Quantum torque sensing with Kerr cavity optomechanics

Recent advances in cavity optomechanical (COM) systems have established their potential as powerful platforms for high-precision quantum measurements, ranging from gravitational wave detection to ultrasensitive mechanical displacement sensing. Yet the benefits of incorporating a Kerr nonlinear medium in such systems, specifically for torque sensing, remain largely unexplored. Here we show theoretically that a Kerr-enhanced COM torque sensor can suppress quantum noise below the standard quantum limit (SQL). By optimizing homodyne detection, we identify the optimal parameter regimes for minimizing the quantum noise. Our analysis shows that, under experimentally feasible parameters, four orders of magnitude enhancement in the force sensitivity can be achieved compared with the scenario without a Kerr nonlinear medium. The scheme is fully compatible with state-of-the-art COM engineering and paves avenues for applications ranging from dark-matter searches to Casimir-torque measurements.