Current noise spectrum of a quantum shuttle

We present a method for calculating the full current noise spectrum S(ω) for the class of nano-electromechanical systems (NEMS) that can be described by a Markovian generalized master equation. As a specific example we apply the method to a quantum shuttle. The noise spectrum of the shuttle has peaks at integer multiples of the mechanical frequency, which is slightly renormalized. The renormalization explains a previously observed small deviation of the shuttle current compared to the expected value given by the product of the natural mechanical frequency and the electron charge. For a certain parameter range the quantum shuttle exhibits a coexistence regime, where the charges are transported by two different mechanisms: shuttling and sequential tunneling. In our previous studies we showed that characteristic features in the zero-frequency noise could be quantitatively understood as a slow switching process between the two current channels, and the present study shows that this interpretation holds also qualitatively at finite frequency.