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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/85391完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林俊達 | zh_TW |
| dc.contributor.advisor | Guin-Dar Lin | en |
| dc.contributor.author | 林宥成 | zh_TW |
| dc.contributor.author | Yu-Chen Lin | en |
| dc.date.accessioned | 2023-03-19T23:16:04Z | - |
| dc.date.available | 2023-12-27 | - |
| dc.date.copyright | 2022-08-15 | - |
| dc.date.issued | 2022 | - |
| dc.date.submitted | 2002-01-01 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/85391 | - |
| dc.description.abstract | 對量子多體物理的瞭解為發展量子科技打下厚實的基礎，例如量子計算、量子通訊、量子量測和量子模擬。在這之中，高保真度技術如多體量子態斷層掃描和長距離量子糾纏生成對實現大規模量子計算是很重要的一環。本論文在一種電路量子電動力學系統: transmon線性原子陣列耦合到一維半無限長傳輸線，去探討多體物理的問題。我們提出使用相空間量，維格納函數，去幫助我們觀測多體量子態。相較於每個量子位元需要獨立去讀出量子態的傳統量測，我們的方案只需要去量測單一集體放光光子，即可推估多體量子態。我們也有討論量子去相干所造成的誤差。此外，我們也從時間返演的角度，研究如何分配量子糾纏，這邊我們透過注入具有自發放射反轉波形的光子去糾纏兩顆遠距離量子位元，即使納入兩顆遠距離量子位元間的時間延遲效應，我們也能去完美產生量子糾纏態。最後，我們去探討 transmon原子高能階所造成的影響，這邊我們打入一個很強的電磁場去把transmon原子激發到高能階，再用一個很弱的電磁場去探測。我們發現在特定參數下，反射信號會有放大的現象，這邊我們發展一套使用拉比邊帶的理論去詮釋，我們的數值結果和實驗很吻合。我們的研究不僅能更加瞭解量子多體物理，也對量子控制和量子光學元件的發展有潛在應用。 | zh_TW |
| dc.description.abstract | A profound understanding of quantum many-body physics lays the foundation for developing a wide range of quantum technologies, including quantum computing, quantum communication, quantum metrology, and quantum simulation. In particular, high-fidelity techniques such as tomography of many-body states and distant entanglement generation are the key ingredients to realize large-scale quantum computation. In this work, we investigate the many-body physics implemented on the circuit QED system, where a linear array of transmons are coupled to a 1D semi-infinite transmission line. We propose a novel scheme to observe the many-body atomic states from the phase space perspective, Wigner function. Compared to the traditional measurements in which the states of each qubit are required to be readout individually, our scheme offers a simple way to infer the many-body states from the collectively emitted photon. Error sources such as the pure dephasing process have been discussed. Also, we study how to distribute quantum entanglement via the concept of time-reversal symmetry, where an input photon, whose temporal profile is the reversal of spontaneous emission, is injected to entangle two distant qubits. We demonstrate that even when the interqubit distance is large such that the time-delay effects play an important role, the desired entangled states can still be generated perfectly. Finally, we explore the multiple-level structures of the transmons, going beyond the two-level model. The higher-level effects are revealed when the transmon is strongly driven and probed by another weak tone. We find that the reflected signals are amplified for certain parameters, which can be explained by our theory regarding of Rabi sidebands. The numerical results coincide well with the experimental results. Our study provides not only a comprehensive understanding of quantum many-body physics, but also potential applications for quantum control and quantum optical devices. | en |
| dc.description.provenance | Made available in DSpace on 2023-03-19T23:16:04Z (GMT). No. of bitstreams: 1 U0001-1807202212013900.pdf: 4684584 bytes, checksum: 5b47e38fd6848fd01dbd744d549853ae (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | Certificate of thesis approval from the oral defense committee i
Acknowledgement v Abstract (Mandarin) vii Abstract (English) ix Table of contents xiii 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Superconducting atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Superradiance and dipole-dipole interaction . . . . . . . . . . . . . . . . 5 1.4 Wigner function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Model and Methodology 11 2.1 Hamiltonian and equations of motion . . . . . . . . . . . . . . . . . . . 11 2.1.1 Single-photon pulse: Shrodinger’s equation approach . . . . . . . 12 2.1.2 Higher-level dipole-dipole interaction: master equation approach 17 2.2 Input-output formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Single-photon output pulse: mode selection . . . . . . . . . . . . . . . . 20 3 Phase space perspective for an efficient single-photon loading on the qubit array 25 3.1 Preparation of a singly-excited many-particle state . . . . . . . . . . . . 25 3.1.1 Emission spectrum of the singly-excited state . . . . . . . . . . . 26 3.1.2 Emission profile of the target state . . . . . . . . . . . . . . . . . 27 3.1.3 Time-reversal waveform for the target state preparation . . . . . 28 3.2 Phase space perspective for the state preparation: Wigner functions . . . 28 3.2.1 Two-qubit system . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2.2 Effect of the pure dephasing process . . . . . . . . . . . . . . . 30 3.2.3 Distinguishability of different singly-excited states . . . . . . . . 31 3.2.4 Coherent state vs. Fock state . . . . . . . . . . . . . . . . . . . . 32 3.3 Radiation eigenmodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Quantum entanglement distribution for two distant qubits 37 4.1 Single atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.1.1 Dynamics of the spontaneous emission . . . . . . . . . . . . . . 37 4.1.2 Lambert W function and series solution . . . . . . . . . . . . . . 39 4.2 Two atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.1 Time-delay effect on the dipole-dipole interaction . . . . . . . . . 43 4.2.2 Long-range entangled state preparation . . . . . . . . . . . . . . 44 5 Reflected signal amplification for a strongly driven transmon 49 5.1 Perturbative expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.2 Reflection coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.3 Rabi sidebands and dressed states . . . . . . . . . . . . . . . . . . . . . 52 5.3.1 Single-sideband theory . . . . . . . . . . . . . . . . . . . . . . . 54 5.3.2 Double-sideband theory . . . . . . . . . . . . . . . . . . . . . . 55 5.4 Comparison between the experiments and simulations . . . . . . . . . . 58 5.5 Theoretical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.5.1 Single-sideband amplification with dressed-state population inversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.5.2 Double-sideband amplification with dressed-state atomic coherence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.5.3 Double-sideband amplification with M12(21) enhancement . . . . 64 5.5.4 Summary of the amplification mechanism . . . . . . . . . . . . . 66 6 Conclusion 67 A Appendix 71 A.1 Virtual-cavity method for the multi-qubit system . . . . . . . . . . . . . 71 A.1.1 Cascaded-cavity model . . . . . . . . . . . . . . . . . . . . . . 71 A.1.2 Virtual-cavity method . . . . . . . . . . . . . . . . . . . . . . . 74 A.2 Master equation of a single multilevel atom . . . . . . . . . . . . . . . . 75 A.2.1 Hamiltonian and master equation . . . . . . . . . . . . . . . . . 75 A.2.2 Driving field and probing field . . . . . . . . . . . . . . . . . . . 82 A.3 Optical Bloch equations of the dressed states . . . . . . . . . . . . . . . 83 A.4 Reflection coefficient under the weakly driving field . . . . . . . . . . . 85 A.5 Rest of simulations for two-tone amplification . . . . . . . . . . . . . . 87 A.6 Inverse matrix method . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Bibliography 91 | - |
| dc.language.iso | zh_TW | - |
| dc.subject | 信號放大 | zh_TW |
| dc.subject | 糾纏態製備 | zh_TW |
| dc.subject | 信號放大 | zh_TW |
| dc.subject | 維格納函數 | zh_TW |
| dc.subject | 糾纏態製備 | zh_TW |
| dc.subject | 維格納函數 | zh_TW |
| dc.subject | signal amplification | en |
| dc.subject | Wigner function | en |
| dc.subject | entangled state preparation | en |
| dc.subject | signal amplification | en |
| dc.subject | Wigner function | en |
| dc.subject | entangled state preparation | en |
| dc.title | 相空間觀點、糾纏態分配與反射信號放大於超導原子陣列在一維半無限長波導量子電動力學系統 | zh_TW |
| dc.title | Phase space perspective, entanglement distribution, and reflected signal amplification for a superconducting atomic array in a 1D semi-infinite waveguide QED system | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 110-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 許耀銓;林晏詳 | zh_TW |
| dc.contributor.oralexamcommittee | IoChun Hoi;Yen-Hsiang Lin | en |
| dc.subject.keyword | 維格納函數,糾纏態製備,信號放大, | zh_TW |
| dc.subject.keyword | Wigner function,entangled state preparation,signal amplification, | en |
| dc.relation.page | 100 | - |
| dc.identifier.doi | 10.6342/NTU202201523 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2022-07-25 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| dc.date.embargo-lift | 2024-07-22 | - |
| 顯示於系所單位： | 物理學系 | |
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| ntu-110-2.pdf | 4.58 MB | Adobe PDF | 檢視/開啟 |
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