  We investigate the multi-phonon interactions in a hybrid system composed of a
nitrogen-vacancy center and a mechanical resonator.We show that, through
appropriate sideband engineering analogy to the Mollow or Lamb-Dicke dynamics,
the enhanced nonlinear interactions can dominate the coupled system. As an
example, we show the preparation of nonclassical states of the mechanical
motion and explore the quantum correlation of $n$-phonon with the engineered
dissipation,based on the large multi-phonon coupling strength attainable in
this sideband structure. This work takes full advantage of the structure and
coherence features of defect centers in diamond, and may be useful for quantum
information processing.
