Phase locking, devil's staircases, Farey trees, and Arnold tongues in driven vortex lattices with periodic pinning

Using numerical simulations, we observe phase locking, Arnold tongues, and devil's staircases for vortex lattices driven at varying angles with respec t to an underlying superconducting periodic pinning array. This rich struct ure should be observable in transport measurements. The transverse V(I) cur ves have a devil's staircase structure, with plateaus occurring near the dr iving angles along symmetry directions of the pinning array. Each of the pl ateaus corresponds to a different dynamical phase with a distinctive vortex structure and flow pattern.