Fluxon cotunneling in coupled Josephson junctions: Perturbation theory

We investigate the effects of fluxon cotunneling and quantum Coulomb drag in a system of two small Josephson junctions coupled by means of mutual capacitance $C_m$. Depending on the value of $C_m$ we identify three different regimes of strong, intermediate and weak coupling. Focusing our attention on the last two regimes we develop a perturbation theory in the interaction and explicitly derive fluxon cotunneling amplitudes at sufficiently small mutual capacitance values. We demonstrate that the Coulomb drag effect survives at any non-zero $C_m$ and evaluate the non-local voltage response that is in general determined by a trade off between two different cotunneling processes. Our predictions can be straightforwardly generalized to bilinear Josephson chains and directly verified in future experiments.