Conventional optical synthesis, the manipulation of the phase and amplitude of spectral components to produce an optical pulse in different temporal modes, is revolutionizing ultrafast optical science and metrology. These technologies rely on the Fourier transform of light fields between time and frequency domains in one-dimensional space. However, within this treatment, it is impossible to incorporate the quantum correlation among photons. Here, we expand the Fourier synthesis into high-dimensional space to deal with the quantum correlation and carry out an experimental demonstration by manipulating the two-photon probability distribution of a biphoton in two-dimensional time and frequency space. As a potential application, we show the manipulation of a heralded single-photon wave packet, which is never explained by the conventional one-dimensional Fourier optics. Our approach opens up a new pathway to tailor the temporal characteristics of a photon wave packet with high-dimensional quantum-mechanical treatment. We anticipate that such high-dimensional treatment of light in time and frequency domains could bridge the research fields between quantum optics and ultrafast optical measurements.

中文翻译：

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二维时频空间中的量子光学合成

传统的光学合成，即操纵光谱分量的相位和幅度以在不同时间模式下产生光脉冲，正在彻底改变超快光学科学和计量学。这些技术依赖于一维空间中时域和频域之间光场的傅立叶变换。然而，在这种处理中，不可能结合光子之间的量子相关性。在这里，我们将傅立叶合成扩展到高维空间以处理量子相关性，并通过在二维时间和频率空间中操纵双光子的双光子概率分布进行实验演示。作为一个潜在的应用，我们展示了对预示的单光子波包的操纵，这是传统的一维傅立叶光学无法解释的。我们的方法开辟了一条新途径，可以通过高维量子力学处理来定制光子波包的时间特性。我们预计，在时域和频域中对光的这种高维处理可以在量子光学和超快光学测量之间架起桥梁。