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

Circuit QED with qutrit: coupling three or more atoms via virtual photon exchange