  In the field of quantum computation and communication there is a compelling
need for quantum-coherent frequency conversion between microwave electronics
and infra-red optics. A promising platform for this is an optomechanical
crystal resonator that uses simultaneous photonic and phononic crystals to
create a co-localized cavity coupling an electromagnetic mode to an acoustic
mode, which then via electromechanical interactions can undergo direct
transduction to electronics. The majority of work in this area has been on
one-dimensional nanobeam resonators which provide strong optomechanical
couplings but, due to their geometry, suffer from an inability to dissipate
heat produced by the laser pumping required for operation. Recently, a
quasi-two-dimensional optomechanical crystal cavity was developed in silicon
exhibiting similarly strong coupling with better thermalization, but at a
mechanical frequency above optimal qubit operating frequencies. Here we adapt
this design to gallium arsenide, a natural thin-film single-crystal
piezoelectric that can incorporate electromechanical interactions, obtaining a
mechanical resonant mode at f_m ~ 4.5 GHz ideal for superconducting qubits, and
demonstrating optomechanical coupling g_om/(2pi) ~ 650 kHz.
