Quantum Weak Force Sensor with Cross‐Kerr Nonlinearity and Parametric Amplification

The sensitivity of optomechanical sensors is fundamentally constrained by the combined effects of shot noise and quantum back‐action. Here we show that the joint action of cross‐Kerr nonlinearity and an optical parametric amplifier (OPA) can effectively suppress these noises. By tailoring the cross‐Kerr strength, the force‐sensing sensitivity can surpass the standard quantum limit (SQL), while an optimal driving power broadens the detection bandwidth. We further find that the system becomes unstable when the detuning falls below . Importantly, the inclusion of an OPA enhances robustness against thermal fluctuations, allowing the sensitivity of force measurement to surpass the SQL even at temperatures up to 300 K. A detailed noise analysis reveals that cross‐Kerr nonlinearity predominantly suppresses back‐action noise, whereas the OPA provides a strong reduction of shot noise. These results establish a promising hybrid strategy for realizing optomechanical sensors that combine high sensitivity with thermal resilience, with broad applications ranging from medical diagnostics to gravitational‐wave astronomy.