  A hybrid quantum system consisting of spatially separated two-level atoms is
studied. Two atoms do not interact directly, but they are coupled via an
intermediate system which is consisting of a superconducting flux qubit
interacting with a mechanical and an electrical resonator which are coupled to
one of the atoms. Moreover, the superconducting flux qubit is driven by a
classical microwave field. Applying the adiabatic elimination an effective
Hamiltonian for the atomic subsystem is obtained. Our results demonstrate that
the entanglement degradation decay as well as the fidelity decay in the
dispersive regime are faster. Moreover, the driven field amplitude possesses an
important role in the entanglement and fidelity evolution.
