Circuit quantum electrodynamics in the ultrastrong-coupling regime

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In circuit quantum electrodynamics1,2,3,4,5,6,7,8,9,10 (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 model11. Here, we report on the first experimental realization of a circuit QED system operating in the ultrastrong-coupling limit12,13, where the atom–cavity coupling rate g reaches a considerable fraction of the cavity transition frequency ωr. Furthermore, we 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 coupling14 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.

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Figure 1: Quantum circuit and experimental set-up.
Figure 2: Qubit microwave spectroscopy and low-power transmission spectra.
Figure 3: Breakdown of the Jaynes–Cummings model.


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We thank G. M. Reuther for discussions and T. Brenninger, C. Probst and K. Uhlig for technical support. We acknowledge financial support by the Deutsche Forschungsgemeinschaft through SFB 631 and the German Excellence Initiative through NIM. E.S. acknowledges financial support from UPV/EHU Grant GIU07/40, Ministerio de Ciencia e Innovación FIS2009-12773-C02-01, Basque Government Grant IT472-10, European Projects EuroSQIP and SOLID. D.Z. acknowledges financial support from FIS2008-01240 and FIS2009-13364-C02-0 (MICINN).

Author information

T.N. fabricated the sample, conducted the experiment and analysed the data presented in this work. F.D. provided important contributions regarding the interpretation of the results. T.N. and F.D. co-wrote the manuscript. J.J.G-R. provided the basic idea and the techniques for the numerical analysis of the data. E.S. and J.J.G-R. supervised the interpretation of the data. D.Z. and T.H. contributed to the understanding of the results and developed an analytical model of our system. H.H. contributed to the numerical analysis and helped with the experiment. E.P.M. contributed strongly to the experimental set-up. M.J.S. and F.H. contributed to discussions and helped edit the manuscript. A.M. and R.G. supervised the experimental part of the work.

Correspondence to T. Niemczyk.

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The authors declare no competing financial interests.

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Niemczyk, T., Deppe, F., Huebl, H. et al. Circuit quantum electrodynamics in the ultrastrong-coupling regime. Nature Phys 6, 772–776 (2010) doi:10.1038/nphys1730

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