  We propose an optomechanical dissipation engineering scheme by introducing an
ancillary mechanical mode with a large decay rate to control the density of
states of the optical mode. The effective linewidth of the optical mode can be
reduced or broadened, manifesting the dissipation engineering. To prove the
ability of our scheme in improving the performances of the optomechanical
system, we studied optomechanical entanglement and phonon cooling. It is
demonstrated that the optomechanical entanglement overwhelmed by thermal phonon
excitations could be restored via dissipation engineering. For the phonon
cooling, an order of magnitude improvement could be achieved. Our scheme can be
generalized to other systems with multiple bosonic modes, which is
experimentally feasible with advances in materials and nanofabrication,
including optical Fabry-Perot cavities, superconducting circuits, and nanobeam
photonic crystals.
