  We present a model to describe a generic circuit QED system which consists of
multiple artificial three-level atoms, namely qutrits, strongly coupled to a
cavity mode. When the state transition of the atoms disobey the selection rules
the process that does not conserve the number of excitations can happen
determinatively. Therefore, we can realize coherent exchange interaction among
three or more atoms mediated by the exchange of virtual photons. In addition,
we generalize the one cavity mode mediated interactions to the multi-cavity
situation, providing a method to entangle atoms located in different cavities.
Using experimental feasible parameters, we investigate the dynamics of the
model including three cyclic-transition three-level atoms, for which the two
lowest-energy levels can be treated as qubits. Hence, we have found that two
qubits can jointly exchange excitation with one qubit in a coherent and
reversible way. In the whole process, the population in the third level of
atoms is negligible and the cavity photon number is far smaller than 1. Our
model provides a feasible scheme to couple multiple distant atoms together,
which may find applications in quantum information processing.
