Fluxon bunching in supercurrent-coupled Josephson junctions

We investigate analytically and numerically the interaction between fluxons of different Josephson junctions coupled through Cooper-pair tunneling. We find that the supercurrent interaction gives rise to attraction between fluxons regardless of their polarity, although fluxons of different polarity are found to interact with a binding energy of an order of magnitude larger than between unipolar fluxons. When bias current is applied to a system of two coupled junctions we can analytically evaluate the range in the difference of the bias currents for which fluxons are bound. The differences in interaction between fluxons of equal and opposite polarity are discussed. Numerical simulations of coupled sine-Gordon equations agree very well with the analytical predictions.