  Optomechanical sensors involving multiple optical carriers can experience
mechanically mediated interactions causing multi-mode correlations across the
optical fields. One instance is laser-interferometric gravitational wave
detectors which introduce multiple carrier frequencies for classical sensing
and control purposes. An outstanding question is whether such multi-carrier
optomechanical sensors outperform their single-carrier counterpart in terms of
quantum-limited sensitivity. We show that the best precision is achieved by a
single-carrier instance of the sensor. For the current LIGO detection system
this precision is already reachable.
