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Single-photon sources are the cornerstone of the optical quantum information process, including quantum computing, simulation, metrology, etc. The practical application requires these sources to be high purity and indistinguishability. A readily available approach is to use heralded single-photon sources to generate photon pairs via spontaneous parametric down-conversion (SPDC). However, the purity of photon pairs generated by SPDC is usually limited by the spectral correlations because of energy conservation. Extra spectral filters and group velocity matching (GVM) can be used to generate spectral uncorrelated photon pairs on-chip. However, the material dispersion of most materials cannot meet the GVM requirements, and extra components will reduce the integration. In this work, we develop a strategy to generate pure single photon on-chip by mode coupling in heterogeneously coupled waveguides. This strategy can tailor the group velocity directly, or shape biphoton wave function through a new degree of freedom that is the non-constant overlap between interacting modes. This allows the generation of high-purity single photons totally on-chip. Design examples based on lithium niobate waveguide are provided to generate spectrally pure photon pairs. This strategy is generic that it is not limited to any material and waveguide system, providing new possibilities in the generation of quantum photons.
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