Continous Measurement of the Energy Eigenstates of a Nanomechanical Resonator without a Non-Demolition Probe

We show that it is possible to perform a continuous measurement that continually projects a nano-resonator into its energy eigenstates by employing a linear coupling with a two-state system. This technique makes it possible to perform a measurement that exposes the quantum nature of the resonator by coupling it to a Cooper-pair Box and a superconducting transmission-line resonator.