  Nonlinear interferometers that replace beamsplitters in Mach-Zehnder
interferometers with nonlinear amplifiers for quantum-enhanced phase
measurements have drawn increasing interest in recent years, but practical
quantum sensors based on nonlinear interferometry remain an outstanding
challenge. Here, we demonstrate the first practical application of nonlinear
interferometry by measuring the displacement of an atomic force microscope
microcantilever with quantum noise reduction of up to 3~dB below the standard
quantum limit, corresponding to a quantum-enhanced measurement of beam
displacement of $\mathrm{1.7~fm/\sqrt{Hz}}$. Further, we show how to minimize
photon backaction noise while taking advantage of quantum noise reduction by
transducing the cantilever displacement signal with a weak squeezed state while
using dual homodyne detection with a higher power local oscillator. This
approach offers a path toward quantum-enhanced broadband, high-speed scanning
probe microscopy.
