Quantitative characterization of the spatial structure of single photons is essential for free-space quantum communication and quantum imaging. We introduce an interferometric technique that enables the complete characterization of a two-dimensional probability amplitude of a single photon. Importantly, in contrast to methods that use a reference photon for the phase measurement, our technique relies on a single photon interfering with itself. Our setup comprises of a heralded single-photon source with an unknown spatial phase and a modified Mach-Zehnder interferometer with a spatial filter in one of its arms. The spatial filter removes the unknown spatial phase and the filtered beam interferes with the unaltered beam passing through the other arm of the interferometer. We experimentally confirm the feasibility of our technique by reconstructing the spatial phase of heralded single photons using the lowest order interference fringes. This technique can be applied to the characterization of arbitrary pure spatial states of single photons.

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单光子束的自参考全息图

单光子空间结构的定量表征对于自由空间量子通信和量子成像至关重要。我们引入了一种干涉测量技术，该技术能够完整表征单个光子的二维概率幅度。重要的是，与使用参考光子进行相位测量的方法相比，我们的技术依赖于与自身干涉的单个光子。我们的设置包括一个未知空间相位的预兆单光子源和一个改进的 Mach-Zehnder 干涉仪，它的一个臂上有一个空间滤波器。空间滤波器去除未知的空间相位，过滤后的光束与穿过干涉仪另一臂的未改变光束发生干涉。我们通过使用最低阶干涉条纹重建预示单光子的空间相位，通过实验证实了我们技术的可行性。该技术可用于表征单光子的任意纯空间状态。