  While quantum mechanics exquisitely describes the behavior of microscopic
systems, one ongoing challenge is to explore its applicability to systems of
larger size and mass. Unfortunately, quantum states of increasingly macroscopic
objects are more easily corrupted by unintentional measurements from the
classical environment. Additionally, even the intentional measurements from the
observer can further perturb the system. In optomechanics, coherent light
fields serve as the intermediary between the fragile mechanical states and our
inherently classical world by exerting radiation pressure forces and extracting
mechanical information. Here we engineer a microwave cavity optomechanical
system to stabilize a nonclassical steady-state of motion while independently,
continuously, and nondestructively monitoring it. By coupling the motion of an
aluminum membrane to two microwave cavities, we separately prepare and measure
a squeezed state of motion. We demonstrate a quantum nondemolition (QND)
measurement of sub-vacuum mechanical quadrature fluctuations. The techniques
developed here have direct applications in the areas of quantum-enhanced
sensing and quantum information processing, and could be further extended to
more complex quantum states.
