发表机构
Graduate School of Engineering, Kochi University of Technology（高知工科大学大学院工学研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过将LG泵浦SPDC分解为分束器变换与空间双模压缩，建立代数框架，推导施密特数解析式，统一描述高阶LG泵浦SPDC的模式结构、守恒律与纠缠维度。
AI 中文摘要
通过自发参量下转换（SPDC）产生的高维空间纠缠为量子信息处理提供了强大的资源，然而当泵浦占据高阶拉盖尔-高斯（LG）模式时，其模式结构变得日益复杂。在此，我们发展了一个代数框架来表征双光子空间模式纠缠，其方法是将LG泵浦的SPDC分解为一个空间模式分束器变换，随后进行空间双模压缩。通过选择双光子LG基矢半径作为泵浦光束半径与晶体诱导关联宽度之间的几何平均值，我们获得了一个自然的模式基矢，在该基矢中这两种操作可以被分开处理。当泵浦光束半径与关联宽度匹配时，空间压缩消失，泵浦的两个圆模式分量在信号光子和闲频光子上被独立地守恒，从而导致轨道角动量和总空间模式数均守恒。我们进一步推导了任意LG泵浦模式和压缩强度下施密特数的解析表达式，揭示了径向和方位角泵浦指数如何控制空间纠缠的维度。这种代数表征为高阶LG泵浦SPDC的模式结构、守恒定律和纠缠维度提供了统一的描述。
英文摘要
High-dimensional spatial entanglement generated via spontaneous parametric down-conversion (SPDC) provides a powerful resource for quantum information processing, yet its mode structure becomes increasingly complex when the pump occupies a higher-order Laguerre--Gaussian (LG) mode. Here, we develop an algebraic framework for characterizing biphoton spatial-mode entanglement by factorizing LG-pumped SPDC into a spatial-mode beam-splitter transformation followed by spatial two-mode squeezing. By choosing the biphoton LG basis radius as the geometric mean of the pump-beam radius and the crystal-induced correlation width, we obtain a natural modal basis in which the two operations can be treated separately. When the pump-beam radius matches the correlation width, spatial squeezing vanishes, and the two circular-mode components of the pump are independently conserved across the signal and idler photons, leading to conservation of both orbital angular momentum and the total spatial mode number. We further derive an analytical expression for the Schmidt number for arbitrary LG pump modes and squeezing strengths, revealing how the radial and azimuthal pump indices govern the dimensionality of the spatial entanglement. This algebraic characterization provides a unified description of the mode structure, conservation laws, and entanglement dimensionality of higher-order-LG-pumped SPDC.
Comments15 pages, 5 figures
