A time-to-digital converter with steady calibration through single-photon detection

Time-to-Digital Converters (TDCs) are a crucial tool in a wide array of fields, in particular for quantum communication, where time taggers performance can severely affect the quality of the entire application. Nowadays, FPGA-based TDCs present a viable alternative to ASIC ones, once the nonlinear behaviour due to the intrinsic nature of the device is properly mitigated. To compensate said nonlinearities, a calibration procedure is required, usually based on an interpolation methods. Here we present the design and the demonstration of a TDC that is FPGA-based and showing a residual jitter of 27 ps, that is scalable for multichannel operation. The application in Quantum Key Distribution (QKD) is discussed with a unique calibration method based on the exploitation of single-photon detection that does not require to stop the data acquisition or to use any interpolation methods, thus increasing accuracy and removing data loss. The calibration was tested in a relevant environment, investigating the device behaviour between 5{\deg}C and 80{\deg}C. Moreover, our design is capable of continuously streaming up to 12 Mevents/s for up to ~1 week without the TDC overflowing.