  Recent years have seen extraordinary progress in creating quantum states of
mechanical oscillators, leading to great interest in potential applications for
such systems in both fundamental as well as applied quantum science. One
example is the use of these devices as transducers between otherwise disparate
quantum systems. In this regard, a promising approach is to build integrated
piezoelectric optomechanical devices, that are then coupled to microwave
circuits. Optical absorption, low quality factors and other challenges have up
to now prevented operation in the quantum regime, however. Here, we design and
characterize such a piezoelectric optomechanical device fabricated from gallium
phosphide in which a 2.9~GHz mechanical mode is coupled to a high quality
factor optical resonator in the telecom band. The large electronic bandgap and
the resulting low optical absorption of this new material, on par with devices
fabricated from silicon, allows us to demonstrate quantum behavior of the
structure. This not only opens the way for realizing noise-free quantum
transduction between microwaves and optics, but in principle also from various
color centers with optical transitions in the near visible to the telecom band.
