Time-frequency Schmidt (TFS) modes of ultrafast quantum states are naturallycompatible with high bit-rate integrated quantum communication networks. Thusthey offer an attractive alternative for the realization of high dimensionalquantum optics. Here, we present a quantum pulse gate based ondispersion-engineered ultrafast frequency conversion in a nonlinear opticalwaveguide, which is a key element for harnessing the potential of TFS modes. Weexperimentally retrieve the modal spectral-temporal structure of our device anddemonstrate a single-mode operation fidelity of 80\%, which is limited byexperimental shortcomings. In addition, we retrieve a conversion efficiency of87.7\% with a high signal-to-noise ratio of 8.8 when operating the quantumpulse gate at the single-photon level.
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