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Cavity quantum electrodynamics with atom-like mirrors


It has long been recognized that atomic emission of radiation is not an immutable property of an atom, but is instead dependent on the electromagnetic environment1 and, in the case of ensembles, also on the collective interactions between the atoms2,3,4,5,6. In an open radiative environment, the hallmark of collective interactions is enhanced spontaneous emission—super-radiance2—with non-dissipative dynamics largely obscured by rapid atomic decay7. Here we observe the dynamical exchange of excitations between a single artificial atom and an entangled collective state of an atomic array9 through the precise positioning of artificial atoms realized as superconducting qubits8 along a one-dimensional waveguide. This collective state is dark, trapping radiation and creating a cavity-like system with artificial atoms acting as resonant mirrors in the otherwise open waveguide. The emergent atom–cavity system is shown to have a large interaction-to-dissipation ratio (cooperativity exceeding 100), reaching the regime of strong coupling, in which coherent interactions dominate dissipative and decoherence effects. Achieving strong coupling with interacting qubits in an open waveguide provides a means of synthesizing multi-photon dark states with high efficiency and paves the way for exploiting correlated dissipation and decoherence-free subspaces of quantum emitter arrays at the many-body level10,11,12,13.

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Fig. 1: Waveguide QED setup.
Fig. 2: Vacuum Rabi splitting.
Fig. 3: Vacuum Rabi oscillations.
Fig. 4: Compound atomic mirrors, N = 4.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


  1. Purcell, E. M., Torrey, H. C. & Pound, R. V. Resonance absorption by nuclear magnetic moments in a solid. Phys. Rev. 69, 37–38 (1946).

    Article  ADS  CAS  Google Scholar 

  2. Dicke, R. H. Coherence in spontaneous radiation processes. Phys. Rev. 93, 99–110 (1954).

    Article  ADS  CAS  Google Scholar 

  3. Gross, M. & Haroche, S. Superradiance: an essay on the theory of collective spontaneous emission. Phys. Rep. 93, 301–396 (1982).

    Article  ADS  CAS  Google Scholar 

  4. Osnaghi, S. et al. Coherent control of an atomic collision in a cavity. Phys. Rev. Lett. 87, 037902 (2001).

    Article  ADS  CAS  Google Scholar 

  5. Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007).

    Article  ADS  CAS  Google Scholar 

  6. Röhlsberger, R., Schlage, K., Sahoo, B., Couet, S. & Rüffer, R. Collective Lamb shift in single-photon superradiance. Science 328, 1248–1251 (2010).

    Article  ADS  Google Scholar 

  7. Scully, M. O. Collective Lamb shift in single photon Dicke superradiance. Phys. Rev. Lett. 102, 143601 (2009).

    Article  ADS  Google Scholar 

  8. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

    Article  ADS  Google Scholar 

  9. Chang, D. E., Jiang, L., Gorshkov, A. V. & Kimble, H. J. Cavity QED with atomic mirrors. New J. Phys. 14, 063003 (2012).

    Article  ADS  Google Scholar 

  10. Albrecht, A. et al. Subradiant states of quantum bits coupled to a one-dimensional waveguide. New J. Phys. 21, 025003 (2019).

    Article  ADS  CAS  Google Scholar 

  11. Ramos, T., Pichler, H., Daley, A. J. & Zoller, P. Quantum spin dimers from chiral dissipation in cold-atom chains. Phys. Rev. Lett. 113, 237203 (2014).

    Article  ADS  Google Scholar 

  12. Mahmoodian, S. et al. Strongly correlated photon transport in waveguide quantum electrodynamics with weakly coupled emitters. Phys. Rev. Lett. 121, 143601 (2018).

    Article  ADS  CAS  Google Scholar 

  13. González-Tudela, A., Paulisch, V., Chang, D. E., Kimble, H. J. & Cirac, J. I. Deterministic generation of arbitrary photonic states assisted by dissipation. Phys. Rev. Lett. 115, 163603 (2015).

    Article  ADS  Google Scholar 

  14. Roy, D., Wilson, C. M. & Firstenberg, O. Strongly interacting photons in one-dimensional continuum. Rev. Mod. Phys. 89, 021001 (2017).

    Article  MathSciNet  Google Scholar 

  15. Lodahl, P., Mahmoodian, S. & Stobbe, S. Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87, 347–400 (2015).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  16. Gu, X., Kockum, A. F., Miranowicz, A., Liu, Y.-x. & Nori, F. Microwave photonics with superconducting quantum circuits. Phys. Rep. 718/719, 1–102 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  17. Dzsotjan, D., Sørensen, A. S. & Fleischhauer, M. Quantum emitters coupled to surface plasmons of a nanowire: a Green’s function approach. Phys. Rev. B 82, 075427 (2010).

    Article  ADS  Google Scholar 

  18. Asenjo-Garcia, A., Hood, J. D., Chang, D. E. & Kimble, H. J. Atom-light interactions in quasi-one-dimensional nanostructures: a Green’s-function perspective. Phys. Rev. A 95, 033818 (2017).

    Article  ADS  Google Scholar 

  19. Kockum, A. F., Johansson, G. & Nori, F. Decoherence-free interaction between giant atoms in waveguide quantum electrodynamics. Phys. Rev. Lett. 120, 140404 (2018).

    Article  ADS  CAS  Google Scholar 

  20. van Loo, A. F. et al. Photon-mediated interactions between distant artificial atoms. Science 342, 1494–1496 (2013).

    Article  ADS  Google Scholar 

  21. Hood, J. D. et al. Atom–atom interactions around the band edge of a photonic crystal waveguide. Proc. Natl Acad. Sci. USA 113, 10507–10512 (2016).

    Article  ADS  CAS  Google Scholar 

  22. Sundaresan, N. M., Lundgren, R., Zhu, G., Gorshkov, A. V. & Houck, A. A. Interacting qubit-photon bound states with superconducting circuits. Phys. Rev. X 9, 011021 (2019).

    CAS  Google Scholar 

  23. Lalumière, K. et al. Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms. Phys. Rev. A 88, 043806 (2013).

    Article  ADS  Google Scholar 

  24. Astafiev, O. et al. Resonance fluorescence of a single artificial atom. Science 327, 840–843 (2010).

    Article  ADS  CAS  Google Scholar 

  25. Cook, R. J. & Kimble, H. J. Possibility of direct observation of quantum jumps. Phys. Rev. Lett. 54, 1023–1026 (1985).

    Article  ADS  CAS  Google Scholar 

  26. Rosario Hamann, A. et al. Nonreciprocity realized with quantum nonlinearity. Phys. Rev. Lett. 121, 123601 (2018).

    Article  ADS  Google Scholar 

  27. Yeh, J.-H., LeFebvre, J., Premaratne, S., Wellstood, F. C. & Palmer, B. S. Microwave attenuators for use with quantum devices below 100 mK. J. Appl. Phys. 121, 224501 (2017).

    Article  ADS  Google Scholar 

  28. Bronn, N. T. et al. High coherence plane breaking packaging for superconducting qubits. Quantum Sci. Technol. 3, 024007 (2018).

    Article  ADS  Google Scholar 

  29. Paulisch, V., Kimble, H. J. & González-Tudela, A. Universal quantum computation in waveguide QED using decoherence free subspaces. New J. Phys. 18, 043041 (2016).

    Article  ADS  Google Scholar 

  30. Mirhosseini, M. et al. Superconducting metamaterials for waveguide quantum electrodynamics. Nat. Commun. 9, 3706 (2018).

    Article  ADS  Google Scholar 

  31. Keller, A. J. et al. Al transmon qubits on silicon-on-insulator for quantum device integration. Appl. Phys. Lett. 111, 042603 (2017).

    Article  ADS  Google Scholar 

  32. Rooks, M. J. et al. Low stress development of poly(methylmethacrylate) for high aspect ratio structures. J. Vacuum Sci. Technol. B 20, 2937–2941 (2002).

    Article  ADS  CAS  Google Scholar 

  33. Chen, Z. et al. Fabrication and characterization of aluminum airbridges for superconducting microwave circuits. Appl. Phys. Lett. 104, 052602 (2014).

    Article  ADS  Google Scholar 

  34. Wu, M.-D., Deng, S.-M., Wu, R.-B. & Hsu, P. Full-wave characterization of the mode conversion in a coplanar waveguide right-angled bend. IEEE Trans. Microw. Theory Technol. 43, 2532–2538 (1995).

    Article  ADS  Google Scholar 

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We thank J.-H. Yeh and B. Palmer for the use of one of their cryogenic attenuators, which reduced thermal noise in the input waveguide line. This work was supported by the AFOSR MURI Quantum Photonic Matter (grant FA9550-16-1-0323), the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (grant PHY-1125565) with the support of the Gordon and Betty Moore Foundation, and the Kavli Nanoscience Institute at Caltech. D.E.C. acknowledges support from the ERC Starting Grant FOQAL, the MINECO Plan Nacional Grant CANS, the MINECO Severo Ochoa grant SEV-2015-0522, the CERCA Programme/Generalitat de Catalunya and the Fundacio Privada Cellex. M.M. is supported through a KNI Postdoctoral Fellowship. X.Z. is supported by a Yariv/Blauvelt Fellowship. A.J.K. and A.S. are supported by IQIM Postdoctoral Scholarships. P.B.D. is supported by a Hertz Graduate Fellowship Award. A.A.-G. is supported by the Global Marie Curie Fellowship under the LANTERN programme.

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Nature thanks Anton Kockum, Peter Lodahl and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Authors and Affiliations



M.M., E.K., P.B.D., A.A.-G., D.E.C. and O.P. came up with the concept and planned the experiment. M.M., E.K., X.Z., P.B.D., A.S. and A.J.K. performed the device design and fabrication. E.K., X.Z., M.M., and A.S. performed the measurements and analysed the data. All authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to Oskar Painter.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Scanning electron microscope image of the fabricated device (false colour highlights).

a, Type I (Q2, Q3) and type II (Q1) mirror qubits coupled to the CPW. b, The central probe qubit (Q4) and lumped-element readout resonator (R4) coupled to the CPW. The inset shows an inductive meander of the lumped-element readout resonator. c, A superconducting quantum interference device (SQUID) loop with asymmetric Josephson junctions for the qubits. d, An airbridge placed across the waveguide to suppress the slotline mode.

Extended Data Fig. 2 Schematic of the measurement chain inside the dilution refrigerator.

The four types of input lines, the output line and their connection to the device inside a magnetic shield are illustrated. Attenuators are expressed as rectangles with labelled power attenuation and capacitor symbols correspond to direct-current blocks. The thin-film attenuator and a circulator (coloured red) are added to the waveguide input line and output line, respectively, in a second version of the setup and a second round of measurements to further protect the sample from thermal noise in the waveguide line. HEMT, high-electron-mobility transistor.

Extended Data Table 1 Qubit characteristics

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-2, Supplementary Tables 1-2, and additional references.

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Mirhosseini, M., Kim, E., Zhang, X. et al. Cavity quantum electrodynamics with atom-like mirrors. Nature 569, 692–697 (2019).

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