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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/85450完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林俊達(Guin-Dar Lin) | |
| dc.contributor.author | Yi-Cheng Wang | en |
| dc.contributor.author | 王奕誠 | zh_TW |
| dc.date.accessioned | 2023-03-19T23:16:46Z | - |
| dc.date.copyright | 2022-07-26 | |
| dc.date.issued | 2022 | |
| dc.date.submitted | 2022-07-18 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/85450 | - |
| dc.description.abstract | 本論文研究單層原子陣列形成的光學鏡的非厄米物理。在這種有光與物質交互作用的開放量子系統中，只關注物質的部分會使得非厄米行為無所不在。傳統 Bloch 能帶理論的分析受到了對非厄米系統的研究的挑戰，其行為取決於邊界條件，並且能量頻譜拓譜在此扮演了重要的角色。本研究討論二維原子陣列在不同邊界條件下的行為。我們發現，藉由降低正方形原子晶格的晶體對稱性，例外點可以出現在動量空間中。從這個例外點的 Riemann 曲面拓樸而來的在複數能量平面上的非尋常卷繞造成了非厄米趨膚效應，其中有大量的特徵態指數性的集中於系統的開放邊界上。我們的結果表明這系統的非厄米趨膚效應是取決於系統的幾何形狀的，並且這些趨膚模態表現出了源於長程交互作用的無標度行為。此外，我們展示不需要做掃頻的量測便可以從有限系統的光的部分獲取塊材能帶結構。 | zh_TW |
| dc.description.abstract | In this thesis, we study the non-Hermitian physics of an optical mirror formed by a single layer of an atomic array. For such an open quantum system with light-matter interaction, the non-Hermitian behavior is ubiquitous when we only focus on the matter aspect. The conventional Bloch band theory is challenged by the studies of non-Hermitian systems, which depend crucially on the boundary conditions, and their energy spectrum topologies play important roles. Here we study the two-dimensional~(2D) atomic arrays under different boundary conditions. We find the occurrence of exceptional points in the reciprocal space by lowering the crystalline symmetry of a square atomic lattice. The nontrivial winding in the complex energy plane arising from the Riemann surface topologies of exceptional points gives rise to the non-Hermitian skin effect, where an extensive number of eigenstates are exponentially localized at open boundaries. We show that the non-Hermitian skin effect here is geometry-dependent, and these skin modes have a scale-free behavior due to the long-range interaction. Furthermore, we can extract the bulk band structures from the light aspect of a finite system, where the detuning-resolved measurement is no longer necessary. | en |
| dc.description.provenance | Made available in DSpace on 2023-03-19T23:16:46Z (GMT). No. of bitstreams: 1 U0001-0707202219212300.pdf: 8187478 bytes, checksum: 4c666cc272e313bf5aabe6e6200ca062 (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | 口試委員審定書 i 致謝 iii 摘要 v Abstract vii Contents ix Chapter 1 Introduction 1 1.1 Background and motivation 1 1.2 Outline of the thesis 3 Chapter 2 Arrays of quantum emitters 5 2.1 Scattering problem 5 2.1.1 Macroscopic theory 6 2.1.2 Free-space resonant dipole-dipole interaction 7 2.1.3 Many-body problem of quantum emitters 9 2.1.4 Coupled dipole equation 11 2.2 Two-dimensional atomic lattice 13 2.2.1 Infinite lattice in free space 14 2.2.2 Emergence of light cone 18 2.2.3 Bravais and non-Bravais lattices 21 2.3 Euler-Maclaurin formula 22 2.3.1 Two-dimensional generalization 23 2.3.2 Correction term 27 2.3.3 Applications on infinite summations 30 2.3.4 Collective Lamb shift at normal incidence 32 2.3.5 Off-diagonal terms 36 2.4 Atomic lattice in a ribbon geometry 37 Chapter 3 Non-Hermitian physics 41 3.1 Exceptional point 42 3.1.1 Exceptional points and PT-symmetry 42 3.1.2 Non-reciprocal coupling and gain/loss 45 3.1.3 Exceptional points and Dirac points 45 3.1.4 Topologies of exceptional points 48 3.2 Non-Hermitian skin effect 50 3.2.1 Breakdown of conventional band theory 50 3.2.2 Non-Hermitian skin effect in Hatano-Nelson model 53 3.2.3 Energy spectra topology 56 3.2.4 Non-Bloch band theory 60 Chapter 4 A non-Hermitian optical atomic mirror 63 4.1 Non-Hermitian degeneracy points in bulk band structures 64 4.1.1 Non-Hermitian symmetry classification and breaking 66 4.2 Geometry-dependent non-Hermitian skin effect in a ribbon geometry 70 4.2.1 Bulk band structure of a ribbon geometry 71 4.2.2 Point-gap topology and skin modes 74 4.2.3 Scale-free localization 77 4.2.4 Breakdown of generalized Brillouin zone and symmetry classification 79 4.3 Geometry-dependent non-Hermitian skin effect in a 2D finite-size atomic array 83 4.3.1 Corner accumulation 85 4.3.2 Scale-free localization 87 Chapter 5 Simulations on optical responses of atomic mirror 89 5.1 The lightest mirror in the world 90 5.2 Scattering matrix and extraction of bulk properties 93 Chapter 6 Summary 97 References 99 | |
| dc.language.iso | en | |
| dc.subject | 能量頻譜拓樸 | zh_TW |
| dc.subject | 偶極-偶極交互作用 | zh_TW |
| dc.subject | 原子陣列 | zh_TW |
| dc.subject | 例外點 | zh_TW |
| dc.subject | 非厄米趨膚效應 | zh_TW |
| dc.subject | 非厄米物理 | zh_TW |
| dc.subject | Dipole-dipole interaction | en |
| dc.subject | Non-Hermitian skin effect | en |
| dc.subject | Exceptional point | en |
| dc.subject | Energy spectrum topology | en |
| dc.subject | Non-Hermitian physics | en |
| dc.subject | Atomic mirror | en |
| dc.title | 光學原子鏡的非厄米物理 | zh_TW |
| dc.title | Non-Hermitian physics of an optical atomic mirror | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 110-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 任祥華(Hsiang-Hua Jen),游至仕(Jhih-Shih You) | |
| dc.subject.keyword | 原子陣列,偶極-偶極交互作用,非厄米物理,能量頻譜拓樸,例外點,非厄米趨膚效應, | zh_TW |
| dc.subject.keyword | Atomic mirror,Dipole-dipole interaction,Non-Hermitian physics,Energy spectrum topology,Exceptional point,Non-Hermitian skin effect, | en |
| dc.relation.page | 103 | |
| dc.identifier.doi | 10.6342/NTU202201338 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2022-07-18 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理學研究所 | zh_TW |
| dc.date.embargo-lift | 2023-07-01 | - |
| 顯示於系所單位： | 物理學系 | |
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