  We study a novel configuration for displacement detection consisting of a
nanomechanical resonator coupled to both, a radio frequency superconducting
interference device (RF SQUID) 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.
