Navigation, bio-tracking devices and gravity gradiometry are amongst the diverse range of applications requiring ultrasensitive measurements of acceleration. We describe an accelerometer that exploits the dispersive and dissipative coupling of the motion of an optical whispering gallery mode (WGM) resonator to a waveguide. A silica microsphere-cantilever is used as both the optical cavity and inertial test-mass. Deflections of the cantilever in response to acceleration alter the evanescent coupling between the microsphere and the waveguide, in turn causing a measurable frequency shift and broadening of the WGM resonance. The theory of this optomechanical response is outlined. By extracting the dispersive and dissipative optomechanical rates from data we find good agreement between our model and sensor response. A noise density of 4.5 $mu$g Hz$^{-1/2}$ with a bias instability of 31.8 $mu$g (g=9.81 ms$^{-2}$) is measured, limited by classical noise larger than the test-mass thermal motion. Closed-loop feedback is demonstrated to reduce the bias instability and long term drift. Currently this sensor outperforms both commercial accelerometers used for navigation and those in ballistocardiology for monitoring blood flowing into the heart. Further optimization would enable short-range gravitational force detection with operation beyond the lab for terrestrial or space gradiometry.
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