Circuit quantum electrodynamics in the ultrastrong-coupling regime

The Jaynes–Cummings model describes the interaction between a two-level system and a small number of photons. It is now shown that the model breaks down in the regime of ultrastrong coupling between light and matter. The spectroscopic response of a superconducting artificial atom in a waveguide resonator indicates higher-order processes. In circuit quantum electrodynamics 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 (QED), where superconducting artificial atoms are coupled to on-chip cavities, the exploration of fundamental quantum physics in the strong-coupling regime has greatly evolved. In this regime, an atom and a cavity can exchange a photon frequently before coherence is lost. Nevertheless, all experiments so far are well described by the renowned Jaynes–Cummings model 11 . Here, we report on the first experimental realization of a circuit QED system operating in the ultrastrong-coupling limit 12 , 13 , where the atom–cavity coupling rate g reaches a considerable fraction of the cavity transition frequency ω r . Furthermore, we present direct evidence for the breakdown of the Jaynes–Cummings model. We reach remarkable normalized coupling rates g / ω r of up to 12% by enhancing the inductive coupling 14 of a flux qubit to a transmission line resonator. Our circuit extends the toolbox of quantum optics on a chip towards exciting explorations of ultrastrong light–matter interaction.