  A millimetric bouncing droplet sustained on a vibrating bath becomes a moving
wave source (particle) through periodically interacting with the local wave
field it generates during the droplet-bath impact. By virtue of such
particle-wave duality, the macroscopic hydrodynamic system imitates enigmatic
behaviors of the quantum realm. Here we show that it is possible to create an
integrated pilot-wave field to better prescribe the droplet trajectories, via
amplified bath capillarity. This is demonstrated with a liquid metal
droplet-bath system in which the local wave field generated by droplet bouncing
is superposed by the global wave field induced by bath meniscus oscillation.
The resulting dual pilot-wave configuration enables a class of directional
chasing motions of two bound dissimilar droplets (heterodimers) in multilevel
hydrodynamic traps (orbits), featuring two quantized regime parameters, namely
the interdroplet binding level and the orbit level. We investigate the dynamics
of the vibrating liquid metal bath, with its level-split ring wave field and
its peculiar vortex field being highlighted. We also rationalize the exotic
droplet motions by considering the interdroplet particle-wave interactions
mediated by the integrated pilot-wave field. It is revealed that a temporal
bouncing phase shift between the two droplets in the heterodimers, due to size
mismatch, gives rise to their horizontal propulsion, while their spatial
binding regime exclusively determines the collective chasing direction. It is
further evidenced that the horizontal in-orbit chasing motion is directly
related to vertical droplet bouncing. Our findings unveil the integrated
pilot-wave field as a trail towards improved droplet guiding, thereby extending
the hydrodynamic particle-wave analogy to optical systems and beyond.
