  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.
