Spatial dependence of plasma oscillations in Josephson tunnel junctions

We report on direct measurements of the plasma oscillations in Josephson tunnel junctions of various spatial dimensions. The effect of the spatial variation of the Cooper-pair phase difference (the Josephson phase) on the dynamics of the junction was investigated by application of a static magnetic field threading the tunneling barrier. We compare measurements where the plasma frequency was tuned either by applying a magnetic field or by raising the temperature. A crossover from short- to long-junction behavior of the functional dependence of the plasma oscillations was observed in the case of an applied magnetic field. Numerical simulations of the governing partial-differential sine-Gordon equation were performed and compared to the experimental results and a perturbation analysis. The theoretical results support the experiments and allow us to interpret the observed crossover as due to the spatial variation of the Josephson phase.