  Cavity optomechanical systems are being widely developed for precision force
and displacement measurements. For nanomechanical transducers, there is usually
a trade-off between the frequency ($f_{M}$) and quality factor ($Q_{M}$), which
limits temporal resolution and sensitivity. Here, we present a monolithic
cavity optomechanical transducer supporting both high $f_{M}$ and high $Q_{M}$.
By replacing the common doubly-clamped, Si$_3$N$_4$ nanobeam with a tuning fork
geometry, we demonstrate devices with the fundamental $f_{M}\approx29$ MHz and
$Q_{M}\approx2.2$$\times10^5$, corresponding to an $f_{M}Q_{M}$ product of
6.35$\times10^{12}$ Hz, comparable to the highest values previously
demonstrated for room temperature operation. This high $f_{M}Q_{M}$ product is
partly achieved by engineering the stress of the tuning fork to be 3 times the
residual film stress through clamp design, which results in an increase of
$f_{M}$ up to 1.5 times. Simulations reveal that the tuning fork design
simultaneously reduces the clamping, thermoelastic dissipation, and intrinsic
material damping contributions to mechanical loss. This work may find
application when both high temporal and force resolution are important, such as
in compact sensors for atomic force microscopy.
