  We study the tunneling conductance of nano-scale quantum ``shuttles'' in
connection with a recent experiment (H. Park et al., Nature, 407, 57 (2000)) in
which a vibrating C^60 molecule was apparently functioning as the island of a
single electron transistor (SET). While our calculation starts from the same
model of previous work (D. Boese and H. Schoeller, Europhys. Lett. 54,
66(2001)) we obtain quantitatively different dynamics. Calculated I-V curves
exhibit most features present in experimental data with a physically reasonable
parameter set, and point to a strong dependence of the oscillator's potential
on the electrostatics of the island region. We propose that in a regime where
the electric field due to the bias voltage itself affects island position, a
"catastrophic" negative differential conductance (NDC) may be realized. This
effect is directly attributable to the magnitude of overlap of final and
initial quantum oscillator states, and as such represents experimental control
over quantum transitions of the oscillator via the macroscopically controllable
bias voltage.
