  We propose a current correlation spectrum approach to probe the quantum
behaviors of a nanome-chanical resonator (NAMR). The NAMR is coupled to a
double quantum dot (DQD), which acts as a quantum transducer and is further
coupled to a quantum-point contact (QPC). By measuring the current correlation
spectrum of the QPC, shifts in the DQD energy levels, which depend on the
phonon occupation in the NAMR, are determined. Quantum behaviors of the NAMR
could, thus, be observed. In particular, the cooling of the NAMR into the
quantum regime could be examined. In addition, the effects of the coupling
strength between the DQD and the NAMR on these energy shifts are studied. We
also investigate the impacts on the current correlation spectrum of the QPC due
to the backaction from the charge detector on the DQD.
