Effects of Thermal and Lévy Noise Sources on the Switching Current Distributions of a Josephson Junction

We discuss the combined effect of Gaussian and α-stable Lévy noise sources on the switching current distribution of a short tunnel Josephson junction, while an external bias current flowing through the junction is linearly swept. At a fixed temperature, if the bias current is repeatedly ramped up from zero, and the value of the bias current at which the system switches to the finite voltage state is recorded, we obtain the distribution of the current values associated to escape events, i.e., the probability distribution of the bias currents at which the junction switches to the finite voltage state from the superconducting zero-voltage state. This information content is promptly available in experiments on Josephson junctions. We demonstrate that a Lévy noise current added to the linearly increased bias current clearly modifies the switching current distribution due to the sole Gaussian-distributed thermal fluctuations. Albeit both Gaussian and Lévy components contribute to the overall noise level, they do not interfere, because they produce switching at different bias levels: the Lévy noise in the lower-current portion of the distribution, the Gaussian noise when the energy barrier becomes comparable to the noise energy. Finally, the analytical expression of the cumulative distribution function of Josephson switching currents can be compared with an analytical estimate.