Spatially resolved study of the dynamics of Josephson tunnel junctions

By scanning superconducting Nb/${\mathrm{Al}}_2$ ${\mathrm{O}}_3$/Nb tunnel junctions of various geometries with an electron beam at low temperatures we have obtained spatially resolved two-dimensional images related with the dynamics of the junctions. In a current-biased junction the local thermal perturbation effected by the beam results in a voltage change ΔV representing a convenient imaging-response signal. The spatial resolution is limited by a characteristic thermal healing length with a value of about 2 μm in our experiments. We analyze our results in terms of the sine-Gordon equation. For the interpretation of the spatially resolved voltage signal ΔV we extend the energetic analysis of the perturbed sine-Gordon system of McLaughlin and Scott by including the beam-induced local thermal perturbation. Our model allows the quantitative comparison of our experimental two-dimensional images with the local dynamics expected from the perturbed sine-Gordon equation. Our experiments include the observation of single-mode and multiple-mode cavity resonances, soliton oscillations, and flux-flow behavior.