  Quantum enhanced sensing is a powerful technique in which nonclassical states
are used to improve the sensitivity of a measurement. For enhanced mechanical
displacement sensing, squeezed states of light have been shown to reduce the
photon counting noise that limits the measurement noise floor. It has long been
predicted, however, that suppressing the noise floor with squeezed light should
produce an unavoidable increase in radiation pressure noise that drives the
mechanical system. Such nonclassical radiation pressure forces have thus far
been hidden by insufficient measurement strengths and residual thermal
mechanical motion. Since the ultimate measurement sensitivity relies on the
delicate balance between these two noise sources, the limits of the quantum
enhancement have not been observed. Using a microwave cavity optomechanical
system, we observe the nonclassical radiation pressure noise that necessarily
accompanies any quantum enhancement of the measurement precision. By varying
both the magnitude and phase of the squeezing, we optimize the fundamental
trade-off between mechanical imprecision and backaction noise in accordance
with the Heisenberg uncertainty principle. As the strength of the measurement
is further increased, radiation pressure forces eventually dominate the
mechanical motion. In this regime, the optomechanical interaction can be
exploited as an efficient quantum nondemolition (QND) measurement of the
amplitude fluctuations of the light field. By overwhelming mechanical thermal
noise with radiation pressure by two orders of magnitude, we demonstrate a
mechanically-mediated measurement of the squeezing with an effective homodyne
efficiency of 94%. Thus, with strong radiation pressures forces, mechanical
motion enhances the measurement of nonclassical light, just as nonclassical
light enhances the measurement of the motion.
