Fast, optimal readout of a tethered optomechanical pressure sensor

Abstract

We demonstrate a fast readout method for tethered optomechanical pressure sensors. The fast readout method allows mechanical ring-down measurement rates that exceed the total mechanical damping rate $Γ_t$. We model the uncertainty of our ring-down measurements with the Cramér-Rao bound, including the effect of thermomechanical noise. Both our data and the Cramér-Rao bound indicate that measurement rates on the order of the mechanical damping rate produce the lowest uncertainty. At low pressures, using the optimal measurement rate allows 10$\times$ faster measurements or 3$\times$ lower uncertainty compared to allowing our sensor to ring down to the thermomechanical noise floor. Our results allow tethered optomechanical pressure sensors to operate at rates comparable to commercially available pressure gauges, removing an obstacle to adoption of optomechanical pressure sensors in industrial settings.