Synchronization of Josephson vortices in multi-junction systems

A largely adopted model for the description of high-temperature superconductors such as BSCCO results in several long Josephson junctions one on the top of the other ('stacked'). The dynamics of the basic nonlinear excitation of the isolated long Josephson junction, the Josephson vortex, is modified by the coupling among the junctions, so the motion of the flux quanta in the various layers is affected by the flux dynamics in all other layers. Two basic states are possible: a synchronous motion, where all junctions are reflected at the edge at the same instant, and an out-of-phase motion, where vortices in each layer are shifted with respect to neighboring vortices. This is of direct interest for applications since flux quanta emit, upon reflection, radiation at frequencies of great interest (above 100 GHz). Research has been directed towards the optimal conditions to favor such emission, that is mainly to retrieve the above described synchronous motion. We discuss the physics behind synchronization of nonlinear elements and we review applications to Josephson arrays. We discuss in the framework of a general model for synchronization, the Kuramoto model, a mechanism that can possibly enhance synchronization, such as coupling to a resonant cavity. We present a version of the Kuramoto model that might include the effects of the strong interaction between the oscillators and the cavity