Minimum requirements for feedback enhanced force sensing

The paper theoretically shows that for linear oscillators neither stationary nor non-stationary linear feedback provide any sensitivity enhancement over that possible with estimation alone. Importantly this result holds true in both the quantum and classical regime and in the presence of non-Gaussian noise terms. It is experimentally demonstrated that detection of a small stationary incoherent force can be enhanced by estimation in the same way as feedback cooling. The system presented is a cavity opto-electromechanical system (COEMS) consisting of an evanescently coupled silica microtoroid integrating high Q mechanical and optical modes. The incoherent signal, which is uncorrelated to the thermal noise, was applied via an electrode which facilitated strong electrical actuation through strong electrical gradient forces. The effect of the incoherent force on the mechanics manifests as an increase in the temperature of the mechanical oscillator. Energy averaging is used to resolve the temperature discrepancies and detect the signal. Enabling force sensitivity through post-processing without the need for feedback techniques greatly simplifies the role of micromechanical oscillators in sensing applications and fundamental research.