Coherent noise cancellation in optomechanical system with double optical modes

The coherent quantum noise cancellation (CQNC) strategy has been performed in the single-mode optomechanical systems to promote an ultra-sensitive metrology protocol to break the standard quantum limit. The key idea of CQNC is that the backaction noises arising from radiation pressure and driving can be offset by coupling the optical mode to a near-resonant ancillary mode. In this work, a continuous weak-force sensing under CQNC is developed in a double-mode optomechanical system consisted of two optical modes with distinct frequencies and a mechanical mode. In particular, under the asymmetrical treatment by driving the higher-frequency optical mode, probing the lower-frequency one, and coupling the probe mode to the ancillary mode, our configuration can be used to resemble the conventional CQNC sensing. It is more important to find that the current CQNC strategy simultaneously stabilizes the double-mode system with respect to both the constrained driving power (the Routh-Hurwitz criterion) and the effective positive mechanical damping (the stable optical-spring condition). Moreover, through exploiting the coupling between the probe mode and the ancillary mode under this nontrivial extension of the CQNC strategy (from the single-mode version to the double-mode one), the rotating-wave term and the counter-rotating term are found to be responsible to the system stability and the noise cancellation, respectively. In realistic situations, our scheme can be practiced in a tripartite optomechanical setup with a membrane in the middle and a twisted-cavity-based weak-torque detector.