Current noise of a single-electron transistor coupled to a nanomechanical resonator

The current noise spectrum of a single-electron transistor (SET) coupled to a nanomechanical resonator is calculated in the classical regime. Correlations between the charge on the SET island and the position of the resonator give rise to a distinctive noise spectrum which can be very different from that of the uncoupled SET. The current noise spectrum of the coupled system contains peaks at both the frequency of the resonator and double the resonator frequency, as well as a strong enhancement of the noise at low frequencies. The heights of the peaks are controlled by the strength of the coupling between the SET and the resonator, the damping of the resonator, and the temperature of the system.