  We propose a scheme to measure the quantum state of a nanomechanical
oscillator cooled near its ground state of vibrational motion. This is an
extension of the nonlinear atomic homodyning technique scheme first developed
to measure the intracavity field in a micromaser. It involves the use of a
detector-atom that is simultaneously coupled to the cantilever via a magnetic
interaction and to (classical) optical fields via a Raman transition. We show
that the probability for the atom to be found in the excited state is a direct
measure of the Wigner characteristic function of the nanomechanical oscillator.
We also investigate the backaction effect of this destructive measurement on
the state of the cantilever.
