Photon-number dependent afterpulsing in superconducting nanostrip single-photon detectors

Superconducting nanostrip single-photon detectors (SNSPD) are wide-spread tools in photonic quantum technologies. Here, we study afterpulsing in commercial SNSPD made of amorphous superconducting material. We find that the probability of an afterpulse is not a constant but depends on the mean number of photons per light pulse including mean numbers much less than one. Our observations exclude the electrical circuit as the primary cause of afterpulsing. We propose a phenomenological model which qualitatively explains our findings via the introduction of slowly relaxing "afterpulsing centers". We argue that two-level systems in amorphous materials are the most plausible physical candidates for the role of such afterpulsing centers.