  In physical systems, decoherence can arise from both dissipative and
dephasing processes. In mechanical resonators, the driven frequency response
measures a combination of both, while time domain techniques such as ringdown
measurements can separate the two. Here, we report the first observation of the
mechanical ringdown of a carbon nanotube mechanical resonator. Comparing the
mechanical quality factor obtained from frequency- and time-domain
measurements, we find a spectral quality factor four times smaller than that
measured in ringdown, demonstrating dephasing-induced decoherence of the
nanomechanical motion. This decoherence is seen to arise at high driving
amplitudes, pointing to a non-linear dephasing mechanism. Our results highlight
the importance of time-domain techniques for understanding dissipation in
nano-mechanical resonators, and the relevance of decoherence mechanisms in
nanotube mechanics.
