  We propose an efficient method to generate a GHZ entangled state of n photons
in n microwave cavities (or resonators) via resonant interaction to a single
superconducting qutrit. The deployment of a qutrit, instead of a qubit, as the
coupler enables us to use resonant interactions exclusively for all
qutrit-cavity and qutrit-pulse operations. This unique approach significantly
shortens the time of operation which is advantageous to reducing the adverse
effects of qutrit decoherence and cavity decay on fidelity of the protocol.
Furthermore, the protocol involves no measurement on either the state of qutrit
or cavity photons. We also show that the protocol can be generalized to other
systems by replacing the superconducting qutrit coupler with different types of
physical qutrit, such as an atom in the case of cavity QED, to accomplish the
same task.
