Spontaneous parametric downconversion is the primary source to generate entangled photon pairs in quantum photonics laboratories. Depending on the experimental design, the generated photon pairs can be correlated in the frequency spectrum, polarization, position-momentum, and spatial modes. Exploring the spatial modes’ correlation has hitherto been limited to the polar coordinates’ azimuthal angle, and a few attempts to study Walsh mode’s radial states. Here, we study the full-mode correlation, on a Laguerre–Gauss basis, between photon pairs generated in a type-I crystal. Furthermore, we explore the effect of a structured pump beam possessing different spatial modes onto bi-photon spatial correlation. Finally, we use the capability to project over arbitrary spatial mode superpositions to perform the bi-photon state’s full quantum tomography in a 16-dimensional subspace.

中文翻译：

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自发下转换产生的相关光子对的全模式表征

自发参数下转换是在量子光子实验室中产生纠缠光子对的主要来源。取决于实验设计，所产生的光子对可以在频谱，极化，位置动量和空间模式上相关。迄今为止，探索空间模态的相关性仅限于极坐标的方位角，并且进行了一些研究沃尔什模态径向状态的尝试。在这里，我们研究了基于Laguerre-Gauss的I型晶体中产生的光子对之间的全模式相关性。此外，我们探索了具有不同空间模式的结构化泵浦光束对双光子空间相关性的影响。最后，