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研究生：	張景陽 Jing-Yang Zhang
論文名稱：	Developing Flux-Driven Josephson Parametric Amplifer
指導教授：	陳永富 Yung-Fu, Chen
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2022
畢業學年度：	110
語文別：	英文
論文頁數：	69
中文關鍵詞：	放大器
外文關鍵詞：	Flux-Driven Josephson Parametric Amplier, Quantum limit noise
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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。

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.

Abstract i
Contents ii
List of Figures iv
Introduction 1
1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Low-Noise Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3 History of the Josephson parametric amplifier . . . . . . . . . . . . . 3
Theory 5
1 Flux-Driven Josephson Parametric Amplifier . . . . . . . . . . . . . . 5
1.1 Quarter Wavelength Resonator . . . . . . . . . . . . . . . . . 6
1.2 Reflected resonator response . . . . . . . . . . . . . . . . . . . 8
1.3 Josephson Effects . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 DC-SQUID . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5 Frequency tunable resonator . . . . . . . . . . . . . . . . . . . 16
1.6 Pump Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Parametric Amplication . . . . . . . . . . . . . . . . . . . . . . . . . 18
3 The Pumpistor Model . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 Expansion of the mixing product . . . . . . . . . . . . . . . . 21
3.2 Phase and negative resistance . . . . . . . . . . . . . . . . . . 22
3.3 Three waves mixing in degenerate mode . . . . . . . . . . . . 23
3.4 Three wave mixing in non-degenerate mode . . . . . . . . . . 26
4 The noise properties of amplifier . . . . . . . . . . . . . . . . . . . . . 28
5 Generation and detection of squeezed states . . . . . . . . . . . . . . 30
5.1 Phase sensitive parametric amplification . . . . . . . . . . . . 30
ii
Experimental Methods and Techniques 32
1 Sample Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2 Sample Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.1 Single e-beam lithography . . . . . . . . . . . . . . . . . . . . 34
2.2 Photolithography . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3 Electron Beam Lithography . . . . . . . . . . . . . . . . . . . 36
2.4 Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5 The summary of the on developing fabrication process in our
lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 Cryogenic Wiring Setup . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Room temperature measurement Setup . . . . . . . . . . . . . . . . . 42
4.1 The input line . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 The output line . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3 The pump line and the DC lines . . . . . . . . . . . . . . . . . 43
Experimental results 45
1 Resonator Characterization . . . . . . . . . . . . . . . . . . . . . . . 45
1.1 Flux-dependence of the resonator frequency . . . . . . . . . . 46
1.2 Power-dependence of the resonator frequency . . . . . . . . . . 47
2 Gain profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.1 Non-degenerate gain . . . . . . . . . . . . . . . . . . . . . . . 48
2.2 Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 Noise calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4 Gain and noise mapping . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 degenerate gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Conclusion 57
Bibliography 59
                                

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