  The spin of a single electron in a suspended carbon nanotube can be read out
by using its coupling to the nano-mechanical motion of the nanotube. To show
this, we consider a single electron confined within a quantum dot formed by the
suspended carbon nanotube. The spin- orbit interaction induces a coupling
between the spin and one of the bending modes of the suspended part of the
nanotube. We calculate the response of the system to pulsed external driving of
the mechanical motion using a Jaynes-Cummings model. To account for resonator
damping, we solve a quantum master equation, with parameters comparable to
those used in recent experiments, and show how information of the spin state of
the system can be acquired by measuring its mechanical motion. The latter can
be detected by observing the current through a nearby charge detector.
