defects[J]. Transactions of China Electrotechnical Society, 2022, 37(2): 469-478. [7] Xue Fen, Hu Jun, Guo Yue, et al.Piezoelectric- piezoresistive coupling MEMS sensors for measure- ment of electric fields of broad bandwidth and large dynamic range[J]. IEEE Transactions on Industrial Electronics, 2020, 67(1): 551-559. [8] 吴昊, 齐波, 李成榕, 等. 基于Kerr效应法的油纸复合绝缘交直流复合电场测量[J]. 电工技术学报, 2013, 28(4): 28-34. Wu Hao, Qi Bo, Li Chengrong, et al.The measurement of AC-DC composite field for oil-paper insulation system based on the Kerr electro-optic effect[J]. Transactions of China Electrotechnical Society, 2013, 28(4): 28-34. [9] 林飞宏, 周吉, 张建培, 等. 反射式小型光学电场传感器[J]. 浙江大学学报(工学版), 2021, 55(11): 2207-2214. Lin Feihong, Zhou Ji, Zhang Jianpei, et al.Reflective miniature optical electric field sensor[J]. Journal of Zhejiang University(Engineering Science), 2021, 55(11): 2207-2214. [10] Bussey L W, Burton F A, Bongs K, et al.Quantum shot noise limit in a Rydberg RF receiver compared to thermal noise limit in a conventional receiver[J]. IEEE Sensors Letters, 2022, 6(9): 1-4. [11] Simons M T, Haddab A H, Gordon J A, et al.Embedding a Rydberg atom-based sensor into an antenna for phase and amplitude detection of radio-frequency fields and modulated signals[J]. IEEE Access, 2019, 7: 164975-164985. [12] Robinson A K, Prajapati N, Senic D, et al.Determining the angle-of-arrival of a radio-frequency source with a Rydberg atom-based sensor[J]. Applied Physics Letters, 2021, 118(11): 114001. [13] Rajasree K S, Karlsson K, Ray T, et al.1.6 GHz frequency scanning of a 482 nm laser stabilized using electromagnetically induced transparency[J]. IEEE Photonics Technology Letters, 2021, 33(15): 780-783. [14] Huang Chutian, Huang Bei, Zhang Bingsheng, et al.An electromagnetically induced transparency inspired antenna sensor for crack monitoring[J]. IEEE Sensors Journal, 2021, 21(1): 651-658. [15] Song Zhengyong, Chu Qiongqiong, Zhu C, et al.Polarization-independentterahertz tunable analog of electromagnetically induced transparency[J]. IEEE Photonics Technology Letters, 2019, 31(15): 1297-1299. [16] Ashkarin I N, Beterov I I, Yakshina E A, et al.Toffoli gate based on a three-body fine-structure-state- changing Förster resonance in Rydberg atoms[J]. Physical Review A, 2022, 106(3): 032601. [17] 焦月春, 赵建明, 贾锁堂. 基于Rydberg原子的超宽频带射频传感器[J]. 物理学报, 2018, 67(7): 137-145. Jiao Yuecun, Zhao Jianming, Jia Suotang.Broadband Rydberg atom-based radio-frequency field sensor[J]. Acta Physica Sinica, 2018, 67(7): 137-145. [18] Veit C, Epple G, Kübler H, et al.RF-dressed Rydberg atoms in hollow-core fibres[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2016, 49(13): 134005. [19] Hao Liping, Xue Yongmei, Fan Jiabei, et al.Precise measurement of a weak radio frequency electric field using a resonant atomic probe[J]. Chinese Physics B, 2020, 29(3): 033201. [20] 张淳刚, 李伟, 张好, 等. 基于调制射频场电磁诱导透明光谱的工频电场测量[J]. 光子学报, 2021, 50(6): 162-168. Zhang Chungang, Li Wei, Zhang Hao, et al.Power frequency electric field measurement based on electromagnetic induced transparent spectrum under radio frequency field[J]. Acta Photonica Sinica, 2021, 50(6): 162-168. [21] 李伟, 张淳刚, 张好, 等. 基于里德伯原子AC- Stark效应的工频电场测量[J]. 激光与光电子学进展, 2021, 58(17): 144-148. Li Wei, Zhang Chungang, Zhang Hao, et al.Power-frequency electric field measurement based on AC-stark effect of Rydberg atoms[J]. Laser & Optoelectronics Progress, 2021, 58(17): 144-148. [22] 崔帅威, 彭文鑫, 李松浓, 等. 基于里德堡原子的工频电场测量[J]. 高电压技术, 2023, 49(2): 644-650. Cui Shuaiwei, Peng Wenxin, Li Songnong, et al.Power frequency electric field measurement based on Rydberg atoms[J]. High Voltage Engineering, 2023, 49(2): 644-650. [23] Boller K, Imamolu A, Harris S E.Observation of electromagnetically induced transparency[J]. Physical Review Letters, 1991, 66(20): 2593-2596. [24] Li Y, Jin S, Xiao M.Observation of an electro- magnetically induced change of absorption in multilevel rubidium atoms[J]. Physical Review A, 1995, 51(3): 1754-1757. [25] Khoa D X, Trong P V, Doai L V, et al.Elec- tromagnetically induced transparency in a five-level cascade system under Doppler broadening: an analytical approach[J]. Physica Scripta, 2016, 91(3): 035401. [26] Hazra R, Hossain M M.Study of multi-window electromagnetically induced transparency (EIT) and related dispersive signals in V-type systems in the Zeeman sublevels of hyperfine states of 87 Rb-D2 line[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2020, 53(23): 235401. [27] Zhang Guiyin, Tao Qiyong, Zhao Zhanlong, et al.Effect of thermal motion on the phenomenon of electromagnetically induced transparency[J]. Optik, 2017, 138: 153-159. [28] Gea-banacloche J, Li Yongqing, Jin Shaozheng, et al. Electromagnetically induced transparency in ladder- type inhomogeneously broadened media: theory and experiment[J]. Physical Review A, 1995, 51(1): 576-584. [29] 赵嘉栋, 张好, 杨文广, 等. 基于里德伯原子电磁诱导透明效应的光脉冲减速[J]. 物理学报, 2021, 70(10): 99-107. Zhao Jiadong, Zhang Hao, Yang Wenguang, et al.Deceleration of optical pulses based on electro- magnetically induced transparency of Rydberg atoms[J]. Acta Physica Sinica, 2021, 70(10): 99-107.