  Nanomechanical oscillators are at the heart of ultrasensitive detectors of
force, mass and motion. As these detectors progress to even better sensitivity,
they will encounter measurement limits imposed by the laws of quantum
mechanics. For example, if the imprecision of a measurement of an oscillator's
position is pushed below the standard quantum limit (SQL), quantum mechanics
demands that the motion of the oscillator be perturbed by an amount larger than
the SQL. Minimizing this quantum backaction noise and nonfundamental, or
technical, noise requires an information efficient measurement. Here we
integrate a microwave cavity optomechanical system and a nearly noiseless
amplifier into an interferometer to achieve an imprecision below the SQL. As
the microwave interferometer is naturally operated at cryogenic temperatures,
the thermal motion of the oscillator is minimized, yielding an excellent force
detector with a sensitivity of 0.51 aN/rt(Hz). In addition, the demonstrated
efficient measurement is a critical step towards entangling mechanical
oscillators with other quantum systems.
