Abstract- One of the main milestones in the study of opto-mechanical system (OMS) is to increase the sensitivity of the measurement of weak forces up to the quantum limit. We have studied the detection of weak force by OMS. In the stable condition, the dynamics of the system behave asymptotically similar to stationary state in which the signal to noise ratio is obtained using covariance matrix. We have shown the maximum sensitivity is reached in the bistablility region. We also studied the destructive effects of thermal noise on the sensitivity of OMS. Our approach is based on the covariance matrix formalism.

Keywords: Opto-mechanics, force measurement, Standard quantum limit.

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