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Elastic scattering is one of the useful approach to control the transmission behavior of microwave photons transporting in microwave quantum networks without energy consumption. Therefore, it has practical significance for the development of microwave quantum devices and the construction of multi-node microwave quantum networks. In view of the existence of the same device, specifically the transmission line embedded by a single Josephson junction, could be described by different circuit models (the series and parallel ones), in this paper we first theoretically analyze the transporting feature for the microwave photons being scattered by the different elastic scattering model, described by either the series or the parallel embedding models, generated by a single LC loop and a nonlinear Josephson junction device, respectively. The classical microwave transport theory predicts that, the series LC loop and the parallel LC loop lead to different microwave photon elastic scattering behaviors, i.e., the series LC circuit yields the resonant reflection and the parallel LC circuit leading alternatively to the resonant transmission. Recently, the transport properties of microwave photons scattered by a Josephson junction embedded in a transmission line had been discussed, and the results suggested that the Josephson junction embedded in the transmission line should be described by a series embedding circuit, which implies the resonant reflection. We argue here that, if the Josephson junction is embedded in parallel in the transmission line, the elastically scattered microwave photons should be transmitted by resonant transmission. In order to test which of the above two different embedding circuit models, yielding the completely different elastic scattering behaviors, is physically correct, we then fabricated such a device, i.e., a single Joseph junction device embedded in a transmission line is prepared, and measured its elastic scattering transmission coefficient at extremely low temperature. The results are consistent with the expected effects of the parallel embedding circuit model, but conflicted with the behaviors predicted by the series embedding circuit model in the literature. Based on the above theoretical and experimental analysis on the elastic scattering of a single Josephson junction device, we further propose a scheme to control the elastic scattering behavior of microwave photons by modulating a DC superconducting quantum interference device with a bypass current, which could be applied to the construction of a microwave quantum network based on elastic scattering node controls.
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Keywords:
- elastic scattering /
- microwave photons /
- Josephson junction /
- superconducting quantum interference device
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图 1 (a) 单节点的微波光子弹性散射等效电路模型, 黑色框代表散射体; (b) 传统的微波散射的二端口网络模型
Figure 1. (a) The single-node microwave photonic elastic scattering equivalent circuit model, with the black box representing the scatterer; (b) The usual microwave scattering two-port networks model.
图 2 (a) 无限长传输线中串联嵌入线性LC回路的等效电路模型示意图; (b) 串联嵌入线性LC回路对微波光子弹性散射的反射谱和透射谱, 内嵌图为与之相对应的相移谱. 这里, 相关参数设置为: $ Z_0/Z_{LC}=10 $
Figure 2. (a) Schematic diagram of the equivalent circuit model of a linear LC loop embedded in series in an infinitely long transmission line; (b) The reflection and transmission spectra of microwave photons elastically scattered by the series-embedded linear LC loop, with the inset showing the corresponding phase shift spectrum. Here, the relevant parameters are set as: $ Z_0/Z_{LC}=10 $
图 3 (a) 无限长传输线中并联嵌入LC回路等效电路模型示意图; (b) 并联嵌入线性LC回路对微波光子弹性散射的反射谱和透射谱, 内嵌图为与之对应的相移谱. 这里, 相关参数设置为: $ Z_0/Z_{LC}=10 $
Figure 3. (a) Schematic diagram of the equivalent circuit model of a linear LC loop parallelly embedded in an infinitely long transmission line; (b) The reflection and transmission spectra of microwave photons elastically scattered by the parallel-embedded linear LC loop, with the inset showing the corresponding phase shift spectrum. Here, the relevant parameters are set as: $ Z_0/Z_{LC}=10 $.
图 4 单个约瑟夫森结作为散射体时不同嵌入等效电路模型示意图 (a) 串联嵌入; (b) 并联嵌入
Figure 4. Schematic diagrams of different embedded equivalent circuit models of a single Josephson junction as the scatterer: (a) Series embedding; (b) Parallel embedding.
图 5 不同嵌入模型下约瑟夫森结的微波光子弹性散射透射谱
Figure 5. The transmission spectra of microwave photons elastically scattered by a Josephson junction with different embedded models.
图 6 约瑟夫森结嵌入共面波导传输线的器件实物图[25] (a) 器件电路实物图, 红框处为约瑟夫森结; (b) 红框处放大的显微镜图像; (c) 橙框处放大的扫描电子显微镜图像, 结区面积为1.26 μm2
Figure 6. The physical image of the device with a Josephson junction embedded in a coplanar waveguide transmission[25]: (a) The physical image of the device circuit, with the Josephson junction marked by the red box; (b) The magnified microscopic image of the red box area; (c) The magnified scanning electron microscope image of the orange box area, where the junction area is 1.26 μm2.
图 7 嵌入共面波导传输线中的单个约瑟夫森结对微波光子的散射特性[25] 插图(a)中红色代表实验测量的约瑟夫森结对微波光子形成的透射谱, 即黑框处放大图像, 而黑色代表约瑟夫森结并联嵌入模型下的理论分析结果; 插图(b)为插图(a)所对应的相移谱
Figure 7. The scattering characteristics of microwave photons by a single Josephson junction embedded in a coplanar waveguide transmission line[25]. In inset (a), the red curve represents the experimentally measured transmission spectrum of microwave photons formed by the Josephson junction. Specifically, it is the magnified image within the black box. The black curve, on the other hand, represents the theoretical analysis results based on the model where the Josephson junction is embedded in parallel. Inset (b) shows the corresponding phase - shift spectrum of inset (a).
图 8 无限长传输线中并联嵌入DC-SQUID等效电路模型示意图, 紫色为磁通偏置线
Figure 8. Schematic diagram of the equivalent circuit model of DC-SQUID parallelly embedded in an infinitely long transmission line, wherein the purple refers to its flux bias.
图 9 不同磁通偏置下, 并联嵌入DC-SQUID对微波光子弹性散射的透射谱及其相移谱. 相关参数设置为: $ Z_0/ $$ Z_{J_0}=10 $ (a) 透射谱; (b) 透射相移谱
Figure 9. The transmission spectra and phase shift spectra of microwave photons elastically scattered by the parallel-embedded DC-SQUID under different magnetic flux biases. The relevant parameters are set as: $ Z_0/Z_{J_0}=10 $. (a) Transmission spectrum; (b) Transmission phase shift spectrum.
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