Detection of weak stochastic forces in a parametrically stabilized micro-optomechanical system

Measuring a weak force is an important task for micromechanical systems, both when using devices as sensitive detectors and, particularly, in experiments of quantum mechanics. The optimal strategy for resolving a weak stochastic signal force on a huge background (typically given by thermal noise) is a crucial and debated topic, and the stability of the mechanical resonance is a further, related critical issue. We introduce and analyze the parametric control of the optical spring, which allows us to stabilize the resonance and provides a phase reference for the oscillator motion, yet conserving a free evolution in one quadrature of the phase space. We also study quantitatively the characteristics of our micro-optomechanical system as detector of stochastic force for short measurement times (for quick, high-resolution monitoring) as well as for the longer-term observations that optimize the sensitivity. We compare a simple strategy based on the evaluation of the variance of the displacement which is a widely used technique) with an optimal Wiener-Kolmogorov data analysis. We show that, due to the parametric stabilization of the effective susceptibility, we can more efficiently implement Wiener filtering, and we investigate how this strategy improves the performance of our system. We finally demonstrate the possibility to resolve stochastic force variations well below 1% of the thermal noise.