工程化超導電路上三維腔量子電動力學系統

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姓名

洪偉晟(Wei-Cheng Hung) 查詢紙本館藏

畢業系所

物理學系

論文名稱

工程化超導電路上三維腔量子電動力學系統
(Engineering 3D Transmon and Cavity for Cavity Quantum Electrodynamics)

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摘要(中)

超導量子電路(Superconducting Quantum Circuit)為近20年熱門的研究領域與實驗
平台，透過電路中巨觀(macroscopy)的電荷與磁通量的量子化現象進而製造出在
量子物理中所需的能階結購。利用超導量子電路進行的實驗有幾個好處，首先是
量測方法為測量電壓與電流訊號，實驗方法較為簡易與普遍，市面上許多常規的
儀器便能用於此類實驗；其次由於電路元件如電容、電感是由人類所設計，因此
實驗條件也大多數能由人類控制，可以做一些用為原子分子平台中比較困難進
行的實驗。而在所有超導量子電路實驗中最熱門的工作為量子位元的製作與操
控，本工作便是重現了其中一種類別的量子位元: 三維共振腔內的量子位元。本
篇詳述了量子位元的背景、與三維共振腔內的量子位元的設計、製造與特徵值量
測。由於本工作為比較草創的階段的實驗，因此仍有許多面向能改進，以結果而
言，三維共振腔內的量子位元是一個快速建構的實驗平台，其同調時間(coherence
time)在沒有極大化優化實驗條件下便能有一微秒，雖不到國外團隊今日之平均
值，但是能對於一些初步的脈衝實驗、設備與線路進行檢測。

摘要(英)

Superconducting Quantum Circuit(SQC) is a popular platform for the Quantum
Electrodynamics(QED) experiment in recent twenty years. With the charge and
the
ux quantization in macroscopy, we can construct the energy levels which are
the basis of quantum mechanics.There are several advantages of processing the quan-
tum experiment on the SQC. First is the quantum system can be measured only
with the voltage and the current. Some of the commercial instruments are enough
for the experiment. Second, atoms are made from the capacitor and the inductor.
Due to the atoms are made from the circuit elements, the feature parameters such as
eld coupling and the transitions can be designed by humans. One of the experiment
branches of the QED on SQC is the Cavity QED in 3-dimensional superconducting
cavity. In this work,we set up a cavity quantum electrodynamics experiment plat-
form on superconducting quantum circuit. In our experiment,we embed a Transmon
in 3D Aluminum cavity and measure the response of the device. It is our rst time
preparing 3D cavity QED system. The coherence in our devices reaches 1s with-
out much improvement. We believe if we process the Transmon or the Cavity with
the surface treatment, we can improve the coherence in more than one order. For
the 1 1s coherence qubit, it is sucient for us to correct the problem in the cable
wiring or the experiment setup. It is also enough for us to do some basic pulses
measurement.

關鍵字(中)

★ 超導量子電路
★ 量子位元
★ 腔量子電動力學

關鍵字(英)

★ Superconducting Quantum Circuit
★ Qubit
★ Cavity Quantum Electrodynamics

論文目次

Abstract i
Contents ii
List of Figures v
1 Introduction 2
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Review of Superconducting Qubits . . . . . . . . . . . . . . . . . . . 4
2 Theory 8
2.1 Superconducting Charge Qubits . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Josephson Junctions . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 The DC SQUID . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.3 Circuit Quantization of Josephson Junction . . . . . . . . . . 13
2.1.4 Cooper Pair Box(CPB) . . . . . . . . . . . . . . . . . . . . . . 16
2.1.5 Transmon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Microwave Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 Scattering Parameters . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Quadrature of Waves . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.3 Transmission Line Theory . . . . . . . . . . . . . . . . . . . . 23
2.2.4 Scattering Matrix and Impedance . . . . . . . . . . . . . . . . 28
2.2.5 Resonator Theory . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.6 Circuit Model of the Resonator in the Experiment . . . . . . 33
2.3 Cavity Quantum Electrodynamics . . . . . . . . . . . . . . . . . . . . 37
2.3.1 Jaynes-Cummings Model . . . . . . . . . . . . . . . . . . . . . 38
2.3.2 Dispersively Coupled Atom . . . . . . . . . . . . . . . . . . . 39
2.3.3 On Resonance Atom . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.4 Quantum Non-demolition Measurement . . . . . . . . . . . . . 43
2.3.5 Purcell Eect . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4 Atom Evolution in Time . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.1 TLS with Coherent Drive . . . . . . . . . . . . . . . . . . . . 47
2.4.2 Rabi Oscillation and Control Pulses . . . . . . . . . . . . . . . 49
2.4.3 Characteristic Timescales (T1; T2; T
2 ) . . . . . . . . . . . . . . 49
2.5 Cavity QED on Superconducting Circuit . . . . . . . . . . . . . . . . 52
3 Simulation of Cavity QED 54
3.1 Simulation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2 Dispersive Shift and Vacuum Rabi Splitting . . . . . . . . . . . . . . 57
3.3 Photon Number Splitting . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.1 Coherent Drive and Coherent State . . . . . . . . . . . . . . . 58
3.3.2 Rotating Wave Transformation . . . . . . . . . . . . . . . . . 65
3.3.3 Simulation of Photon Number Splitting . . . . . . . . . . . . . 68
3.4 Rabi Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.4.1 Time Domain Response of the Atom and Probe Field . . . . . 71
3.4.2 Simulation of Rabi Oscillation . . . . . . . . . . . . . . . . . . 74
4 Experimental Setup 76
4.1 3D Cavity Design and Simulation . . . . . . . . . . . . . . . . . . . . 76
4.1.1 3D Aluminum Cavity Design . . . . . . . . . . . . . . . . . . . 78
4.1.2 Electromagnetic Wave Simulation of 3D Cavity . . . . . . . . 79
4.2 3D Transmon Design and Simulation . . . . . . . . . . . . . . . . . . 81
4.2.1 Design and Layout . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.2 Electrical Property Simulation . . . . . . . . . . . . . . . . . . 83
4.2.3 Fabrication and Device Images . . . . . . . . . . . . . . . . . 84
4.3 Qubit Control :Pulse Modulation . . . . . . . . . . . . . . . . . . . . 87
4.3.1 Up-conversion and Down-conversion . . . . . . . . . . . . . . . 87
4.3.2 Instruments and Programming Flow . . . . . . . . . . . . . . 88
4.4 Cryogenic Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.4.1 Vacuum Can . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.4.2 Mixture Circulation . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5 Device Wiring and Measurement Setup . . . . . . . . . . . . . . . . . 93
5 Results 96
5.1 Cavity Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2 Continuous Wave Qubit Spectroscopy . . . . . . . . . . . . . . . . . . 99
5.2.1 Dispersive Shift . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2.2 Qubit Transitions . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2.3 Photon Number Calibration . . . . . . . . . . . . . . . . . . . 103
5.3 Qubit Pulses Measurement . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3.1 Pulses Cavity Spectroscopy . . . . . . . . . . . . . . . . . . . 104
5.3.2 Rabi Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.3.3 T1 Relaxation Measurement . . . . . . . . . . . . . . . . . . . 109
5.3.4 T2 Dephasing Measurement . . . . . . . . . . . . . . . . . . . 110
5.4 Table List of the Results . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.5 Qubit and Cavity near Resonance . . . . . . . . . . . . . . . . . . . . 113
6 Conclusion 116
Bibliography 118

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指導教授

陳永富(Yung-Fu Chen)

審核日期

2021-7-14

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