[论文解读] Localization and scattering of a photon in quasiperiodic qubit arrays

Xinyin Zhang, Yongguan Ke+5 more|arXiv (Cornell University)|Jan 29, 2026

Quantum Mechanics and Non-Hermitian Physics被引用 0

一句话总结

论文研究在准周期间距的量子比特阵列耦合波导中的光子散射，揭示了连续谱的局域化亚辐射态和传输中的迁移边界。

ABSTRACT

We study the localization and scattering of a single photon in a waveguide coupled to qubit arrays with quasiperiodic spacings. As the quasiperiodic strength increases, localized subradiant states with extremely long lifetime appear around the resonant frequency and form a continuum band. In stark contrast to the fully disordered waveguide QED where all states are localized, we analytically find that the fraction of localized states is up to $(3-\sqrt{5})/2$ when the modulation frequency is $(1+\sqrt{5})/2$. The localized and delocalized states can be related to excitation in flat and curved inverse energy bands under the approximation of large-period modulation. When the quasiperiodic strength is weak, an extended subradiant state can support the transmission of a photon. However, as the quasiperiodic strength increases, localized subradiant states can completely block the transmission of a single photon in resonance with the subradiant states, and enhance the overall reflection. At a fixed quasiperiodic strength, we also find mobility edge in transmission spectrum, below and above which the transmission is either turned on and off as system size increases. Our work give new insights into the localization in non-Hermitian systems.

研究动机与目标

• 理解准周期间距如何影响耦合到波导的量子比特阵列中单激发态的局域化。
• 将激发局域化性质与光子散射与传输联系起来。
• 识别准周期强度对亚辐射态和传输特征的影响。
• 描述传输谱中迁移边界的存在性。

提出的方法

• 三部分哈密顿量：H_R = H_A + H_F + H_I，适用于准周期量子比特间距。
• 实空间的传输矩阵方法用于获得单光子反射与透射。
• 动量空间的格林函数方法通过G(ω)和H_eff将散射与亚辐射本征态联系起来。
• 较大周期调制近似，将局域化/离域化状态与平带/曲率逆能带联系起来。
• 用斐波那契/Renyi样的有理近似来推导局部化态的分数来自周期近似。

实验结果

研究问题

• RQ1 准周期调制如何影响耦合到波导的单激发态在波导量子电动力学系统中的局域化？
• RQ2 局域化/离域化的亚辐射态与光子反射/透射之间的关系是什么？
• RQ3 在准周期WQED系统中是否会出现传输中的迁移边界，以及它如何取决于系统尺寸和频率？

主要发现

• 随着准周期强度增加，局域化的亚辐射态在共振频率附近形成连续谱。
• 当调制频率为(1+√5)/2时，局部化态的分数可以达到(3−√5)/2。
• 在共振处，局部化态阻塞光子传输，而离域化的亚辐射态可以支持传输。
• 由于局域化增强，总体反射随准周期强度的增加而提高。
• 存在传输迁移边界，显示为随着光子频率变化和系统尺寸变化的局域化转变。
• 两种解析方法（传输矩阵法和格林函数法）得到相同结果，将散射与亚辐射态性质联系起来。