  We numerically examine the manipulation of vortices interacting with a moving
trap representing a magnetic force tip translating across a superconducting
sample containing a periodic array of pinning sites. As a function of the tip
velocity and coupling strength, we find five distinct dynamic phases, including
a decoupled regime where the vortices are dragged a short distance within a
pinning site, an intermediate coupling regime where vortices in neighboring
pinning sites exchange places, an intermediate trapping regime where individual
vortices are dragged longer distances and exchange modes of vortices occur in
the surrounding pins, an intermittent multiple trapping regime where the trap
switches between capturing one or two vortices, and a strong couping regime in
which the trap permanently captures and drags two vortices. In some regimes we
observe the counterintuitive behavior that slow moving traps couple less
strongly to vortices than faster moving traps; however, the fastest moving
traps are generally decoupled. The different phases can be characterized by the
distances the vortices are displaced and the force fluctuations exerted on the
trap. We find different types of stick-slip motion depending on whether
vortices are moving into and out of pinning sites, undergoing exchange, or
performing correlated motion induced by vortices outside of the trap. Our
results are general to the manipulation of other types of particle-based
systems interacting with periodic trap arrays, such as colloidal particles or
certain types of frictional systems.
