  Optical parametric oscillations (OPOs) - a non-linear process involving the
coherent coupling of an optically excited two particle pump state to a signal
and an idler states with different energies - is a relevant mechanism for
optical amplification as well as for the generation of correlated photons. OPOs
require states with well-defined symmetries and energies: the fine-tuning of
material properties and structural dimensions to create these states remains a
challenge for the realization of scalable OPO-based functionalities in
semiconductor nanostructures. Here, we demonstrate a pathway towards this goal
based on the control of confined microcavity exciton-polaritons modulated by
the spatially and time varying dynamical potentials produced by a surface
acoustic waves (SAW). The exciton-polariton are confined in um-sized
intra-cavity traps fabricated by structuring a planar semiconductor microcavity
during the epitaxial growth process. OPOs in these structures benefit from the
enhanced non-linearities of confined systems. We show that SAW fields induce
state-dependent and time-varying energy shifts, which enable the energy
alignment of the confined levels with the appropriate symmetry for OPO
triggering. Furthermore, the dynamic acoustic tuning, which is fully described
by a theoretical model for the modulation of the confined polaritons by the
acoustic field, compensates for fluctuations in symmetry and dimensions of the
confinement potential thus enabling a variety of dynamic OPO regimes. The
robustness of the acoustic tuning is demonstrated by the synchronous excitation
of an array of confined OPOs using a single acoustic beam, thus opening the way
for the realization of scalable non-linear on-chip systems.
