  In cavity QED, the mutual interaction between natural atomic systems in
presence of a radiation field was ignored due to its negligible impact compared
with the coupling to the field. The newly engineered artificial atomic systems
(such as quantum dots and superconducting circuits) proposed for quantum
information processing enjoy strong interaction with same type of systems or
even with other types in hybrid structures, which is coherently controllable
and moreover they can be efficiently coupled to radiation fields. We present an
exact analytic solution for the time evolution of a composite system of two
interacting two-level quantum systems coupled to a single mode radiation field,
which can be realized in cavity (circuit) QED. We show how the non-classical
dynamical properties of the composite system are affected and can be tuned by
introducing and varying the mutual coupling between the two systems.
Particularly, the collapse-revival pattern shows a splitting during the revival
intervals as the coupling ratio (system-system to system-field) increases,
which is a sign of an interruption in the system-radiation energy exchange
process. Furthermore, the time evolution of the bipartite entanglement between
the two systems is found to vary significantly depending on the coupling ratio
as well as the initial state of the composite system resulting in either an
oscillatory behavior or a collapse-revival like pattern. Increasing the
coupling ratio enhances the entanglement, raises its oscillation average value
and emphasizes the collapse-revival like pattern. However, raising the coupling
ratio beyond unity increases the revival time considerably. The effect of the
other system parameters such as detuning and radiation field intensity on the
system dynamics has been investigated as well.
