Displacement detection with a vibrating rf superconducting interference device: Beating the standard linear limit

We study a configuration for displacement detection consisting of a nanomechanical resonator coupled to both a radio frequency superconducting interference device and to a superconducting stripline resonator. We employ an adiabatic approximation and rotating wave approximation and calculate the displacement sensitivity. We study the performance of such a displacement detector when the stripline resonator is driven into a region of nonlinear oscillations. In this region the system exhibits noise squeezing in the output signal when homodyne detection is employed for readout. We show that displacement sensitivity of the device in this region may exceed the upper bound imposed upon the sensitivity when operating in the linear region. On the other hand, we find that the high displacement sensitivity is accompanied by a slowing down of the response of the system, resulting in a limited bandwidth.