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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研究生：	呂孝晟 Xiao-Cheng Lu
論文名稱：	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 Full Electron Beam Lithographic Fabrication Process of Coplanar Waveguide Cavity and Superconducting Qubit Coupled Systems
指導教授：	陳永富 Yung-Fu Chen 陳啟東 Chii-Dong 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：	2020
畢業學年度：	108
語文別：	中文
論文頁數：	73
中文關鍵詞：	全電子束微影製程、共平面波導共振腔、超導人造原子、量子位元、拉比震盪、能量鬆弛時間
外文關鍵詞：	Full electron beam fabrication process, Coplanar waveguide resonator, Superconducting artificial atom, Xmon Qubit, Rabi oscillation, Energy relaxation time
相關次數：	點閱：10 下載：0
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在這篇學位論文是為了免去光學微影製程，雖然使用光學曝光時間短，但是在設計需要改變設計時需要重新設計光罩，且在轉換成使用電子束曝光小結構後，還需要將原先大結構的金屬表面做清潔再製作小結構的部分。而使用全電子束微影製程技術時，在大結構的設計需要修改時，可以直接從設計圖修改，讓製程及理解物理上可以更有效率。使用全電子束微影製程的共平面波導共振器的結構為λ/4的共振器，且共平面波導的結構為Al − AlOx − Al，而製作出來的Internal quality fator Qi分為(147443, 151580, 131220)、 (157687, 114718, 71185)。第一片為XQ-SA-09-1的三個共平面波導共振器，第二片為XQ-SA-09-7，這三個共平面波導共振器分別為5.5GHz、6.0GHz、 6.5GHz。分別在XQ-SA-09-1的第三個共振腔以及XQ-SA-09-7的第一個共振器看到共振器的頻率與超導人造原子的訊號耦合出現在Dispersive regime。再利用傑尼斯-卡明斯模型 (Jaynes-Cummings model)得到Qubit與共振器的耦合強度在XQ- SA-09-1的第三個共振器為g = 29.3MHz、XQ-SA-09-7的第一個共振器為g = 26.0MHZ，透過觀察到Qubit的第二激發態計算出Qubit的充電能為EC = 220MHz。在時域上的量測觀測到拉比震盪以及Qubit的能量鬆弛時間T 1 ≃ 1.03μs。

This thesis is a new way to fabricate on-chip circuit qauntum elec- trodynamic(cQED) system. Typical process is seperatelly fabricating coplanar waveguide resonator and superconducting artificial atom, which we only interest the lowest two level, a.k.a. qubit. Coplanar waveguide resonators are fabricated by photolithgraphy and qubits are fabricated by electron beam lithography. Here we use full electron beam lithgraphy to construct our device. Means that, resonator and qubits are fabricated simultaneously. The type of the resonator we use is λ/4, and the struc- ture is Al − AlOx − Al. But this do not affect our internal quality factor Qi which can reach (147443, 151580, 131220), (157687, 114718, 71185), these two data respectively three resonators with 5.5, 6, 6.5GHz on the two different devices. Here we also observed power dependent dis- persive shift of two of the resonators. Fitted by the Jaynes-Cummings model, then we get the coupling strength between resonators and qubits, 29.3,26.0MHz. The second excited state of Xmon Qubit is observed and the charging energy EC = 220MHz is then determined. In the time domain measurement, Rabi oscillation and T1 energy relaxation time T 1 ≃ 1.03μs is also observed and determined.

頁次 
中文摘要 ............................................................................................. i 
英文摘要............................................................................................. ii
 謝誌 .................................................................................................... iii 
目錄 .................................................................................................... iv 
圖目錄 ................................................................................................ vi 
表目錄................................................................................................ x 
一、 簡介與研究理論 ............................................................ 1
1 研究動機........................ 1
2 超導量子位元 ..................... 2
2.1 BCS超導理論 ..................... 2
2.2 約瑟夫森效應 ..................... 2
2.3 DC約瑟夫森效應 ................... 3
2.4 AC約瑟夫森效應 ................... 4
2.5 約瑟夫能量....................... 5
2.6 RCSJ模型 ....................... 6
2.7 超導量子干涉儀 .................... 7
2.8 約瑟夫森結的量子行為 ................ 8
2.9 庫柏對盒子....................... 10
2.10 Transmon Qubit .................... 11
2.11 Xmon Qubit ...................... 13 
3 共振器與傳輸線 .................... 14
3.1 LC振盪電路 ...................... 14
3.2 傳輸線理論....................... 16
3.3 共平面波導與共振器.................. 19
3.4 電路二次量子化 .................... 20
4 電路量子電動力學................... 20
二、 元件製程與量測 ............................................................ 24
1 晶片設計與製程步驟.................. 24
2 製程儀器介紹 .....................25
2.1 電子束曝寫系統 .................... 26
2.2 電子槍蒸鍍系統 .................... 27
3 大小電流電子束微影.................. 27
3.1 大小電流轉換時的校準 ................ 28
3.2 曝寫劑量........................28
3.3 大小電流微影製程參數 ................ 29
4 室溫電性量測 .....................36
5 低溫微波量測 .....................38
5.1 3He/4He稀釋製冷機 .................. 38
5.2 微波量測架構 .....................38
三、 實驗結果與討論 ............................................................ 40 
1 製程影響樣品之結構討論 ............... 40
1.1 電子束蒸鍍系統造成二次電子 ............ 40
1.2 約瑟夫森結的結構................... 40
1.3 共振腔的結構 .....................42
2 電性量測與微波量測頻譜 ............... 44
 四、 結論 .............................................................................. 55 
參考文獻 ............................................................................................. 57
                                

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