  Engineered micro- and nanomechanical resonators with ultra-low dissipation
constitute the ideal systems for applications ranging from high-precision
sensing such as magnetic resonance force microscopy, to quantum transduction
between disparate quantum systems. Traditionally, the improvement of the
resonator's performance - often quantified by its Qf product (where Q is
quality factor and f is frequency) - through nanomechanical engineering such as
dissipation dilution and strain engineering, has been driven by human intuition
and insight. Such an approach is inefficient and leaves aside a plethora of
unexplored mechanical designs that potentially achieve better performance.
Here, we use a computer-aided inverse design approach known as topology
optimization to structurally design mechanical resonators with optimal
performance of the fundamental mechanical mode. Using the outcomes of this
approach, we fabricate and characterize ultra-coherent nanomechanical
resonators with record-high Qf products, entering a quantum coherent regime
where coherent oscillations are observed at room temperature. Further
refinements to the model describing the mechanical system are likely to improve
the Qf product even more. The proposed approach - which can be also used to
improve phononic crystal and coupled-mode resonators - opens up a new paradigm
for designing ultra-coherent micro- and nanomechanical resonators for
cutting-edge technology, enabling e.g. novel experiments in fundamental physics
(e.g. search for dark matter and quantum nature of gravity) and extreme sensing
of magnetic fields, electric fields and mass with unprecedented sensitivities
at room temperature.
