Optimization of Crystal Length in Pulse-Pumped Up-Conversion Single-Photon Detector for Decoding Femtosecond Time-Bin Qubits

In advancing ultrafast quantum communication and computing, it is crucial to develop precise time-resolved measurement techniques for single-photon pulses. However, the measurement of photonic qubits, especially time-bin qubits, is limited by the temporal resolution of single-photon detectors, typically around tens of picoseconds. In this study, we developed a pulse-pumped up-conversion single-photon detector (UCSPD) using periodically poled Mg-doped stoichiometric lithium tantalate (PPMg:SLT) crystals of varying lengths to optimize femtosecond up-conversion. We evaluated the UCSPD’s efficiency and temporal resolution using a convolution model that accounts for group delay in nonlinear crystals. Our results demonstrate that the model calculations enable the accurate prediction of the crystal length dependence of temporal resolution and up-conversion efficiency without fitting parameters. The UCSPD achieved 415 fs resolution and 10.1 \% efficiency with a 2 mm crystal, enabling successful characterization of time-bin qubits with 800 fs pulse intervals.