AI 中文总结
该研究揭示量子古伊相位会在纠缠光子对的纵向传播空间产生非局域相位奇点，明确其拓扑荷、位置及符号的决定因素，确立传播距离为纠缠光子对拓扑结构的坐标空间。
AI 中文摘要
相位奇点是一类拓扑缺陷，围绕其相位会以2π的整数倍缠绕。在纠缠多光子态中，这类奇点可非局域地出现在联合波函数中，而非仅存在于单个子系统的场中。本文证明，量子古伊相位会在纠缠光子对的二维纵向传播空间中产生非局域相位奇点（NPSs）。我们研究由拉盖尔-高斯光束泵浦的自发参量下转换产生的光子对，其中信号光子和闲频光子分别在不同的纵向距离上独立传播。随径向模式变化累积的古伊相位会引发双光子空间模式分量间的相消干涉，产生具有量子化相位缠绕的孤立强度零点。对于泵浦光的径向模式数p，NPS的拓扑荷大小为p，而其传播位置和电荷符号由泵浦光的瑞利范围和相位匹配函数决定。我们进一步确定了形成这类奇点所需的径向模式结构，结果表明可分离双光子态无法支持孤立的纵向NPSs。本研究将非局域奇异光学从横向空间关联扩展至纵向传播动力学，并确立了传播距离作为纠缠光子对拓扑结构的坐标空间。
英文摘要
Phase singularities are topological defects around which the phase winds by an integer multiple of $2π$. In entangled multiphoton states, they can emerge nonlocally in the joint wavefunction rather than in the field of either subsystem alone. Here we show that the quantum Gouy phase generates nonlocal phase singularities (NPSs) in the two-dimensional longitudinal propagation space of entangled photon pairs. We consider photon pairs produced via spontaneous parametric down-conversion pumped by a Laguerre--Gaussian beam, with the signal and idler photons propagating independently over different longitudinal distances. The accumulated radial-mode-dependent Gouy phases induce destructive interference among biphoton spatial-mode components, producing isolated intensity nulls with quantized phase winding. For a pump with radial mode number $p$, the NPS topological charges have magnitude $p$, whereas their propagation positions and charge signs are governed by the Rayleigh ranges of the pump and phase-matching functions. We further identify the radial-mode structure required for their formation, showing that separable biphoton states cannot support isolated longitudinal NPSs. Our results extend nonlocal singular optics from transverse spatial correlations to longitudinal propagation dynamics and establish propagation distance as a coordinate space for topological structures in entangled photon pairs.
