Measuring nanomechanical motion with a microwave cavity interferometer

In recent years microfabricated microwave cavities have been extremely successful in a wide variety of detector applications. In this article we focus this technology on the challenge of quantum-limited displacement detection of a macroscopic object. We measure the displacement of a nanomechanical beam by capacitively coupling its position to the resonant frequency of a superconducting transmission-line microwave cavity. With our device we realize near state-of-the-art mechanical force sensitivity (3 $\rm{aN/\sqrt{Hz}}$) and thus add to only a handful of techniques able to measure thermomechanical motion at 10's of milliKelvin temperatures. Our measurement imprecision reaches a promising 30 times the expected imprecision at the standard quantum limit, and we quantify our ability to extract measurement backaction from our results as well as elucidate the important steps that will be required to progress towards the full quantum limit with this new detector.