臺灣博碩士論文加值系統

本論文研究在晶片上兩個超導transmon量子位元與微波共振腔之間的交互作用。每一個transmon包含了可以被磁通量調控的約瑟芬接合以及用指叉式電容來降低transmon 的等效充電能 (charging energy)，如此可以抑制由電荷擾動所造成的雜訊。本實驗的微波共振腔是半波長共平面波導，共振頻率為5.96GHz，選擇材料為鈮(Niobium)。沒有外加磁場，transmon 的躍遷頻率分別為10.1GHz 和9.3GHz。Transmon的躍遷頻率可以被磁場調控到和微波共振腔的共振頻率相同。在本實驗中，當transmon和微波共振腔之間零失調(zero detuning)時，觀察到反交叉(anti-crossing)現象，這證明了量子位元和共振腔之間有同調性的交互作用。利用Jaynse-Cummings model來擬合共振腔共振頻率附近的反交叉現象，發現量子位元與共振腔之間的耦合強度(coupling strength)分別為165MHz和160MHz。根據以上擬合，在兩量子位元之間零失調時，也有觀察到反交叉現象，這起因於兩量子位元的交互作用產生的糾纏現象。

Coherent interaction between two superconducting transmon qubits and an on-chip microwave cavity is studied. Each transmon consists a flux-tuned Josephson junction and a shunting multi-finger capacitor, which is for reducing the effective charging energy of the transmon so as to suppress the noise induced by the charge fluctuation. Our microwave cavity is a half-wavelength coplanar waveguide made of Nb with resonance frequency of 5.96GHz. With no flux bias, the transition frequencies of each transmon are 10.1GHz and 9.3GHz respectively. They can be tuned to meet the cavity resonance frequency by increasing the flux bias. In our experiment, anticrossing features appear around qubit-cavity zero detuning points, showing the coherent interaction between qubits and the cavity. By fitting the anticrossing features around the cavity resonance with the Jaynse-Cummings model, the qubit-cavity coupling strengths of the two transmons are estimated to be 165MHz and 160MHz, respectively. According to this information, we also located the qubit-qubit zero detuning points, where another anticrossing features are shown. They are corresponding to the entanglement of the two transmons due to the effective qubit-qubit interaction.

口試委員會審定書 I
誌謝 II
中文摘要 III
英文摘要 IV
圖目錄 VII

第一章 簡介 1
1-1 研究動機 1
1-2 約瑟芬效應 3
1-3 共振器(oscillator) 9
1-4 傳輸線(transmission line) 10
1-5 電路的量子化 13
1-6 電路型量子電動力學(circuit quantum electrodynamics) 17
1-7 真空拉比分裂(vacuum Rabi splitting) 19
1-8 量子非破壞性量測(quantum non-demolition measurement) 20
第二章 元件製程與量測 22
2-1 晶片結構與設計 22
2-2 製程機台介紹 23
2-3 光微影術製作共振腔 27
2-5 室溫的阻值量測 33
2-6 稀釋製冷機(dilution refrigerator) 34
第三章 實驗結果與討論 36
3-1 量子位元與共振腔的強耦合 36
3-2 量子位元的躍遷能量 37
3-3 兩個量子位元在共振腔之系統描述 38
3-4 兩個量子位元與共振腔的強耦合 39
3-5 兩個量子位元透過共振腔之間的間接耦合 40
第四章 結論 41
參考文獻 43

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