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.
