  The nonlinearity is an important feature in the field of optomechanics.
Employing atomic coherence, we put forward a scheme to enhance the nonlinearity
of the cavity optomechanical system. The effective Hamiltonian is derived,
which shows that the nonlinear strength can be enhanced by increasing the
number of atoms at certain range of parameters. We also numerically study the
nonlinearity enhancement beyond the effective Hamiltonian. Furthermore, we
investigate the potential usage of the nonlinearity in performing quantum
nondemolition (QND) measurement of the bosonic modes. Our results show that the
present system exhibits synchronization, and the nonlinear effects provide us
an effective method in performing QND.
