A High Quality Factor Carbon Nanotube Mechanical Resonator at 39 GHz

We measure the mechanical resonances of an as-grown suspended carbon nanotube, detected via electrical mixing in the device. A sequence of modes extending to 39 GHz is observed with a quality factor of 35 000 in the highest mode. This unprecedentedly high combination corresponds to a thermal excited state probability below 10(-8) and a relaxation time of 140 ns with microsecond relaxation times for lower modes. The effect of electron tunneling on the mechanical resonance is found to depend on frequency as the tunneling time becomes comparable to the vibration period.