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姓名	張景陽(Jing-Yang Zhang)  查詢紙本館藏	畢業系所	物理學系
論文名稱	(Developing Flux-Driven Josephson Parametric Amplifer)
相關論文	★ 單電子偵測器原理及製作與二維電子氣量子點電荷傳輸行為 ★ 單電子系統中的電子穿隧事件 ★ 石墨烯與超導金屬介面的電子穿隧行為 ★ 實驗觀測混合式單電子箱中之共同穿隧事件 ★ 石墨烯/超導體/石墨烯元件之古柏電子對分裂現象探討 ★ 雙局部閘極石墨烯/超導體/石墨烯元件中古柏電子對分離現象觀測 ★ 不連續鉛顆粒/單層二硫化鉬系統之超導鄰近效應觀測 ★ 二維電子氣體中量子點接觸 與量子點製作及量測 ★ 二硫化鉬及二硫化鎢電晶體的 低頻雜訊行為 ★ 單一超導量子位元控制與狀態讀取 ★ 超導量子干涉元件製作 ★ 工程化超導電路上三維腔量子電動力學系統 ★ Characterizing single-qubit gate fidelity on superconducting qubits ★ Virtual Potentials in Electric Circuit and Motion of Brownian Gyrator ★ 超導雙量子位元電路的實現 ★ 全電子束微影製程的共平面波導與超導量子位元耦合系統
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摘要(中)	量子參量放大器是一個低噪聲放大器通常應用在超導電路上的量子電動力學。在這篇工作中我們使用的量子參量放大器是參考至2008年Yamamoto的設計。它包含了連接直流超導量子干涉元件和地短路的四分之一波長的共振腔。這個元件的特色是它可以透過改變外加磁場的值進而改變直流超導量子干涉元件的電感值也就代表間接改變了四分之一波長的共振腔的共振頻率。這個元件可以應用在我們實驗室的兩個計畫中，其中一個是使用singel shot 量測的計畫另一個是尋找Axion 軸子的計畫。其中這個元件的優勢在於它添加的噪聲可以小到接近量子極限的噪聲。在這篇論文中我們會介紹這個元件的理論、製作以及它的特性。
摘要(英)	Josephson parametric amplifiers(JPA), the low-noise amplifier for applications in Circuit Quantum Electrodynamics. In the presented work, flux-driven JPA we use, which was introduced by Yamamoto in 2008. It consists of a quarter wavelength coplanar waveguide for the resonator, which connects to the superconducting quantum interference device (DC-SQUID) and is short to ground. This device allows for tunning the resonate frequency by applying a magnetic flux for changing the total inductance. Periodic modulations of the flux inputting from the pump line affect the inductance of the DC-SQUID loop leading to amplification of the input signal in the resonator. This amplifier can be used in two projects in our lab one is the single shot qubit readout and another is the Axion search. The benefit of this device is the quantum limit added noise. In this thesis, we will introduce the theory, fabrication, and the characteristic of this device.
關鍵字(中)	★ 放大器	關鍵字(英)	★ Flux-Driven Josephson Parametric Amplier ★ Quantum limit noise ★ Superconducting Circuit
論文目次	Abstract i Contents ii List of Figures iv 1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Low-Noise Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 History of the Josephson parametric amplifier . . . . . . . . . . . . . 3 2 Theory 5 2.1 Flux-Driven Josephson Parametric Amplifier . . . . . . . . . . . . . . 5 2.1.1 Quarter Wavelength Resonator . . . . . . . . . . . . . . . . . 6 2.1.2 Reflected resonator response . . . . . . . . . . . . . . . . . . . 8 2.1.3 Josephson Effects . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.4 DC-SQUID . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.5 Frequency tunable resonator . . . . . . . . . . . . . . . . . . . 16 2.1.6 Pump Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Parametric Amplication . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 The Pumpistor Model . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 Expansion of the mixing product . . . . . . . . . . . . . . . . 21 2.3.2 Phase and negative resistance . . . . . . . . . . . . . . . . . . 22 2.3.3 Three waves mixing in degenerate mode . . . . . . . . . . . . 23 2.3.4 Three wave mixing in non-degenerate mode . . . . . . . . . . 26 2.4 The noise properties of amplifier . . . . . . . . . . . . . . . . . . . . . 28 2.5 Generation and detection of squeezed states . . . . . . . . . . . . . . 30 2.5.1 Phase sensitive parametric amplification . . . . . . . . . . . . 30 ii 3 Experimental Methods and Techniques 32 3.1 Sample Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2 Sample Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.1 Single e-beam lithography . . . . . . . . . . . . . . . . . . . . 34 3.2.2 Photolithography . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.3 Electron Beam Lithography . . . . . . . . . . . . . . . . . . . 36 3.2.4 Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2.5 The summary of the on developing fabrication process in our lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3 Cryogenic Wiring Setup . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.4 Room temperature measurement Setup . . . . . . . . . . . . . . . . . 42 3.4.1 The input line . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.4.2 The output line . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.4.3 The pump line and the DC lines . . . . . . . . . . . . . . . . . 43 4 Experimental results 45 4.1 Resonator Characterization . . . . . . . . . . . . . . . . . . . . . . . 45 4.1.1 Flux-dependence of the resonator frequency . . . . . . . . . . 46 4.1.2 Power-dependence of the resonator frequency . . . . . . . . . . 47 4.2 Gain profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.2.1 Non-degenerate gain . . . . . . . . . . . . . . . . . . . . . . . 48 4.2.2 Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2.3 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.3 Noise calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.4 Gain and noise mapping . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.5 degenerate gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5 Conclusion 57 Bibliography 59
參考文獻	[1] Tsuyoshi Yamamoto, K Inomata, M Watanabe, K Matsuba, T Miyazaki, William D Oliver, Yasunobu Nakamura, and JS Tsai. Flux-driven josephson parametric amplier. Applied Physics Letters, 93(4):042510, 2008. [2] JY Mutus, TC White, Evan Jerey, Daniel Sank, Rami Barends, Joerg Bochmann, Yu Chen, Zijun Chen, Ben Chiaro, Andrew Dunsworth, et al. Design and characterization of a lumped element single-ended superconducting microwave parametric amplier with on-chip ux bias line. Applied Physics Letters, 103(12):122602, 2013. [3] TC White, JY Mutus, I-C Hoi, R Barends, B Campbell, Yu Chen, Z Chen, B Chiaro, A Dunsworth, E Jerey, et al. Traveling wave parametric ampli- er with josephson junctions using minimal resonator phase matching. Applied Physics Letters, 106(24):242601, 2015. [4] Kyle M Sundqvist and Per Delsing. Negative-resistance models for parametrically ux-pumped superconducting quantum interference devices. EPJ Quantum Technology, 1(1):1{21, 2014. [5] Martin Goppl, A Fragner, M Baur, R Bianchetti, Stefan Filipp, Johannes M Fink, Peter J Leek, G Puebla, L Steen, and Andreas Wallra. Coplanar waveguide resonators for circuit quantum electrodynamics. Journal of Applied Physics, 104(11):113904, 2008. 60 [6] Philip Krantz. The Josephson parametric oscillator{From microscopic studies to single-shot qubit readout. Chalmers Tekniska Hogskola (Sweden), 2016. [7] L Zhong, EP Menzel, R Di Candia, P Eder, M Ihmig, A Baust, M Haeberlein, E Homann, K Inomata, T Yamamoto, et al. Squeezing with a ux-driven josephson parametric amplier. New Journal of Physics, 15(12):125013, 2013. [8] Yu-Lin Wu, Hui Deng, Hai-Feng Yu, Guang-Ming Xue, Ye Tian, Jie Li, Ying-Fei Chen, Shi-Ping Zhao, and Dong-Ning Zheng. Fabrication of al/alox/al josephson junctions and superconducting quantum circuits by shadow evaporation and a dynamic oxidation process. Chinese Physics B, 22(6):060309, 2013.
指導教授	陳永富(Yung-Fu, Chen)	審核日期	2022-8-2
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