光學原子鏡的非厄米物理

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。

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.