  The coupling between electrons and phonons is at the heart of many
fundamental phenomena in physics. In nature, this coupling is generally
predetermined for both, molecules and solids. Tremendous advances have been
made in controlling electrons and phonons in engineered nanosystems, yet,
control over the coupling between these degrees of freedom is still widely
lacking. Here, we use a new generation of carbon nanotube devices with movable
ultra-clean single and double quantum dots embedded in a mechanical resonator
to demonstrate the tailoring of the interactions between electronic and
mechanical degrees of freedom on the nanoscale. Exploiting this tunable
coupling, we directly image the spatial structure of phonon modes and probe
their parity in real space. Most interestingly, we demonstrate selective
coupling between individual mechanical modes and internal electronic degrees of
freedom. Our results open new vistas for engineering bulk quantum phenomena in
a controlled nanoscale setting and offer important new tools for entangling the
electronic and mechanical degrees of freedom at the quantum level.
