  We report fast readout of the motion of a carbon nanotube mechanical
resonator. A close-proximity high electron mobility transistor amplifier is
used to increase the bandwidth of the measurement of nanotube displacements
from the kHz to the MHz regime. Using an electrical detection scheme with the
nanotube acting as a mixer, we detect the amplitude of its mechanical motion at
room temperature with an intermediate frequency of 6 MHz and a timeconstant of
780 ns, both up to five orders of magnitude faster than achieved before. The
transient response of the mechanical motion indicates a ring-down time faster
than our enhanced time resolution, placing an upper bound on the contribution
of energy relaxation processes to the room temperature mechanical quality
factor.
