In cavity quantum electrodynamics (QED) 1-3 , light-matter interaction is probed at its most fundamental level, where individual atoms are coupled to single photons stored in three-dimensional cavities. This unique possibility to experimentally explore the foundations of quantum physics has greatly evolved with the advent of circuit QED 4-13 , where on-chip superconducting qubits and oscillators play the roles of two-level atoms and cavities, respectively. In the strong coupling limit, atom and cavity can exchange a photon frequently before coherence is lost. This important regime has been reached both in cavity and circuit QED, but the design flexibility and engineering potential of the latter allowed for increasing the ratio between the atom-cavity coupling rate g and the cavity transition frequency ωr above the percent level 8,14,15 . While these experiments are well described by the renowned Jaynes-Cummings model 16 , novel physics is expected when g reaches a considerable fraction of ωr. Promising steps towards this so-called ultrastrong coupling regime 17,18 have recently been taken in semiconductor structures 19,20 . Here, we report on the first experimental realization of a superconducting circuit QED system in the ultrastrong coupling limit and present direct evidence for the breakdown of the Jaynes-Cummings model. We reach remarkable normalized coupling rates g/ωr of up to 12 % by enhancing the inductive coupling of a flux qubit 21 to a transmission line resonator using the nonlinear inductance of a Josephson junction 22 . Our circuit extends the toolbox of quantum optics on a chip towards exciting explorations of the ultrastrong interaction between light and matter.In the strong coupling regime, the atom-cavity coupling rate g exceeds the dissipation rates κ and γ of both, cavity and atom, giving rise to coherent light-matter oscillations and superposition states. This regime was reached in various types of systems operating at different energy scales [1][2][3][23][24][25] . At microwave frequencies, strong coupling is feasible due to the enormous engineerability of superconducting circuit QED systems 4,5 . Here, small cavity mode volumes and large dipole moments of artificial atoms 26 enable coupling rates g of about 15 1 % of the cavity mode frequency ω r . Nevertheless, as in cavity QED, the quantum dynamics of these systems follows the Jaynes-Cummings model, which describes the coherent exchange of a single excitation between the atom and the cavity mode. Although the Hamiltonian of a realistic atom-cavity system contains so-called counterrotating terms allowing the simultaneous creation ior annihilation of an excitation in both atom and cavity mode, these terms can be safely neglected for small normalized coupling rates g/ω r . However, when g becomes a significant fraction of ω r , the counterrotating terms are expected to manifest, giving rise to exciting effects in QED.The ultrastrong coupling regime is difficult to reach in traditional quantum optics, but was recently realized in a solid-stat...

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We report the observation of strong coupling between the exchange-coupled spins in a gallium-doped yttrium iron garnet and a superconducting coplanar microwave resonator made from Nb. The measured coupling rate of 450 MHz is proportional to the square root of the number of exchange-coupled spins and well exceeds the loss rate of 50 MHz of the spin system. This demonstrates that exchange-coupled systems are suitable for cavity quantum electrodynamics experiments, while allowing high integration densities due to their spin densities of the order of one Bohr magneton per atom. Our results furthermore show, that experiments with multiple exchange-coupled spin systems interacting via a single resonator are within reach.