Programmable Spatiotemporal Quantum Parametric Mode Sorter

We experimentally demonstrate a programmable parametric mode sorter of high-dimensional signals in a composite spatiotemporal Hilbert space through mode-selective quantum frequency up-conversion. As a concrete example and with quantum communication applications in mind, we consider the Laguerre-Gaussian and Hermite-Gaussian modes as the spatial and temporal state basis for the signals, respectively. By modulating the spatiotemporal profiles of the up-conversion pump, we demonstrate the faithful selection of signal photons in those modes and their superposition modes. Our results show an improvement in the quantum mode-sorting performance by coupling the up-converted light into a single-mode fiber and/or operating the up-conversion at the edge of phase matching. Optimizing pump temporal profiles allows us to achieve more than 12-dB extinction for mutually unbiased basis (MUB) sets of the spatiotemporal modes. This fully programmable and efficient system could be a viable resource for quantum communications, quantum computation, and quantum metrology.