量子參數放大器（Quantum Parametric Amplifier）是一種低雜訊放大器，能有效提升微弱信號的信噪比，從而在測量中提供更佳的性能。本研究採用了約瑟夫森參量放大器的結構設計：將指叉電容耦合至四分之一波長共振腔傳輸線的末端，並接上超導量子干涉元件，最終接地。我們通過設計變化傳輸線的阻抗值來增加約瑟夫森參量放大器的頻寬。
與其他超導參數放大器的研究不同，我們使用石英作為基板，並採用超導溫度較高的鈮製程進行製造。這項製程由我們與中研院天文所的王明杰博士合作完成。超導量子干涉元件能夠通過外加磁通量的週期性變化來調整共振頻率，我們將其設定為本實驗室量子位元讀取的中心頻率。此外，我們製造了一系列測試元件，針對電容和共振器進行優化，以找出最佳參數配置。
在本研究中，我們還自行開發了Matlab程式，用於模擬約瑟夫森參量放大器，並研究了臨界電流、阻抗值、非線性電感和電容值對增益與頻寬的影響。本文將介紹該元件的工作原理、光罩設計以及模擬計算結果。

Quantum parametric amplifiers (QPAs) are low-noise amplifiers that effectively enhance weak signals, providing improved signal-to-noise ratios in measurements. In this study, we adopted a Josephson parametric amplifier design: the interdigital capacitor is coupled to the end of a quarter-wavelength resonator transmission line and connected to a superconducting quantum interference device (SQUID), which is then grounded. We increased the bandwidth of the Josephson parametric amplifier by varying the impedance of the transmission line.
Unlike other studies on superconducting parametric amplifiers, we used quartz as the substrate and employed a high-temperature superconducting niobium process for fabrication. This process was completed in collaboration with Dr. Ming-Jye Wang from the Academia Sinica Institute of Astronomy and Astrophysics Superconducting Device Laboratory (ASIAA SDL). The SQUID can adjust its resonance frequency through periodic changes in externally applied magnetic flux, and we have set it to the center frequency for qubit readout in our laboratory. Additionally, we fabricated a series of test components for capacitors and resonators to find the optimal parameter configuration.
In this research, we also developed a custom Matlab program to simulate the Josephson parametric amplifier, investigating the effects of variations in critical current, impedance, nonlinear inductance, and capacitance on gain and bandwidth. This paper introduces the operating principles of the device, mask design, and simulation results.

參考資料
1. M. A.Castellanos-Beltran, et al., Amplification and squeezing of quantum noise with a tunable Josephson metamaterial. Nature Physics, 2008. 4(12).
2. Jinmyeong Kim, e.a., Josephson Parametric Amplifier in Axion Experiments. Physics Today 63 (9), 38–43 (2010);.
3. Baleegh Abdo, et al., Josephson amplifier for qubit readout. Applied Physics Letters, 2011. 99(16).
4. Dirk van Delft, e.a., The discovery of superconductivity. Physics Today, 2010. 63(9).
5. B. D. JOSEPHSON, Possible new effects in superconductive tunnelling. Physics Letters, 1962. 1(7).
6. T. Van Duzer, e.a., Principles of Superconductive Devices and Circuits. 1999: Prentice Hall.
7. W.H. Louisell, Coupled Mode and Parametric Electronics. 1960: Wiley.
8. T.Yamamoto, et al., Flux-driven Josephson parametric amplifier. Applied Physics Letters, 2008. 93(4).
9. J. Y. Mutus, et al., Strong environmental coupling in a Josephson parametric amplifier. Applied Physics Letters, 2014. 104(26).
10. Tanay Roy, et al., Broadband parametric amplification with impedance engineering: Beyond the gain-bandwidth product. Applied Physics Letters, 2015. 107(26).
11. Osamu Aso , e.a., Four-Wave Mixing in Optical Fibers and Its Applications. Furukawa Review, No. 19. 2000.
12. Stefan Pogorzalek, et al., Hysteretic Flux Response and Nondegenerate Gain of Flux-Driven Josephson Parametric Amplifiers. Physical Review Applied, 2017. 8(2).
13. R.Garg, , et al., <Microstrip_Lines>.
14. M. M. Khapaev, Extraction of inductances of plane thin film superconducting circuits. Superconductor Science and Technology, 1997. 10(7).
15. M.Göppl, et al., Coplanar waveguide resonators for circuit quantum electrodynamics. Journal of Applied Physics, 2008. 104(11).