Detecting quantum-coherent nanomechanical oscillations using the current-noise spectrum of a double quantum dot

We consider a nanomechanical resonator coupled to a double quantum dot. We demonstrate how the finite-frequency current-noise spectrum through the double quantum dot can be used to distinguish classical and quantum behavior in the nearby nanoelectromechanical resonator. We also show how the full-frequency current-noise spectrum gives important information on the combined double quantum dot-resonator energy spectrum. Finally, we point out regimes where the quantum state of the resonator becomes squeezed and also examine the cross-correlated electron-phonon current noise.