Sensitivity of the mixing-current technique for the detection of mechanical motion in the coherent tunnelling regime

In a recent publication we have studied theoretically the sensitivity of the mixing-current technique to detect nanomechanical motion by coupling the oscillator to a single-electron transistor in the incoherent tunnelling regime: hT > kBT). In order to reach the best sensitivity we find that one should enter the strong coupling regime, as described in the recent publication (Micchi et al 2015 Phys. Rev. Lett. 115 206802) where a mechanical bistability is described. In this regime the electronic detection device strongly modifies the effective potential of the oscillator and the non-linearities determine the form of the displacement fluctuation spectrum. We find theoretical upper bounds to the sensitivity for the detection of the oscillation amplitude of the oscillator. It turns out that it is convenient to work as close as possible to the bistability.