Soliton excitations in Josephson tunnel junctions

A detailed numerical study of a sine-Gordon model of the Josephson tunnel junction is compared with experimental measurements on junctions with different $\frac{L}{{\lambda }_J}$ ratios. The soliton picture is found to apply well on both relatively long ($\frac{L}{{\lambda }_J}=6\mathrm{}$) and intermediate ($\frac{L}{{\lambda }_J}=2\mathrm{}$) junctions. We find good agreement for the current-voltage characteristics, power output, and for the shape and height of the zero-field steps (ZFS). Two distinct modes of soliton oscillations are observed: (i) a bunched or congealed mode giving rise to the fundamental frequency $f_1$ on all ZFS's and (ii) a "symmetric" mode which on the $N\mathrm{th}$ ZFS yields the frequency $N{f}_1$ Coexistence of two adjacent frequencies is found on the third ZFS of the longer junction ($\frac{L}{{\lambda }_J}=6\mathrm{}$) in a narrow range of bias current as also found in the experiments. Small asymmetries in the experimental environment, a weak magnetic field, e.g., is introduced via the boundary conditions of our numerical model. This gives a junction response to variations in the applied bias current close to that observed experimentally.