約瑟夫森參數放大器之量測流程整合與特性分析

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研究生：	邱羽君 Yu-Jiun Chiu
論文名稱：	約瑟夫森參數放大器之量測流程整合與特性分析
指導教授：	陳永富
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：	2025
畢業學年度：	113
語文別：	中文
論文頁數：	68
中文關鍵詞：	Josephson 參數放大器、LabVIEW 、Python 擬合、集總元件式結構
相關次數：	點閱：17 下載：0
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本研究提出並實現了一種集總元件式參數放大器（Lumped-Element Josephson, LJPA），並建立完整的自動化量測與資料分析流程以驗證其性能。結合 LabVIEW 與 Python 平台，系統可自動掃描磁通偏壓與幫浦功率，同步分析反射參數 $S_{21}$ 並擬合共振頻率對磁通的變化，以萃取零磁通電流 ($I_{\text{zero,flux}}$) 與磁通電流週期性（$I_{periodicity}$）等參數。量測結果顯示，本研究所製作之 LJPA 於幫浦頻率 11.2–11.9 GHz、磁通偏壓 0.33–0.45 $\Phi_0$ 範圍內表現最佳，增益可達 25 dB，頻寬約 100–200 MHz，具穩定且可重現之放大特性。進一步透過條件分析模組（$\text{Gain} > 18~\text{dB}$、$\text{BW} > 0.03~\text{GHz}$ ），能自動辨識可操作區域並執行細部掃描，以鎖定最佳操作點。本研究成功建立 LJPA 操作參數搜尋量測與分析流程，不僅提升操作效率與資料準確性，也驗證集總式設計在高增益與寬頻放大應用上的潛力。

This study presents the design and characterization of a lumped-element Josephson Parametric Amplifier (LJPA) and establishes a fully automated measurement and analysis framework. By integrating LabVIEW and Python, the system automatically scans flux bias and pump power, analyzes reflection data ($S_{21}$), and extracts key parameters such as the zero-flux current ($I_{\text{zero,flux}}$) and flux current periodicity.

Experimental results show that the LJPA exhibits optimal performance at pump frequencies of 11.2–11.9 GHz and flux bias between 0.33–0.45 $\Phi_0$, achieving up to 25 dB gain and 100–200 MHz bandwidth with stable and reproducible behavior. A conditional analysis module ($\text{Gain} > 18~\text{dB}$, $\text{Bandwidth} > 0.03~\text{GHz}$ ) further identifies the optimal operation region for precise tuning.

This study successfully established a complete measurement and analysis workflow for searching the operating parameters of LJPA, which not only improves operational efficiency and data accuracy but also verifies the potential of the lumped-element design for achieving high gain and wideband amplification applications.

Abstract i
目錄     ii
圖目錄   iv
序諭     1
約瑟夫森參數放大器理論     3
1 參數放大器原理與放大器結構     3
2 約瑟夫森效應     5
3 超導量子干渉SQUID磁通調變原理     6
3.1 SQUID結構的有效臨界電流     6
3.2 約瑟夫森接面的等效電感     6
3.3 LC共振頻率公式     7
3.4 磁通調變下的共振頻率週期性應用     7
4 約瑟夫森參數放大器量測特性簡介     8
5 約瑟夫森參數放大器增益與頻寬特性     10
6 操作參數選擇原則與理論基礎     12
LabVIEW設計與實驗架設     16
1 LabVIEW程式簡介     16
2 實驗裝置與硬體架設     17
2.1 低溫配線設置     18
2.2 輸入訊號線     20
2.3 輸出訊號線     20
2.4 幫浦訊線與直流偏壓線     20
3 LabVIEW 量測程式流程設計與實驗     20
3.1 Flux Dependence 量測模設計     22
3.2 磁通標定與頻率對應分析組     28
3.3 操作參數搜尋量測模組     30
實驗結果與討論     40
1 實驗條件與量測參數設定     40
2 Flux Dependence量测結果     41
3 Python 擬合輿 LabVIEW 參數驗流程     43
4 操作參數搜尋量測結果與分析     44
4.1 增益(Gain)二維分布     45
4.2 頻寬(Bandwidth)二維分布     46
5 條件分析與細部搜尋結果     49
5.1 10.7 GHz     49
5.2 11.2 GHz     50
5.3 11.9 GHz     50
5.4 12.6 GHz     50
5.5 不同幫浦頻率之最佳幫浦功率增益頻譜比較     53
6 LJPA操作參數整合分析與趨勢討論     54
結論     57
參考文獻     59
                                

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