We study effective light-matter interactions in a circuit QED system
consisting of a single LC resonator, which is coupled symmetrically to
multiple superconducting qubits. Starting from a minimal circuit model, we
demonstrate that in addition to the usual collective qubit-photon coupling the
resulting Hamiltonian contains direct qubit-qubit interactions, which have a
drastic effect on the ground and excited state properties of such circuits in
the ultrastrong coupling regime. In contrast to a superradiant phase transition
expected from the standard Dicke model, we find an opposite mechanism, which at
very strong interactions completely decouples the photon mode and projects the
qubits into a highly entangled ground state. These findings resolve previous
controversies over the existence of superradiant phases in circuit QED, but
they more generally show that the physics of two- or multi-atom cavity QED
settings can differ significantly from what is commonly assumed.Comment: 11 pages, 8 figure
