We report the experimental observation of a spatiotemporal Hong-Ou-Mandel (HOM) interference of biphoton states of extremely high Schmidt number. Two-photon interference of 1500 spatial modes and a total of more than $3\times {10}^6$ spatiotemporal modes is evidenced by measuring momentum spatial coincidences, without any prior selection of the photons in time and space coincidence, between the pixels of the far-field images of two strongly multimode spontaneous parametric down-conversion (SPDC) beams propagating through a HOM interferometer. The outgoing SPDC beams are recorded on two separate detector arrays operating in the photon-counting regime. The properties of HOM interference are investigated both in the time and space domains. We show that the two-photon interference exhibits temporal and two-dimensional spatial HOM dips with visibilities of 60% and widths in good agreement with the spatiotemporal coherence properties of the biphoton state. Moreover, we demonstrate that maxima of momentum spatial coincidences are evidenced within each image, in correspondence with these dips.

中文翻译：

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极高施密特数的双光子态的时空Hong-Ou-Mandel干涉成像

我们报告了时空Hong-Ou-Mandel（HOM）干扰的极高施密特数双光子态的实验观察。1500个空间模式的双光子干涉，总和超过$3\times {10}^6$时空模式是通过测量在通过HOM干涉仪传播的两个强多模自发参量下转换（SPDC）光束的远场图像的像素之间测量动量空间一致而没有在时间和空间一致的光子的任何事先选择的情况下证明的。发出的SPDC光束记录在以光子计数方式工作的两个单独的探测器阵列上。在时域和空域均研究了HOM干扰的特性。我们表明，双光子干涉表现出时空和二维空间HOM倾角，可见性为60％，宽度与双光子态的时空相干特性良好吻合。此外，我们证明了在每张图像中都证明了动量空间重合的最大值，