Weak Force Sensing Based on Optical Parametric Amplification in a Cavity Optomechanical System Coupled in Series with Two Oscillators

In the realm weak force sensing, an important issue is to suppress fundamental noise (quantum noise and thermal noise), as they limit the accuracy of force measurement. In this study, a weak force sensing scheme that combines a degenerate optical parametric amplifier (OPA) and an auxiliary mechanical oscillator into a cavity optomechanical system to reduce quantum noise is investigated. It is demonstrated that the noise reduction of two coupled oscillators depends on their norm mode splitting. and provide a classic analogy and quantum perspective for further clarification. Besides, the noise reduction mechanism of OPA is to reduce the fluctuation of photon number and enhance the squeezing of the cavity field. A specific design is proposed that aimed at enhancing the joint effect of both, beyond what can be achieved using OPA alone or two series coupled oscillators. This scheme provides a new perspective for deeper understanding of cavity field squeezing and auxiliary oscillator in force sensing.