  The ultrastrong coupling of single-electron tunneling and nanomechanical
motion opens exciting opportunities to explore fundamental questions and
develop new platforms for quantum technologies. We have measured and modelled
this electromechanical coupling in a fully-suspended carbon nanotube device and
report a ratio of $g_m/\omega_m = 1.3$, where $g_m/2\pi = 420\pm20$~MHz is the
coupling strength and $\omega_m/2\pi=324$~MHz is the mechanical resonance
frequency. This is well within the ultrastrong coupling regime and the highest
among current electromechanical platforms. Even higher ratios could be achieved
with improvement on device design.
