  We demonstrate coupling between the motions of two independently trapped ions
with a separation distance of 620 $\mu$m. The ion-ion interaction is enhanced
via a room-temperature electrically floating metallic wire which connects two
surface traps. Tuning the motion of both ions into resonance, we show flow of
energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by
strong surface electric-field noise in our device. Our ion wire-ion system
demonstrates that room-temperature conductors can be used to mediate and tune
interactions between independently trapped charges over distances beyond those
achievable with free-space dipole-dipole coupling. This technology may be used
to sympathetically cool or entangle remotely trapped charges and enable
coupling between disparate physical systems.
