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We propose to use cavity optomechanical systems in the regime of opticalbistability for the detection of weak harmonic forces. Due to theoptomechanical coupling an external force on the mechanical oscillatormodulates the resonance frequency of the cavity and consequently the switchingrates between the two bistable branches. A large difference in the cavityoutput fields then leads to a strongly amplified homodyne signal. We determinethe switching rates as a function of the cavity detuning from extensivenumerical simulations of the stochastic master equation as appropriate forcontinuous homodyne detection. We develop a two-state rate equation model thatquantitatively describes the slow switching dynamics. This model is solvedanalytically in the presence of a weak harmonic force to obtain approximateexpressions for the power gain and signal-to-noise ratio that we then compareto force detection with an optomechanical system in the linear regime.

Detection of weak forces based on noise-activated switching in bistable optomechanical systems