Probing the quantum behavior of a nanomechanical resonator coupled to a double quantum dot

We propose a current correlation spectrum approach to probe the quantum behaviors of a nanomechanical 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.