  Optomechanical crystals are a promising device platform for quantum
transduction and sensing. Precise targeting of the optical and acoustic
resonance frequencies of these devices is crucial for future advances on these
fronts. However, fabrication disorder in these wavelength-scale nanoscale
devices typically leads to inhomogeneous resonance frequencies. Here we achieve
in-situ, selective frequency tuning of optical and acoustic resonances in
silicon optomechanical crystals via electric field-induced nano-oxidation using
an atomic-force microscope. Our method can achieve a tuning range >2 nm (0.13%)
for the optical resonance wavelength in the telecom C-band, and >60 MHz (1.2%)
for the acoustic resonance frequency at 5 GHz. The tuning resolution of 1.1 nm
for the optical wavelength, and $150$ kHz for the acoustic frequency allows us
to spectrally align multiple optomechanical crystal resonators using optimal
oxidation patterns determined via an inverse design protocol. Our results
establish a method for precise post-fabrication tuning of optomechancical
crystals. This technique can enable coupled optomechanical resonator arrays,
scalable resonant optomechanical circuits, and frequency matching of
microwave-optical quantum transducers.
