Noise spectrum of a tunnel junction coupled to a nanomechanical oscillator

A nanomechanical resonator coupled to a tunnel junction is studied. The oscillator modulates the transmission of the junction, changing the current and the noise spectrum. The influence of the oscillator on the noise spectrum of the junction is investigated, and the noise spectrum is obtained for arbitrary frequencies, temperatures and bias voltages. We find that the noise spectrum consists of a noise floor and a peaked structure with peaks at zero frequency, the oscillator frequency and twice the oscillator frequency. The influence of the oscillator vanishes if the bias voltage of the junction is lower than the oscillator frequency. We demonstrate that the peak at the oscillator frequency can be used to determine the oscillator occupation number, showing that the current noise in the junction functions as a thermometer for the oscillator.