近幾年中，量子電腦與量子計算當今重要的科技發展方向，而量子科技的核心是量子位元件的研製。量子位元的操作需靠人造原子與光子交互作用，其量子狀態的操作需在超低溫環境(大約10 mK)下進行，以及精密微波操控技術。本論文的目的主要再架設量測量子位元的低溫量測系統與共振腔設計。
本篇論文中的實驗系統使用稀釋致冷機降溫，經過多個遞減的溫度層將系統溫度降低至10 mK的樣品空間，過程中為了減少熱傳導及雜訊進入也在輸入端安裝了衰減器。當微波訊號從10 mK輸出時，避免雜訊干擾先使用了超導傳輸線再接上了低溫放大器進行第一次放大使訊號與雜訊產生區隔，之後在系統外室溫處在接上室溫放大器進行二次放大。根據人造原子製程的普遍躍遷頻段，將實驗中所使用的量測系統工作頻段設定在4~12 GHz。低溫放大器為微波訊號輸出後，最有可能影響訊號正確性的元件，而放大器的雜訊溫度(noise temperature)大約為 5K，因此量測系統上會一個大小約為 -130 dB的白雜訊，其大小和單光子相近
將人造原子置於共振腔內是為了增強與光子之間的耦合效應，而在本篇論文分別針對二維共面波導的測量以及三維共振腔的理論設計、利用3D電磁模擬軟體模擬和實驗量測。實驗中的二維共面波導共振頻率為8.24 GHz，樣品為半導體人造原子，目前實驗僅針對 T=10 mK 下腔體的品質因子和共振頻率進行測量。而為了涵蓋系統4~12 GHz的工作頻段，我設計了四種共振頻率且分別有銅和鋁兩種不同材質的三維共振腔。目前在三組三維共振腔的低溫量測中，本篇論文所設計的腔體其光子損耗率 κ/2π 達到30 kHz已具被使光子與人造原子產生強耦合作用的條件，因此我認為此量測系統具有能讓人造原子與光子產生強耦合的電磁場環境。

In recent years, quantum computers and quantum computing have become the important scientific and technological development directions and the development of Quantum bit (qubit) is the core of the quantum technology. The operation of qubits depends on the interaction between artificial atoms and photons, the quantum state needs to be operate in an ultra-low temperature environment (approximately 10 mK) and precision microwave manipulation techniques. The purpose of this dissertation is mounting the cryogenic measurement system for qubits experiment and the resonant cavity design.
The experiment in the thesis uses a dilution refrigerator as a cryogenic system to lower the system temperature to 10 mK sample space through the multiple descending temperature layers. In the process, mount attenuator at the input to reduce heat conduction and noise. When the microwave signal is output from the 10 mK space, superconducting transmission line use first to avoid the noise interference, then the low temperature amplifier performs the first amplification to separate the signal from noise, and then the room temperature amplifier outside the fridge perform the secondary amplification. According to the general transition frequency of the artificial atom process, the operating frequency band of the measurement system is set at 4~12 GHz. The low temperature amplifier is a device most likely to affect the signal. Therefore, we use a 50 ohms resistor to measure the noise temperature from the low temperature amplifier, and estimate the noise.
In order to enhance the coupling effect with photons, we put the artificial atoms in the resonant cavity. In this article, we focus on the measurement of two-dimensional coplanar waveguide (thanks to dr. J.W. Wang, a former laboratory member for the design and the simulation data) and design, simulate by HFSS and measurement of 3D cavity. The resonant frequency of the two-dimensional coplanar waveguide in the experiment is 8.24 GHz, and the sample is a semiconductor artificial atom, the experiment only measures the quality factor and resonant frequency of the cavity under T=10 mK. In order to cover the 4 to 12 GHz operating frequency band of the system, I designed 3D cavity with four resonance frequencies with copper and aluminum two different materials. At present, three groups of low temperature data have been measured, the photon loss rate of the 3D cavity in this paper compared with the literature that has achieved a strong coupling effect, we considered that there is an electromagnetic field environment that can make artificial atoms and photons strongly coupled.

摘要 i
Abstrate ii
致謝 iii
目錄 iv
第一章 緒論 1
第二章 理論 3
2.1 人造原子與光子的交互作用-腔/電路-量子電動力學(cavity/circuit-QED) 3
2.2 傑恩斯-卡明斯模型（Jaynes-Cummings model） 5
2.2.1 二能階系統(Quantum two level system) 6
2.2.2 耦合強度(The coupling strength) 7
2.2.3真空拉比分裂VRS (vacuum Rabi splitting) 9
2.3理論總結與實驗設計目標 10
第三章 微波量測系統架設與驗證 13
3.1 微波元件與低溫量測系統整合 13
3.2 單獨微波元件檢測 18
3.3 低溫放大器雜訊檢測 22
3.3.1 強森-奈奎斯雜訊(Johnson-Nyquist noise) 23
3.3.2 雜訊溫度測量 26
3.4實驗小結 30
第四章 傳輸線與共振腔理論 31
4.1傳輸線模型(transmission line) 31
4.2品質因子(Quality factor) 33
4.3三維共振腔-體積模態 34
第五章 共振腔設計 38
5.1二維共面波導(2D coplanar wav eguide) 38
5.2三維共振腔(3D cavity) 41
5.3三維共振腔理論模擬 43
第六章 理論模擬與實驗結果 48
6.1 二維共面波導(2D coplanar waveguide) 49
6.2 三維共振腔實驗數據及分析 51
6.3 實驗小結 63
第七章 總結 64
附錄 65

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