An isochronous ultralow loss torsion micropendulum for chip-scale microgravity*

The pendulum is one of the oldest gravimeters, featuring frequency-based readout limited by geometric nonlinearity. While modern gravimeters focus on displacement-based spring-mass or free-fall designs, the advent of nanofabrication techniques invites a revisiting of the pendulum, motivated by the prospect of low-loss, compact, isochronous operation, leveraging precise dimensional control. Here we exploit advances in strain-engineered nanomechanics---specifically, strained silicon nitride nanoribbon suspensions---to realize a pendulum with a 0.1 mg silicon test mass levitated in torsion with an ultra-low damping rate of 10 $\mu$Hz and a parametric sensitivity to gravity in excess of 5 Hz/$g_{0}$. The low thermal acceleration, $2\times10^{-9}g_{0}/\sqrt{Hz}$, gives access to a parametric gravity resolution of $10^{-8}g_{0}$ for drive amplitudes of 100 mrad and integration times within the free decay time, of interest for both commercial applications and fundamental experiments. We present progress toward this goal, demonstrating free and self-sustained oscillators with frequency stabilities as little as 80 nHz at 200 s, corresponding to a gravity resolution of $5\times10^{-7}g_{0}$. We also show how the Duffing nonlinearity of the suspension can be used to cancel the pendulum nonlinearity, paving the way toward a fully isochronous, high-$Q$ micromechanical clock.