  Applications of cavity optomechanics span from gravitational wave detection
to the study of quantum motion states in mesoscopic mechanical systems. The
engineering of resonators supporting strongly interacting mechanical and
optical modes is central to these developments. However, current technological
and experimental approaches limit the accessible mechanical frequencies to a
few GHz, imposing hard constraints on quantum mechanical studies. Here we
demonstrate the optical control of 20-100~GHz mechanical modes confined in the
three dimensions within semiconductor nano-optomechanical pillar cavities. We
use a time-resolved transient optical reflectivity technique and access both
the energy spectrum and dynamics of the mechanical modes at the picosecond
timescale. A strong increase of the optomechanical coupling upon reducing the
pillar size is observed together with unprecedent room temperature Q-frequency
products above $10^{14}$. The measurements also reveal sideband generation in
the optomechanical response. Such resonators can naturally integrate quantum
wells and quantum dots, enabling novel applications in cavity quantum
electrodynamics and high frequency nanomechanics.
