非厄米狄拉克系统中PT对称破缺下的古伊相位

中文摘要 AI 辅助

我们研究由准厄米质量狄拉克哈密顿量描述的相对论性类波束波包，揭示非厄米动力学中的异常古伊相位行为。研究表明，古伊相位可作为全局$\boldsymbol{\textit{PT}}$对称破缺阈值的灵敏探针：在全局未破缺的准厄米区域，古伊相位保持纯实数；越过奇异点后，古伊相位改变符号并获得虚部。在奇异点处，古伊相位变化在小质量极限下消失，但在大质量时达到最大，揭示出从有效经典行为向类波量子行为的反直觉转变。我们提出一项实验方案，通过监测光在损耗波导中传播的衰减来测量破缺区域中非厄米古伊相位的分量。这些结果凸显了非厄米古伊相位在光子学应用中的潜力，包括阈值条件的确定以及具有增益和损耗的系统的设计与控制。

英文摘要

We study relativistic beam-like wave packets governed by a quasi-Hermitian massive Dirac Hamiltonian and uncover anomalous Gouy-phase behavior in non-Hermitian dynamics. We show that the Gouy phase provides a sensitive probe of the global $\mathcal{PT}$-symmetry-breaking threshold: it remains purely real in the globally unbroken, quasi-Hermitian regime, while, after crossing the exceptional point, the Gouy phase changes sign and acquires an imaginary component. At the exceptional point, the Gouy-phase variation vanishes in the small-mass limit but becomes maximal for large masses, revealing a counterintuitive crossover from effectively classical to increasingly wave-like quantum behavior. We propose an experimental scheme to measure the components of the non-Hermitian Gouy phase in the broken regime by monitoring the attenuation of a light beam propagating through a lossy waveguide. These results highlight the potential of the non-Hermitian Gouy phase for photonic applications, including the determination of threshold conditions and the design and control of systems with gain and loss.

发表机构

• Universidade Federal do Piauí (UFPI)（皮奥伊联邦大学）
• University of Coimbra（科英布拉大学）

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