In long Josephson junctions with multiple discontinuities of the Josephson phase, fractional vortex molecules are spontaneously formed. At each discontinuity point a fractional Josephson vortex carrying a magnetic flux $|Phi|<Phi_0$, $Phi_0approx 2.0
7times 10^{-15}$ Wb being the magnetic flux quantum, is pinned. Each vortex has an oscillatory eigenmode with a frequency that depends on $Phi/Phi_0$ and lies inside the plasma gap. We experimentally investigate the dependence of the eigenfrequencies of a two-vortex molecule on the distance between the vortices, on their topological charge $wp=2piPhi/Phi_0$ and on the bias current $gamma$ applied to the Josephson junction. We find that with decreasing distance between vortices, a splitting of the eigenfrequencies occurs, that corresponds to the emergence of collective oscillatory modes of both vortices. We use a resonant microwave spectroscopy technique and find good agreement between experimental results and theoretical predictions.
We consider a fractional Josephson vortex in a long 0-kappa Josephson junction. A uniformly applied bias current exerts a Lorentz force on the vortex. If the bias current exceeds the critical current, an integer fluxon is torn off the kappa-vortex an
d the junction switches to the voltage state. In the presence of thermal fluctuations the escape process takes place with finite probability already at subcritical values of the bias current. We experimentally investigate the thermally induced escape of a fractional vortex by high resolution measurements of the critical current as a function of the topological charge kappa of the vortex and compare the results to numerical simulations for finite junction lengths and to theoretical predictions for infinite junction lengths. To study the effect caused by the junction geometry we compare the vortex escape in annular and linear junctions.
