  We report on an electrical detection method of ultrasensitive carbon nanotube
mechanical resonators. The noise floor of the detection method is reduced using
a RLC resonator and an amplifier based on a high electron mobility transistor
cooled at 4.2 K. This allows us to resolve the resonance frequency of nanotube
resonators with an unprecedented quality. We show that the noise of the
resonance frequency measured at 4.2 K is limited by the resonator itself, and
not by the imprecision of the measurement. The Allan deviation reaches ~10^-5
at 125 ms integration time. When comparing the integration time dependence of
the Allan deviation to a power law, the exponent approaches ~1/4. The Allan
deviation might be limited by the diffusion of particles over the surface of
the nanotube. Our work holds promise for mass spectrometry and surface science
experiments based on mechanical nano-resonators.
