  Time-frequency Schmidt (TFS) modes of ultrafast quantum states are naturally
compatible with high bit-rate integrated quantum communication networks. Thus
they offer an attractive alternative for the realization of high dimensional
quantum optics. Here, we present a quantum pulse gate based on
dispersion-engineered ultrafast frequency conversion in a nonlinear optical
waveguide, which is a key element for harnessing the potential of TFS modes. We
experimentally retrieve the modal spectral-temporal structure of our device and
demonstrate a single-mode operation fidelity of 80\%, which is limited by
experimental shortcomings. In addition, we retrieve a conversion efficiency of
87.7\% with a high signal-to-noise ratio of 8.8 when operating the quantum
pulse gate at the single-photon level.
