Fundamental Quantum Limits of Multicarrier Optomechanical Sensors

Optomechanical sensors involving multiple optical carriers can experience mechanically mediated interactions causing multimode 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 multicarrier 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.

Figure 1

An instance of an optomechanical sensor—a laser-interferometric gravitational wave detector with multiple different frequency carrier modes. Circulating light couples to the mechanical motion of the mirrors inside the interferometer arms. $\widehat{\mathbf{a}}$ and $\widehat{\mathbf{b}}$ describe the field of the carrier-mode sidebands, entering and exiting the interferometer, respectively, at the dark port.