  Carbon nanotube (CNT) electromechanical resonators have demonstrated
unprecedented sensitivities for detecting small masses and forces. The
detection speed in a cryogenic setup is usually limited by the CNT contact
resistance and parasitic capacitance. We report the use of a heterojunction
bipolar transistor (HBT) amplifying circuit near the device to measure the
mechanical amplitude at microsecond timescales. A Coulomb rectification scheme,
in which the probe signal is at much lower frequency than the mechanical drive
signal, allows investigation of the strongly non-linear regime. The behaviour
of transients in both the linear and non-linear regimes is observed and modeled
by including Duffing and non-linear damping terms in a harmonic oscillator
equation. We show that the non-linear regime can result in faster mechanical
response times, on the order of 10 microseconds for the device and circuit
presented, potentially enabling the magnetic moments of single molecules to be
measured within their spin relaxation and dephasing timescales.
