Probing multipartite entanglement in a coupled Jaynes-Cummings system

We show how to probe multipartite entanglement in N coupled Jaynes-Cummings cells where the degrees of freedom are the electronic energies of each of the N atoms in separate single-mode cavities plus the N single-mode fields themselves. Specifically we propose probing the combined system as though it is a dielectric medium. The spectral properties and transition rates directly reveal multipartite entanglement signatures. It is found that the Hilbert space of the N cell system can be confined to the totally symmetric subspace of two states only that are maximally entangled W states with $2N$ degrees of freedom.