研究結果顯示，界面能夠提供超越均勻陣列的激發動力學控制能力。對於不同原子間距的原子陣列，原子間距的不匹配可在界面附近誘發激發反射，且此效應可延伸至多區域結構，進而產生激發捕獲效應。對於整齊–無序界面，整齊區域與無序區域之間的競爭會導致局域化–離域化行為，其中整齊區域的尺寸強烈影響長時間激發分佈。在外部驅動下，界面陣列表現出豐富的穩態相，包括交互作用誘發的耗盡，以及取決於原子間距配置的不同傳輸行為。在多激發區域中，高階量子關聯與糾纏熵顯示，隨著整齊系統尺寸增加，關聯會受到抑制並呈現熱化趨勢。此外，藉由引入位置相依的方向性，本論文建立了一個結構化波導量子電動力學框架，其中工程化的手性能夠產生不同的激發圖樣，包括中心化、波動式、蛙跳式與色散式動力學。這些行為與亞輻射本徵模之間的干涉密切相關，並且在實際可達的耦合效率下仍保持穩健。最後，本論文進一步延伸至非線性波導量子電動力學中的高階量子關聯。這些發現不僅加深了對波導量子電動力學中界面驅動多體動力學的理論理解，也為非線性波導量子電動力學、可程式化手性光子系統，以及基於波導的量子技術在傳輸控制、態工程與量子資訊應用方面的未來發展提供了方向。;Waveguide quantum electrodynamics (wQED) provides a versatile platform for exploring collective light–matter interactions， long-range photon-mediated couplings， and nonequilibrium excitation dynamics in low-dimensional open quantum systems. This dissertation investigates how interfaces in waveguide-coupled atomic arrays reveals the behavior of quantum excitations， from single-excitation transport to multi-excitation dynamics and high-order quantum correlations. The main objective is to clarify how intentionally introduced inhomogeneities—such as dissimilar interatomic spacing， clean–disordered boundaries， partial driving， and structured directionality—reshape excitation propagation， trapping， localization， depletion， and correlation dynamics in interfaced atomic arrays， followed by the overview of nonlinear wQED.
The study is primarily theoretical and is based on master-equation formulations for open waveguide-QED systems， effective non-Hermitian descriptions in either low-energetic sector or numerical simulations of full quantum dynamics. These approaches are applied to one-dimensional arrays of waveguide-coupled emitters with chiral and dissipative couplings， motivated by experimentally relevant nanophotonic and waveguide platforms.
The results show that interfaces provide powerful control over excitation dynamics beyond those found in homogeneous arrays. For dissimilar atomic arrays， the mismatch of interatomic spacing can induce excitation reflection near the interface， and these effects can be extended to multiple-zone configurations resulting in excitation trapping effect. For clean–disordered interfaces， the competition between clean and disordered regions leads to localization–delocalization behavior， where the clean-zone size strongly influences the long-time excitation distribution. Under external driving， interfaced arrays exhibit rich steady-state phases， including interaction-induced depletion and distinct transport behavior depending on interatomic spacing configuration. In the multi-excitation regime， high-order quantum correlations and entanglement entropy reveal suppression of correlations and thermalizing tendencies as the clean system size increases. Furthermore， by introducing site-dependent directionality， a structured wQED framework is established in which engineered chirality generates distinct excitation patterns， including centering， wave-like， leap-frog， and dispersive dynamics. These behaviors are shown to be closely connected to interference among subradiant eigenmodes and remain robust under realistic coupling efficiencies. Finally， the dissertation extends toward high-order quantum correlations in nonlinear waveguide QED. The findings not only deepen the theoretical understanding of interface-driven many-body dynamics in waveguide QED， but also point toward future developments in nonlinear wQED， programmable chiral photonic systems， and waveguide-based quantum technologies for transport control， state engineering， and quantum information applications.
