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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 管希聖(Hsi-Sheng Goan) | |
| dc.contributor.author | Zhi-Yuan Chen | en |
| dc.contributor.author | 陳智圓 | zh_TW |
| dc.date.accessioned | 2022-11-23T09:07:32Z | - |
| dc.date.available | 2021-11-08 | |
| dc.date.available | 2022-11-23T09:07:32Z | - |
| dc.date.copyright | 2021-11-08 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-08-30 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/79686 | - |
| dc.description.abstract | 量子糾纏是量子通訊與量子計算的其中一個核心資源。其中，複合系統因為可以結合每個子系統的優勢，在實驗上以及理論上都有被研究，並且具有相當的潛力。許多量子計算、量子通訊以及量子感測的複合系統都牽涉到橋接光學頻段與微波頻段的光子。在這份工作中，我們研究如何藉由光機電介面來增強與控制光學頻段與微波頻段的光子的量子糾纏。我們考慮一個三光子共振腔與機械振子組成的複合系統，並且假設其中一個光子是微波頻段，另外兩個是微波頻段，或著是反過來。機械振子跟共振腔都有噪聲跟散逸。藉由強雷射的驅動，可以增強並且線性化光壓交互作用，以達到簡化分析的功用。我們採用成分的量子糾纏（entanglement of formation）來衡量雙系統的量子糾纏。在過去的研究中，研究人員解析地在頻率空間得到了最佳化的微波與光學光子的量子糾纏，其中所解的式子頻率被假定為零，且沒有考慮雷射驅動隨時間的變化。我們更近一步在時間域的量子糾纏，並且假定了隨時變的雷射驅動。而在最佳化方法的部分，我們使用傅立葉級數作為驅動函數的擬設，並且利用下山單純形演算法來求得最佳化參數，參數包含了驅動雷射的振幅與相位，其中，旋轉波近似並沒被使用。我們的結果展示了至少兩倍於微波與光學光子間的、最佳的、不隨時變驅動情況下的成分的量子糾纏。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-23T09:07:32Z (GMT). No. of bitstreams: 1 U0001-2508202110410000.pdf: 13369255 bytes, checksum: 0bbadde6a4354fd82206ed0567af7947 (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | 口試委員會審定書 iii 誌謝 1 Acknowledgements 3 摘要 5 Abstract 7 1 Introduction 19 2 The Basic Concepts 23 2.1 Gaussian States of Continuous Variable Systems . . . . . . . . . . . . . . 23 2.1.1 Continuous Variables and Canonical Commutation Relations . . . 24 2.1.2 Quadratic Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.3 Gaussian State . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.4 Covariance Matrix and First Moment . . . . . . . . . . . . . . . 26 2.2 Quantum Langevin Equation and Input-output Formalism . . . . . . . . . 27 2.2.1 Quantum Langevin Equation . . . . . . . . . . . . . . . . . . . . 28 2.2.2 Input-output Formalism . . . . . . . . . . . . . . . . . . . . . . 29 2.3 Optomechanical System . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4 Entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4.1 Quantification of Quantum Entanglement . . . . . . . . . . . . . 31 2.4.2 Partial Transposition and Logarithmic Negativity . . . . . . . . . 32 2.4.3 Entanglement of Formation . . . . . . . . . . . . . . . . . . . . 34 3 System Dynamics 37 3.1 Model System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.1.1 Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.1.2 Simplified Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . 42 3.1.3 Initial Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Potential Experimental Realization . . . . . . . . . . . . . . . . . . . . . 43 3.2.1 Established Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2.2 Possible Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3 Quantum Stochastic Differential Equation and Master Equation . . . . . . 45 3.3.1 Input-Output Formalism for Covariance Matrix . . . . . . . . . . 45 3.3.2 Ito and Stratonovich Form of Stochastic Differential equation . . 46 3.3.3 Derive Master Equation from Ito Form . . . . . . . . . . . . . . 47 3.3.4 Input-System Expectation Value . . . . . . . . . . . . . . . . . . 48 3.4 System Covariance Matrix Evolution . . . . . . . . . . . . . . . . . . . . 53 3.5 Ansatz for Driving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.5.1 Varying-frequency Ansatz . . . . . . . . . . . . . . . . . . . . . 55 3.5.2 Fourier Series Ansatz . . . . . . . . . . . . . . . . . . . . . . . . 55 3.6 Integrated Output Operator . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.7 Frequency Domain Solution . . . . . . . . . . . . . . . . . . . . . . . . 57 3.7.1 Heisenberg Equation in Frequency Domain . . . . . . . . . . . . 57 3.7.2 Frequency Domain and Time Domain Correspondence . . . . . . 60 4 Numerical Calculation and Optimization 63 4.1 Integrated Output Covariance Matrix . . . . . . . . . . . . . . . . . . . . 65 4.2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.1 Classical Evolution Stability . . . . . . . . . . . . . . . . . . . . 68 4.2.2 System Evolution Stability . . . . . . . . . . . . . . . . . . . . . 69 4.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5 Results and Discussion 73 5.1 Frequency Domain Check . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.2 Static Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.3 Entanglement of Formation versus Logarithmic Negativity . . . . . . . . 75 5.4 Average Excitation Number . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5 Fourier Ansatz versus Frequency Ansatz . . . . . . . . . . . . . . . . . . 75 5.6 Optimization Time Choice . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.7 Integration Time Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.8 Output Optimization and System Optimization . . . . . . . . . . . . . . 78 5.9 Best Optimization Time for System . . . . . . . . . . . . . . . . . . . . 81 5.10 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6 Conclusions 103 A Optimized Parameters 107 A.1 Implementation 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 A.2 Implementation 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 A.3 Implementation 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 A.4 Implementation 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 A.5 Implementation 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 A.6 Implementation 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 A.7 Implementation 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 A.8 Implementation 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 A.9 Implementation 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Bibliography 113 | |
| dc.language.iso | en | |
| dc.title | 光機電介面下光學頻段與微波頻段的光量子糾纏最佳化 | zh_TW |
| dc.title | Optimal Entanglement between Microwave and Optical Photons via Optomechanical Interfaces | en |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.author-orcid | 0000-0002-8051-4444 | |
| dc.contributor.oralexamcommittee | 林俊達(Hsin-Tsai Liu),李瑞光(Chih-Yang Tseng),陳岳男,周忠憲 | |
| dc.subject.keyword | 量子糾纏,量子計算,量子光學,光振子系統, | zh_TW |
| dc.subject.keyword | Entanglement,Quantum Computing,Quantum Optics,Optomechanical System, | en |
| dc.relation.page | 116 | |
| dc.identifier.doi | 10.6342/NTU202102833 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2021-08-30 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理學研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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