  Single electron transistors (SETs) fabricated from single-walled carbon
nanotubes (SWNTs) can be operated as highly sensitive charge detectors reaching
sensitivity levels comparable to metallic radio frequency SETs (rf-SETs). Here
we demonstrate how the charge sensitivity of the device can be improved by
using the mechanical oscillations of a single-walled carbon nanotube quantum
dot. To optimize the charge sensitivity $\delta Q$, we drive the mechanical
resonator far into the nonlinear regime and bias it to an operating point where
the mechanical third order nonlinearity is cancelled out. This way we enhance
$\delta Q$, from 6 $\mu e/\sqrt{\textrm{Hz}}$ for the static case, to 0.97 $\mu
e/\sqrt{\textrm{Hz}}$, at a probe frequency of $\sim$ 1.3 kHz.
