  For an assembly of particles interacting with a two dimensional periodic
substrate, a series of commensuration effects can arise when the number of
particles is an integer multiple of the number of substrate minima. Such
commensuration effects can appear for vortices in type-II superconductors with
periodic pinning or for colloidal particles on optical landscapes. Under bulk
external driving, the pinning or drag on the particles is strongly enhanced at
commensuration. Here we consider the active rheology of a single particle
driven through an assembly of particles coupled to a periodic substrate at
different commensurate conditions. For increasing density at fixed driving
force, we observe nonmonotonic drag along with what we call an
anti-commensuration effect where the drag or pinning effectiveness is reduced
in commensurate states, opposite from the behavior typically observed under
bulk driving. The velocity enhancement or drag reduction appears when the
background particles form a crystalline state that is coupled more strongly to
the substrate than to the driven particle, while under incommensurate
conditions, the background particles are disordered and produce enhanced drag
on the probe particle. The velocity noise of the driven particle has a narrow
band signature at commensuration and a broad band signature away from
commensuration. We map out the regions in which viscous flow, periodic flow,
and a pinned phase appear. We show that the effects we observe are robust on
both square and triangular substrate arrays and for both vortices in type-II
superconductors and colloidal particles on optical landscapes.
