  We consider the motion of the end mirror of a cavity inside which a two-level
atom trapped. The fast vibrating mirror induces nonlinear couplings between the
cavity field and the atom. We analyze this optical effect by showing the
population of the atom in its internal degrees of freedom as a function of
time. On the other side, fast atom-field variables result in an additional
potential for the atomic center-of-mass motion and the mirror vibration,
leading to entanglement in the motion and the vibration. The entanglement has
been numerically simulated and discussed.
