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研究生： 張乃軒
Nai-Hsuan Chang
論文名稱： Design and Performance Verification of Flux-Driven Josephson Parametric Amplifier
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： 2023
畢業學年度： 111
語文別： 中文
論文頁數： 63
中文關鍵詞： 約瑟夫森參量放大器 、超導電路
外文關鍵詞： Josephson Parametric Amplifier, Superconducting circuit
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    • 約瑟夫森參量放大器是一種外加噪聲可以低至半光子量子理論極限的線性放大器，其優異的噪聲表現能有效地降低系統噪聲，使小訊號的量測有更好的信噪比。其應用包括了超導量子位元的single shot量測、暗物質軸子探測、微波量子雷達等。這篇文章採用的約瑟夫森參量放大器版本是參考至2008年Yamamoto的設計，其結構為一個四分之一波長微波共振腔透過超導量子干涉元件接地；由於超導量子干涉元件的電感會隨著外加磁通量而產生週期性的變化，因此此元件為工作頻率可調的元件。 衡量一個約瑟夫森參量放大器性能的指標有增益和頻寬的乘積、外加噪聲、調頻能力。我們的元件在4.6 GHz-5.05 GHz的增益頻寬乘積達到20-60 MHz，且外加噪聲也低於一個光子能量。內文會介紹此元件的理論、設計以及量測表現。

    Josephson Parametric Amplifier(JPA) is a linear amplifier whose add noise can be as low as the half-photon quantum limit. Its excellent noise performance can effectively reduce the system noise and enable the measurement of small signals to have a better signal-to-noise ratio. Its applications include single shot measurement of superconducting qubits, dark matter axion detection, microwave quantum radar etc.
    The version of the JPA used in this work is based on the design of Yamamoto in 2008. It is structurally a quarter-wavelength microwave resonator grounded by a superconducting quantum interference device (SQUID). The inductance of SQUID
    will periodically depend on the external magnetic flux, so the operating frequency is adjustable. The criteria to judge the JPA performance includes the Gain Bandwidth Product, added noise, and frequency tunability. Our JPA has a Gain-Bandwidth Product of 20-60 MHz at 4.6 GHz-5.05 GHz, and the added noise is lower than one photon. The thesis will introduce the theory, design and the measurement results of this device.

    1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Parametric Amplification . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Amplifier Added Noise and System Noise . . . . . . . . . . . . . . . . 4 2 Theory 6 2.1 Quantum Limits on Noise in Linear Amplifiers . . . . . . . . . . . . . 6 2.2 Josephson Tunneling Effect . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Josephson Junction . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2 DC-SQUID . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Operation Principle of Josephson Parametric Amplifier . . . . . . . . 11 2.3.1 Input-Output Theory . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.2 Equivalent Circuit to Duffing Oscillator . . . . . . . . . . . . . 13 2.3.3 Eigenfrequency Modulation (Three Photon Mixing) . . . . . . 14 2.3.4 Sinusoidal Driving Force (Four Photon Mixing) . . . . . . . . 17 2.3.5 Phase Sensitive Gain . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 Lumped Element Model for a Transmission Line Resonator . . . . . . 19 2.5 Flux-Driven Josephson Parametric Amplifier . . . . . . . . . . . . . . 24 3 Experimental Setup 28 3.1 Device Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 Device Wiring and Measurement Setup . . . . . . . . . . . . . . . . 29 4 Experimental results 33 4.1 Flux-Dependence of the Resonator Frequency . . . . . . . . . . . . . 33 4.2 Non-Degenerate Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2.1 Working Range . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2.2 Gain Bandwidth Performance . . . . . . . . . . . . . . . . . . 37 4.2.3 System Noise Improvement . . . . . . . . . . . . . . . . . . . 37 4.2.4 Saturation Power . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2.5 Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . 42 4.3 Degenerate Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4 Noise Squeezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5 Conclusion 48 Bibliography 50

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