  In a hybrid quantum system composed of two quantum wells placed inside a
cavity with a moving end mirror pumped by bichromatic coherent light, we
address the formation of squeezed states of a mechanical resonator. The exciton
mode and mechanical resonator interact indirectly via microcavity fields. Under
the conditions of the generated coupling, we predict squeezing of the
mechanical-mode beyond the resolved side-band regime with existing experimental
parameters. Finally, we show that the robustness of this squeezing against
thermal fluctuations is important for practical applications of such systems.
