非厄米特拓樸光學原子鏡

Abstract

近年來，具有次波長間距的二維原子陣列在光與物質交互作用中展現出豐富的量子光學、拓撲與非厄米特物理現象。打破時間反演對稱性會產生拓撲非平庸的能帶結構，並伴隨穩定的邊界態出現，而打破旋轉對稱性則會產生非厄米特現象，如例外點（exceptional points, EPs）與非厄米特趨膚效應（non-Hermitian skin effect, NHSE）。然而，這兩種對稱性同時被破壞所導致的物理行為仍有待深入探討。本論文研究一個受晶格變形與外加磁場控制的二維原子陣列，原子之間透過長程偶極–偶極交互作用耦合。在固定原子間距的條件下，透過連續調變晶格幾何形狀（在蜂巢、方形與三角形晶格之間變形），我們觀察到在整個變形過程中例外點穩定出現。這些例外點在能帶空間中分隔具有不同陳數（Chern number）的拓撲相，其間由一個無能隙的中介相連接；當變形強度小於臨界值時，該中介相對於有限磁場仍具穩定性。例外點所對應的非平庸拓撲結構導致複數能譜繞行行為，進而產生非厄米特趨膚效應，使大量本徵態在系統邊界發生方向性局域，此現象對晶格幾何高度敏感。此外，我們發現同時具備拓撲性與非厄米特性的膚態–拓撲態（skin-topological modes）出現，並進一步證明磁場可抑制非厄米特趨膚效應，使本徵態的空間分布恢復對稱性。本研究揭示了非厄米特系統中的多樣相結構，並提供一種透過幾何與對稱性破缺來操控開放量子系統的新視角。

Recent advances in light–matter interactions in two-dimensional atomic arrays with subwavelength spacing have revealed rich phenomena in quantum optics, topology, and non-Hermitian physics. Breaking time reversal symmetry leads to topological bands with robust edge states, while breaking rotational symmetry gives rise to non-Hermitian phenomena such as exceptional points (EPs) and the non-Hermitian skin effect (NHSE). However, the consequences of breaking both symmetries simultaneously remain largely unexplored. This thesis investigates the system under continuous lattice deformation and magnetic fields, with long range dipole–dipole interactions. By smoothly tuning the lattice geometry between honeycomb, square, and triangular forms while maintaining fixed atomic spacing, we observe the emergence of EPs throughout the deformation process. These EPs separate topological phases with distinct Chern numbers via a gapless intermediate phase that remains stable under finite magnetic fields when the deformation is subcritical. The nontrivial topology of the EPs leads to complex spectral winding, which underlies the NHSE and causes directional localization of bulk eigenstates near the boundaries in a geometry-sensitive manner. We also identify skin-topological modes that combine features of non-Hermiticity and topology, and find that applying a magnetic field can suppress the skin effect by restoring spatial symmetry in the eigenstate profiles. These results reveal a rich non-Hermitian phase structure and offer new perspectives on controlling open quantum systems through geometry and symmetry breaking.