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...

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.

To determine the in vivo fluxes of the central metabolism we have developed a comprehensive approach exclusively based on the fundamental enzyme reactions known to be present, the fate of the carbon atoms of individual reactions, and the metabolite balance of the culture. No information on the energy balance is required, nor information on enzyme activities, or the directionalities of reactions. Our approach combines the power of 'H-detected 13C nuclear magnetic resonance spectroscopy t o follow individual carbons with the simplicity of establishing carbon balances of bacterial cultures. We grew a lysine-producing strain of Corynebacterium glutamicum to the metabolic and isotopic steady state with [l-'3Clglucose and determined the fractional enrichments in 27 carbon atoms of 11 amino acids isolated from the cell. Since precursor metabolites of the central metabolism are incorporated in an exactly defined manner in the carbon skeleton of amino acids, the fractional enrichments i n carbons of precursor metabolites (oxaloacetate, glyceraldehyde 3-phosphate, erythrose 4-phosphate, etc.) became directly accessible. A concise and generally applicable mathematical model was established using matrix calculus to express all metabolite mass and carbon labeling balances. An appropriate all-purpose software for the iterative solution of the equations is supplied. Applying this comprehensive methodology t o C. glutamicum, all major fluxes within the central metabolism were determined. The result is that the flux through the pentose phosphate pathway is 66.4% (relative to the glucose input flux of 1.49 mmol/g dry weight h), that of entry into the tricarboxylic acid cycle 62.2%, and the contribution of the succinylase pathway of lysine synthesis 73.7%. Due t o the large amount and high quality of measured data in vivo exchange reactions could also be quantitated with particularly high exchange rates within the pentose phosphate pathway for the ribose 5-phosphate transketolase reaction. Moreover, the total net flux of the anaplerotic reactions was quantitated as 38.0%. Most importantly, we found that in vivo one component within these anaplerotic reactions is a back flux from the carbon 4 units of the tricarboxylic acid cycle to the carbon 3 units of glycolysis of

† authors with equal contribution to this work Superconducting qubits 1,2 behave as artificial two-level atoms and are used to investigate fundamental quantum phenomena. In this context, the study of multi-photon excitations 3,4,5,6,7 occupies a central role. Moreover, coupling superconducting qubits to on-chip microwave resonators has given rise to the field of circuit QED 8,9,10,11,12,13,14,15 . In contrast to quantum-optical cavity QED 16,17,18,19 , circuit QED offers the tunability inherent to solid-state circuits. In this work, we report on the observation of key signatures of a two-photon driven Jaynes-Cummings model, which unveils the upconversion dynamics of a superconducting flux qubit 20 coupled to an on-chip resonator. Our experiment and theoretical analysis show clear evidence for the coexistence of one-and two-photon driven level anticrossings of the qubit-resonator system. This results from the symmetry breaking of the system Hamiltonian, when parity becomes a not well-defined property 21 . Our study provides deep insight into the interplay of multiphoton processes and symmetries in a qubit-resonator system.In cavity QED, a two-level atom interacts with the quantized modes of an optical or microwave cavity. The information on the coupled system is encoded both in the atom and in the cavity states. The latter can be accessed spectroscopically by measuring the transmission properties of the cavity 16 , whereas the former can be read out by suitable detectors 18,19 . In circuit QED, the solid-state counterpart of cavity QED, the first category of experiments was implemented by measuring the microwave radiation emitted by a resonator (acting as a cavity) strongly coupled to a charge qubit 8 . In a dual experiment, the state of a flux qubit was detected with a DC superconducting quantum interference device (SQUID) and vacuum Rabi oscillations were observed 10 . More recently, both approaches have been exploited to extend the toolbox of quantum optics on a chip 11,12,13,14,15,22 . Whereas all these experiments employ one-photon driving of the coupled qubit-resonator system, multi-photon studies are available only for sideband transitions 15 or bare qubits 3,4,5,6,7 . The experiments discussed in this work explore, to our knowledge for the first time, the physics of the two-photon driven Jaynes-Cummings dynamics in circuit QED. In this context, we show that the dispersive interaction between the qubit and the two-photon driving enables real level transitions. The nature of our experiment can be understood as an upconversion mechanism, which transforms the two-photon coherent driving into single photons of the Jaynes-Cummings dynamics. This process requires energy conservation and a not well-defined parity 21 of the interaction Hamiltonian due to the symmetry breaking of the qubit potential. Our experimental findings reveal that such symmetry breaking can be obtained either by choosing a suitable qubit operation point or by the presence of additional spurious fluctuators 23 .The main elements of our setup, ...

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