Characterization of Linear Measurements in Cavity Optomechanics: Examples and Applications

Detailed understanding of physical measurements is essential for devising efficient metrological strategies and measurement-feedback schemes and finding fundamental limitations on measurement sensitivity. In the quantum regime, measurements modify the state of the system through measurement backaction as a direct consequence of the Heisenberg principle. In cavity optomechanics and electromechanics, many strategies exist for measuring mechanical motion using electromagnetic fields, each leading to different competition between measurement imprecision and backaction. While this range of techniques allows broad applications, it makes direct comparison of different methods difficult. We develop a formalism for quantifying the performance of optomechanical measurements using a few relevant figures of merit. Our approach is inspired by similar characterizations in quantum optics and quantifies the ability to distinguish different quantum states and preservation of signal in the presence of measurement noise. We demonstrate our concept on the most common optomechanical measurements and perform detailed analysis of errors in optomechanical QND measurements. This knowledge allows us then to propose a strategy for QND measurements in levitodynamics using coherent scattering. Our results complement existing knowledge of linear optomechanical interactions and open the way to new understanding of optomechanical measurements, allowing also new applications of optomechanical devices.