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The electromagnetic induced transparency (EIT) to atomic systems and its various applications have been extensively investigated, both theoretically and experimentally. In this paper, we study how to similarly verify these phenomena in the waveguide coupled to the transmission line resonators. By making use of real space quantum scattering theory, we calculate the transmission spectrum of the waveguide photons scattered by a single quarter-wavelength transmission line resonator. Our experimental results show that the resonant microwave transporting along the feedline is completely reflected by the resonator. This is similar to the situation of the light absorbed by the resonant atomic medium, and thus its transmission is significantly suppressed. Like the EIT phenomena in atomic gas, wherein the resonant absorption can be significantly suppressed by applying a strong pumping light to control the optical properties of medium, the transport properties of the resonant microwave can be investigated by coupling it into an auxiliary quarter-wavelength resonator in this paper. If the frequency of the auxiliary quarter-wavelength resonator is different from the resonant frequency, the calculated transmission spectrum shows that the coupling with auxiliary quarter-wavelength resonator induces the complete transmission of the resonant microwave. This is one of the features of the EIT-like effect, and can be simply explained as the frequency renormalization of the coupling resonators. Also, by adjusting the coupling strength between the resonators, the width of the microwave transmission spectrum window can be manipulated. Our experimental observations verify such an argument, but the phase shift mutation (another typical signs of the EIT effect) of the resonant microwave cannot be observed. In physics, this is because the interference between the transmitted microwave and the reflected micowave with different frequencies does not take place in the coupling region between the two resonators. It is expected that the effects with the complete EIT-like phenomena can be observed, in future, by fabricating the sample of two quarter-wavelength transmission line resonators with the same frequency, and thus the coupling between the two resonators can be controlled. -
Keywords:
- electromagnetic induced transparency /
- quarter wavelength microwave resonators /
- real space quantum transport theory /
- coupled-induced transport transparency
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Google Scholar
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图 1 单个四分之一波长谐振腔与波导的耦合示意图, 其中谐振腔的中心导体一端经电容与馈线波导耦合, 另一端则直接与零电位导体连接
Figure 1. Travelling waves scattered by a single quarter wavelength resonator, the load end of the device is capacitively coupled to the feedline and another end is grounded.
图 2 左、右行光子与谐振器有效耦合强度的比值不同时, 馈线中传输微波光子的透射谱
Figure 2. Transmission spectra of microwave transporting along the feedline scattered by a single quarter wavelength resonator with different coupling strengths for the left (right) travelling photons.
图 3 单个四分之一波长共面波导谐振器样品图, 图中打红叉的谐振器已经短接
Figure 3. Sample diagram of single quarter wavelength coplanar waveguide resonator. The resonators with the red crosses have been shorted.
图 4 单个四分之一波长共面波导谐振器
$S_{21}$ 参数曲线图(即透射谱) (a) 4.0 GHz谐振器的$S_{21}$ ; (b) 4.05 GHz谐振器的$S_{21}$ Figure 4. Experimentally measured transmission curves of two single quarter wavelength coplanar waveguide resonators with the frequencies being
$4.0$ GHz (a) and$4.05$ GHz (b), respectively.
图 5 两个插指耦合四分之一波长共面波导谐振腔对波导中行波微波的散射构型, 这里, 谐振腔的中心导体的一端经耦合电容与波导耦合, 另一端与地短路
Figure 5. Configuration of the travelling microwaves transporting along the waveguide scattered by the fingerly coupled quarter-wavelength coplanar waveguide resonators. Here, one end of the central conductor of the resonator is coupled to waveguide via a coupling capacitance, and the other end is directly grounded.
图 6 两个不同本征频率的耦合谐振器透射谱图, 两透射谷之间的频率间隔随着耦合强度的增加而增大
Figure 6. Transmission spectra of the microwave scattered by two coupled resonators with different eigenfrequencies. It is seen that the frequency interval between the two dips increases with the coupling strength between the resonators.
图 7 两个共振频率不同的耦合四分之一波长共面波导谐振器的样品图(图中打红叉的谐振器已经短接)
Figure 7. Experimental sample of two quarter wavelength coplanar waveguide resonators with different resonant frequencies. The resonators with the red crosses have been shorted.
图 8 两个耦合四分之一波长共面波导谐振器的微波透射谱
Figure 8. Coupled sample diagram of two quarter wavelength coplanar waveguide resonators.
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[1] Harris S E 1989 Phys. Rev. Lett. 62 1033
Google Scholar
[2] Boller K J, Imamoğlu A, Harris S E 1991 Phys. Rev. Lett. 66 2593
[3] Guo Y H, Yan L S, Pan W, Luo B, Wen K H, Guo Z, Luo X G 2012 Opt. Express 20 24348
Google Scholar
[4] Wang T L, Cao M Y, Zhang Y P, Zhang H Y 2019 Opt. Mater. Express 9 1562
Google Scholar
[5] Di K, Xie C D, Zhang J 2011 Phys. Rev. Lett. 106 153602
Google Scholar
[6] Zhao C Y, Zhang L, Zhang C M 2019 Pramana-J. Phys. 92 37
Google Scholar
[7] Yan B, Gao F, Xu T, Ma H F, Zhong K S, Zheng Z X 2019 Mater. Res. Express. 6 115802
Google Scholar
[8] 邸克 2013 博士学位论文 (太原: 山西大学)
Di K 2013 Ph. D. Dissertation (Taiyuan: Shanxi University) (in Chinese)
[9] 詹孝贵 2013 博士学位论文 (武汉: 华中科技大学)
Zhan X G 2013 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese)
[10] Zheng C, Jiang X S, Hua S Y, Chang L, Li G Y, Fan H B, Xiao M 2012 Opt. Express 20 18319
Google Scholar
[11] 赵嘉栋, 张好, 杨文广, 赵婧华, 景明勇, 张临杰 2021 物理学报 70 103201
Google Scholar
Zhao J D, Zhang H, Yang W G, Zhao J H, Jing M Y, Zhang L J 2021 Acta Phys. Sin. 70 103201
Google Scholar
[12] Zang T C, Chen Y Q, Ding Y Q, Sun Y, Wu Q Y 2020 AIP Adv. 10 115002
Google Scholar
[13] Abdul J, Rashad R, Omar S, Muhammad A, Farooq A T 2021 Sci. Rep. 11 2983
Google Scholar
[14] Li H J, Wang Y W, Wei L F, Zhou P J, Wei Q, Cao C H, Fang Y R, Yu Y, Wu P H 2013 Chin. Sci. Bull. 58 2413
[15] Liu X, Guo W, Wang Y, Dai M, Wei L F, Dober B, McKenney C M, Hilton G C, Hubmayr J, Austermann J E, Ullom J N, Gao J, Vissers M R 2017 Appl. Phys. Lett. 111 252601
Google Scholar
[16] Gao J S 2008 Ph. D. Dissertation (Pasadena: California Institute of Technology)
[17] Gao H Y, Zhai D H, Gao J S, Wei L F 2020 J. Appl. Phys. 128 214302
Google Scholar
[18] Srinivasan K, Painter O 2007 Nuture 450 862
Google Scholar
[19] Choi Y S, Davano M, Lee K H 2007 Appd. Phys. Lett. 90 191108
Google Scholar
[20] Shen J T, Fan S 2009 Phys. Rev. A. 79 023837
Google Scholar
[21] Shen J T, Fan S 2005 Phys. Rev. Lett. 95 213001
Google Scholar
[22] Yan C H, Wei L F, Jia W Z, Shen J T 2011 Phys. Rev. A 84 045801
Google Scholar
[23] Lodahl P, Mahmoodian S, Stobbe S, Rauschenbeutel A, Schneeweiss P, Volz J, Pichler H, Zoller P 2017 Nature 541 473
Google Scholar
[24] 梁浩, 李剑生, 郭云胜 2015 物理学报 64 144101
Google Scholar
Liang H, Li J S, Guo Y S 2015 Acta Phys. Sin. 64 144101
Google Scholar
[25] Zheng H, Baranger H U 2013 Phys. Rev. Lett. 110 113601
Google Scholar
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