Noise limit of a torsion pendulum under optomechanical control

In most torsion pendulum experiments, the force resolution is dominantly limited by thermal noise, which is proportional to the pendulum's intrinsic rigidity. Thus, increasing the rigidity directly, such as through increasing torsion fiber's diameter, will decrease the resolution. Here, we present a method to improve the rigidity of a pendulum indirectly through optomechanical control. In this method, for appropriate typical parameter values, the rigidity can be improved greatly. Meanwhile, the extra noise introduced, which our analysis focuses on, can be regulated within the thermal noise level, i.e., the force resolution may not decrease after optomechanical control. This can balance the conflict between large rigidity and high resolution.