Noise in a superconducting single-electron transistor resonator driven by an external field

We investigate the noise properties of a superconducting single-electron transistor (SSET) coupled to a harmonically driven resonator. Using a Langevin equation approach, we calculate the frequency spectrum of the SSET charge and calculate its effect on the resonator field. We find that the heights of the peaks in the frequency spectra depend sensitively on the amplitude of the resonator oscillation and hence suggest that the heights of these peaks could act as a sensitive signal for detecting the small changes in the amplitude of the drive. The previously known results for the effective amplitude-dependent damping and temperature provided by the SSET for the case of a low-frequency resonator are generalized for all resonator frequencies