Weak optomechanical coupling sensing based on self-Kerr nonlinearity

The precise measurement of weak optomechanical coupling is fundamentally limited by the inevitable thermal noise and the stringent parameter control. To overcome these limitations, we propose what we feel is a novel sensing scheme based on self-Kerr nonlinearity. Remarkably, the self-Kerr nonlinearity induced by the Born-Oppenheimer (BO) adiabatic separation between the optical and mechanical modes enables a sensitivity scaling law proportional to g^-7/3, which is the source of extraordinary sensitivity to weak optomechanical coupling. By developing an effective indirectly coupled dual-cavity model featuring self-Kerr nonlinearity and applying Gaussian quantum information theory, we demonstrate that a weak optomechanical coupling can be detected with both an excellent signal-to-noise ratio (SNR) and high precision. Specifically, our scheme improves the SNR and precision by several orders of magnitude, surpassing the capabilities of conventional nonlinear response methods. This work elucidates a fundamental mechanism based on self-Kerr nonlinearity for achieving ultra-high sensitivity in non-Hermitian sensors, thereby paving the way for the development of high-performance sensors in anharmonic systems and advancing the field of ultrasensitive quantum metrology.