  It is shown that an optical parametric amplifier inside a cavity can
considerably improve the cooling of the micromechanical mirror by radiation
pressure. The micromechanical mirror can be cooled from room temperature 300 K
to sub-Kelvin temperatures, which is much lower than what is achievable in the
absence of the parametric amplifier. Further if in case of a precooled mirror
one can reach millikelvin temperatures starting with about 1 K. Our work
demonstrates the fundamental dependence of radiation pressure effects on photon
statistics.
