  The quantum measurement of any observable naturally leads to noise added by
the act of measurement. Approaches to evade or reduce this noise can lead to
substantial improvements in a wide variety of sensors, from laser
interferometers to precision magnetometers and more. In this paper, we develop
a measurement protocol based upon pioneering work by the gravitational wave
community which allows for reduction of added noise from measurement by
coupling an optical field to the momentum of a small mirror. As a specific
implementation, we present a continuous measurement protocol using a
double-ring optomechanical cavity. We demonstrate that with
experimentally-relevant parameters, this protocol can lead to significant
back-action noise evasion, yielding measurement noise below the standard
quantum limit over many decades of frequency.
