Coupled dynamics of an atom and an optomechanical cavity

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.