  We show that the interaction between vortices and sound waves in atomic
Bose-Einstein condensates can be elucidated in a double-well trap: with one
vortex in each well, the sound emitted by each precessing vortex can be driven
into the opposing vortex (if of the same polarity). This cross-talk leads to a
periodic exchange of energy between the vortices which is long-range and highly
efficient. The increase in vortex energy (obtained by numerical simulations of
the Gross-Pitaevskii equation) is significant and experimentally observable as
a migration of the vortex to higher density over just a few precession periods.
Similar effects can be controllably engineered by introducing a precessing
localised obstacle into one well as an artificial generator of sound, thereby
demonstrating the parametric driving of energy into a vortex.
