  Many fascinating properties of biological active matter crucially depend on
the capacity of constituting entities to perform directed motion, e.g.,
molecular motors transporting vesicles inside cells or bacteria searching for
food. While much effort has been devoted to mimicking biological functions in
synthetic systems, such as transporting a cargo to a targeted zone, theoretical
studies have primarily focused on single active particles subject to various
spatial and temporal stimuli. Here we study the behavior of a self-propelled
particle carrying a passive cargo in a travelling activity wave and show that
this active-passive dimer displays a rich, emergent tactic behavior. For
cargoes with low mobility, the dimer always drifts in the direction of the wave
propagation. For highly-mobile cargoes, instead, the dimer can also drift
against the traveling wave. The transition between these two tactic behaviors
is controlled by the ratio between the frictions of the cargo and the
microswimmer. In slow activity waves the dimer can perform an active surfing of
the wave maxima, with an average drift velocity equal to the wave speed. These
analytical predictions, which we confirm by numerical simulations, might be
useful for the future efficient design of bio-hybrid microswimmers.
