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.
@article{arxiv.0908.1415,
title = {Measuring the quantum state of a nanomechanical oscillator},
author = {Swati Singh and Pierre Meystre},
journal= {arXiv preprint arXiv:0908.1415},
year = {2009}
}