Abstract

A mechanical resonator is a physicist|[rsquo]|s most tangible example of a harmonic oscillator. With the advent of micro and nanoscale mechanical resonators, researchers are rapidly progressing towards a tangible harmonic oscillator with motion that requires a quantum description. Challenges include freezing out the thermomechanical motion to leave only zero-point quantum fluctuations |[delta]|xzp and, equally importantly, realizing a Heisenberg-limited displacement detector. Here, we introduce a detector that can be in principle quantum limited and is also capable of efficiently coupling to the motion of small-mass, nanoscale objects, which have the most accessible zero-point motion. Specifically, we measure the displacement of a nanomechanical beam using a superconducting transmission-line microwave cavity. We realize excellent mechanical force sensitivity (3|[thinsp]|aN|[thinsp]|Hz|[minus]|1/2), detect thermal motion at tens of millikelvin temperatures and achieve a displacement imprecision of 30 times the standard quantum limit.