Universal Features of Counting Statistics of Thermal and Quantum Phase Slips in Nanosize Superconducting Circuits

We perform measurements of phase-slip-induced switching current events on different types of superconducting weak links and systematically study statistical properties of the switching current distributions. We employ two types of devices in which a weak link is formed either by a superconducting nanowire or by a graphene flake subject to proximity effect. We demonstrate that independently of the nature of the weak link, higher moments of the distribution take universal values. In particular, the third moment (skewness) of the distribution is close to $\ensuremath{-}1$ both in thermal and quantum regimes. The fourth moment (kurtosis) also takes a universal value close to 5. The discovered universality of skewness and kurtosis is confirmed by an analytical model. Our numerical analysis shows that introduction of extraneous noise into the system leads to significant deviations from the universal values. We suggest using the discovered universality of higher moments as a robust tool for checking against undesirable effects on noise in various types of measurements.