基于冷里德堡原子电磁感应透明的微波电场测量

周飞; 贾凤东; 刘修彬; 张剑; 谢锋; 钟志萍

doi:10.7498/aps.72.20222059

摘要

在磁光阱中利用冷原子温度低, 多普勒展宽小的优势获得了窄线宽的里德堡电磁感应透明(EIT)谱峰, 结合Autler-Townes分裂效应(EIT-AT分裂)分别测量了多个频率的微波电场强度. 结果显示, EIT-AT分裂间距与微波电场强度呈很好的线性关系, EIT-AT分裂方法可测量的微波电场强度线性区的下限可达222$ {\text{μ}}{\rm{V}}/{\rm{c}}{\rm{m}} $, 这个下限比传统热原子蒸汽池中EIT-AT分裂线性区的下限5 $ {\rm{m}}{\rm{V}}/{\rm{c}}{\rm{m}} $提高了大约22倍, 这对极弱微波电场的绝对校准非常有帮助. 我们进一步利用EIT共振处探测光透过率的变化测量微波电场强度, 对应的最小测量值可以小于$ 1\;{\text{μ}}{\rm{V}}/{\rm{c}}{\rm{m}} $, 相应的灵敏度可达到1 μV·cm^–1·Hz^–1/2. 这些结果展示了冷原子样品在微波电场测量及其绝对校准方面的优势.

关键词:

Abstract

Microwave electric fields are measured by using cold Rydberg atoms. We obtain spindle-shaped cold atomic clouds in a magneto-optical trap and then pump the cold atoms to quantum state 5S_1/2, F = 2, m_F = 2 by using an optical-pump laser. We obtain the Rydberg electromagnetic induction transparency (EIT) spectrum peak with narrow linewidth by the low temperature and small residual Doppler broadening. The results show that the typical EIT linewidth with 16 μK cold atoms is about 460 kHz which is 15 times narrower than that of 7 MHz obtained in the thermal vapor cell. The microwave electric field amplitude is measured by Autler-Townes splitting (EIT-AT splitting) in the cold atoms at frequencies of 9.2, 14.2 and 22.1 GHz, receptively. The results show that there is a good linear relationship between the EIT-AT splitting interval and the microwave electric field amplitude. The lower limit of the microwave electric field amplitude that can be measured in the linear region can reach as low as 222 μV/cm, which is about 22 times larger than the lower limit in the traditional thermal vapor cell about of 5 mV/cm. The improvement of the lower limit by EIT-AT splitting method is roughly proportional to the narrowing EIT line width by cold atom samples. This demonstrates that benefiting from the smaller residual Doppler effect and the narrower EIT linewidth in cold atoms, the cold atom system is more advantageous in the experimental measuring of the weak microwave electric field amplitude by using the EIT-AT splitting method. This is of great benefit to the absolute calibration of very weak microwave electric fields. Furthermore, the lower limit of the microwave electric field amplitude that can be measured is smaller than 1 μV/cm by using the change of transmittance of the prober laser at the EIT resonance, and the corresponding sensitivity can reach 1 μV·cm^–1·Hz^–1/2. These results demonstrate the advantages of cold atomic sample in microwave electric field measurement and its absolute calibration.

Keywords:

microwave electric field Sensor /
Rydberg atom /
electromagnetically induced transparency

作者及机构信息

1.
中国科学院大学物理科学学院, 北京　100049

2.
清华大学核能与新能源技术研究院, 先进核能技术协同创新中心, 先进反应堆工程与安全教育部重点实验室, 北京　100084

3.
中国科学院大学, 中国科学院拓扑量子计算卓越中心, 北京　100190

通信作者: 贾凤东, fdjia@ucas.ac.cn ; 谢锋, fxie@tsinghua.edu.cn ;

基金项目: 北京市自然科学基金 (批准号: 1212014)、中国科学院重点研究计划(批准号: XDPB08-3)和中央高校基本科研业务费专项资金和国家重点研发计划(批准号: 2017YFA0304900, 2017YFA0402300)资助的课题.

Authors and contacts

1.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

2.
Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China

3.
China and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Jia Feng-Dong, fdjia@ucas.ac.cn ; Xie Feng, fxie@tsinghua.edu.cn ;

Funds: Project supported by the Natural Science Foundation of Beijing, China (Grant No. 1212014), the Key Research Program of the Chinese Academy of Sciences (Grant No. XDPB08-3), the Fundamental Research Funds for the Central Universities, and the National Key R&D Program of China (Grant Nos. 2017YFA0304900, 2017YFA0402300).

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施引文献

图 1 冷原子里德堡EIT的实验装置示意图. 一对方形梯度磁场线圈和三对MOT冷却光/再泵浦光将原子囚禁成一个长条形的冷原子云. 一对亥姆霍兹线圈(Bias 线圈)提供一个与冷原子云长轴方向平行的均匀弱磁场, 作为量子化轴. 探测光和耦合光相对传输, 并调整到与冷原子云长轴重合, 实验中利用1/4玻片将探测光和耦合光的偏振分别调节为σ⁺ 和σ ^–.

Fig. 1. Scheme of the cold Atom Rydberg EIT-AT experiments. A pair of square gradient magnetic field coils and three pairs of MOT light are used to cool and trap a cigar-shaped atom cloud. The Bias coil is used to provide a uniform weak magnetic field parallel to the long axis of the elongated cold atom cloud as the quantization axis. In the experiment, a 1/4 wave plate is used to change the polarization of the probe laser and coupling laser into σ⁺ and σ^–.

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图 2 冷原子样品制备的时序图及EIT-AT的实验过程

Fig. 2. Time schedule of preparation of cold atomic sample and procedure of EIT-AT experiments.

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图 3 本文进行微波测量所用到的能级图　(a) 微波频率为14.2 GHz时的能级图 (b) 微波频率为9.2 GHz时的能级图 (c) 微波频率为22. 1 GHz时的能级图

Fig. 3. Atomic energy level schemes of microwave measurements: (a) Atomic energy level scheme for microwave frequency at 14.2 GHz; (b) atomic energy level scheme of for microwave frequency at 9.2 GHz; (c) atomic energy level scheme of for microwave frequency at 22.1 GHz.

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图 4 冷原子中典型的EIT-AT分裂光谱. 图中的黄色、紫色、绿色、蓝色、红色和黑色曲线自上而下分别代表微波电场强度为0.007, 0.558, 1.114, 2.222, 3.523和5.583 mV/cm 时的测量结果. 冷原子实验中探测光的强度和光斑直径为500 nW和100 μm, 耦合光强度和光斑直径为60 mW和300 μm.

Fig. 4. Examples EIT-AT splitting spectra obtained in cold atoms with different microwave intensities. The yellow, purple, green, blue, red and black curves in the figure represent the measurement results when the microwave electric field intensity is 0.007, 0.558, 1.114, 2.222, 3.523 and 5.583 mV /cm, respectively. In the cold atom experiment, the power and diameter of the probe laser are 500 nW and 100 μm, respectively, the power and diameter of the coupling laser are 60 mW and 300 μm, respectively.

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图 5 微波频率为14.2 GHz时, 冷原子和热原子EIT-AT分裂测量结果的比较. 图中蓝色方框代表冷原子测量结果, 红色圆圈代表热原子测量结果. 具体实验参数如下: 冷原子实验中探测光的强度和光斑直径分别为500 nW和100 μm, 耦合光强度和光斑直径分别为60 mW和300 μm. 热原子实验中探测光的强度和光斑直径分别为60 μW和800 μm, 耦合光强度和光斑直径分别为40 mW 和900 μm. 热原子实验数据来自^[15]

Fig. 5. Comparison of EIT-AT splitting measurements results in cold and thermal atoms samples at microwave frequency of 14.2 GHz. The blue boxes represent the results in cold atomic sample and the red circles represent the results in hot atomic sample. The experimental parameters are as follows: In the cold atom experiment, the power and diameter of the probe laser are 500 nW and 100 μm, the power and diameter of the coupling laser are 60 mW and 300 μm; In the thermal atom experiment, the power and diameter of the probe laser are 60 μW and 800 μm, the power and diameter of the coupling laser are 40 mW and 900 μm. The data of the thermal atom experiment are taken from^[15].

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图 6 9.2 GHz的微波测量结果　(a) 通过EIT-AT分裂测量的结果, 蓝色方框代表实验结果, 测量线性区的下限可以到 (300±30) μV/cm. 红色实线代表线性公式(1)式的计算结果; (b) 通过EIT透明峰的探测光透过率测量的结果, 蓝色方框代表实验结果, 红色实线代表四能级模型结合多普勒效应的数值计算结果^[42]. 测量下限可以到(656±60 n) V/cm

Fig. 6. Microwave measurement results at 9.2 GHz by cold atoms: (a) Results measured by the EIT-AT splitting, the blue boxes represent the experimental results, the lower limit of the measurement linear region can achieve (300±30) μV/cm. The solid red line represents the calculation results of Eq. (1). (b) The measured results of the transmittance of the probe laser of the EIT peak. The blue boxes represent the experimental results and the red solid line represents the numerical calculation results of the four-level model combined with the Doppler effect ^[42]. The lower measurement limit can be achieved as (656±60) nV/cm.

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图 7 22.1 GHz的微波测量结果　(a) 通过EIT-AT分裂测量的结果, 蓝色方框代表实验结果, 线性区的下限可以测到 (312±20) μV/cm. 红色实线代表线性公式(1)的计算结果; (b) 通过探测光的透过率测量的结果, 蓝色方框代表实验结果, 红色实线代表四能级模型结合多普勒效应的数值计算结果, 测量的下限可以到 (297±21) nV/cm, 相应的灵敏度可达到1 μV·cm^–1·Hz^–1/2

Fig. 7. Microwave measurement results at 22.1 GHz by cold atoms: (a) Results measured by the EIT-AT splitting, the blue boxes represent the experimental results, the lower limit of the measurement linear region can achieve (312±20) μV/cm. The solid red line represents the calculation results of Eq. (1). (b) The measured results of the transmittance of the probe laser of the EIT transparency peak. The blue boxes represent the experimental results and the red solid line represents the numerical calculation results of the four-level model combined with the Doppler effect ^[42]. The lower measurement limit can be achieved (297±21) nV/cm. The corresponding sensitivity can reach 1 μV·cm^–1·Hz^–1/2.

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基于冷里德堡原子电磁感应透明的微波电场测量