Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate

We demonstrate a high-dimensional mode-sorter for single photons based on a multi-output quantum pulse gate, which we can program to switch between different temporal-mode encodings including pulse modes, frequency bins, time bins, and their superpositions. This device can facilitate practical realizations of quantum information applications such as high-dimensional quantum key distribution, and thus enables secure communication with enhanced information capacity. We characterize the mode-sorter through a detector tomography in 3 and 5 dimensions and find a fidelity up to $0.958\pm 0.030$ at the single-photon level.