  The recently increasing explorations for cavity optomechanical coupling
assisted by a single atom or an atomic ensemble have opened an experimentally
accessible fashion to interface quantum optics and nano (micro) -mechanical
systems. In this paper, we study in details such composite quantum dynamics of
photon, phonon and atoms, specified by the triple coupling, which only exists
in this triple hybrid system: The cavity QED system with a movable end mirror.
We exactly diagonalize the Hamiltonian of the triple hybrid system under the
parametric resonance condition. We find that, with the rotating-wave
approximation, the hybrid system is modeled by a generalized spin-orbit
coupling where the orbital angular momentum operator is defined through a
Jordan-Schwinger realization with two bosonic modes, corresponding to the
mirror oscillation and the single mode photon of the cavity. In the
quasi-classical limit of very large angular momentum, this system will behave
like a standard cavity-QED system described by the Jaynes-Cummings model as the
angular momentum operators are transformed to bosonic operators of a single
mode. We test this observation with an experimentally accessible system with
the atom in the cavity with a moving mirror.
