Two-fluxon dynamics in an annular Josephson junction

Two-fluxon state in an annular Josephson junction in the presence of external magnetic field is studied analytically, numerically, and experimentally. We obtain an analytical expression for the potential of interaction between the fluxons moving at arbitrary velocities (without the use of the “nonrelativistic” approximation). Treating the fluxons as quasiparticles, we then derive equations of motion for them. Direct simulations of the full extended sine-Gordon equation are in good agreement with results produced by the analytical model, in a relevant parameter region. Experimental data qualitatively agree with the numerical results.