Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Coherent control of a multi-qubit dark state in waveguide quantum electrodynamics

Nature Physics volume 18, pages 538–543 (2022)Cite this article

Subjects

Abstract

Superconducting qubits in a waveguide have long-range interactions mediated by photons that cause the emergence of collective states. Destructive interference between the qubits decouples the collective dark states from the waveguide environment. Their inability to emit photons into the waveguide render dark states a valuable resource for preparing long-lived quantum many-body states and realizing quantum information protocols in open quantum systems. However, they also decouple from fields that drive the waveguide, making manipulation a challenge. Here we show the coherent control of a collective dark state that is realized by controlling the interactions between four superconducting transmon qubits and local drives. The dark state’s protection against decoherence results in decay times that exceed those of the waveguide-limited single qubits by more than two orders of magnitude. Moreover, we perform a phase-sensitive spectroscopy of the two-excitation manifold and reveal bosonic many-body statistics in the transmon array. Our dark-state qubit provides a starting point for implementing quantum information protocols with collective states.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Collective states in waveguide QED.
Fig. 2: Measuring dark and bright states.
Fig. 3: Coherent control of the dark state.
Fig. 4: Phase-sensitive spectroscopy of the two-excitation manifold.

Similar content being viewed by others

Data availability

The data that support the findings of this study are available on Zenodo (https://zenodo.org/record/5772190).

Code availability

The code used for data analysis and simulated results is available from the corresponding author upon reasonable request.

References

  1. Sheremet, A. S., Petrov, M. I., Iorsh, I. V., Poshakinskiy, A. V. & Poddubny, A. N. Waveguide quantum electrodynamics: collective radiance and photon-photon correlations. Preprint at https://arxiv.org/abs/2103.06824 (2021).

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

    Article  MathSciNet  Google Scholar 

  3. Masson, S. J. & Asenjo-Garcia, A. Atomic-waveguide quantum electrodynamics. Phys. Rev. Research 2, 043213 (2020).

    Article  ADS  Google Scholar 

  4. Goban, A. et al. Atom–light interactions in photonic crystals. Nat. Commun. 5, 3808 (2014).

    Article  ADS  Google Scholar 

  5. Corzo, N. V. et al. Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide. Phys. Rev. Lett. 117, 133603 (2016).

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Forn-Díaz, P. et al. Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime. Nat. Phys. 13, 39–43 (2017).

    Article  Google Scholar 

  9. Hoi, I.-C. et al. Generation of nonclassical microwave states using an artificial atom in 1D open space. Phys. Rev. Lett. 108, 263601 (2012).

    Article  ADS  Google Scholar 

  10. Kannan, B. et al. Generating spatially entangled itinerant photons with waveguide quantum electrodynamics. Sci. Adv. 6, eabb8780 (2020).

    Article  ADS  Google Scholar 

  11. 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).

    Google Scholar 

  12. Kim, E. et al. Quantum electrodynamics in a topological waveguide. Phys. Rev. X 11, 011015 (2021).

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  15. 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 

  16. Goban, A. et al. Superradiance for atoms trapped along a photonic crystal waveguide. Phys. Rev. Lett. 115, 063601 (2015).

    Article  ADS  Google Scholar 

  17. Kim, J.-H., Aghaeimeibodi, S., Richardson, C. J. K., Leavitt, R. P. & Waks, E. Super-radiant emission from quantum dots in a nanophotonic waveguide. Nano Lett. 18, 4734–4740 (2018).

    Google Scholar 

  18. Mlynek, J. A., Abdumalikov, A. A., Eichler, C. & Wallraff, A. Observation of Dicke superradiance for two artificial atoms in a cavity with high decay rate. Nat. Commun. 5, 5186 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Brehm, J. D. et al. Waveguide bandgap engineering with an array of superconducting qubits. npj Quantum Mater. 6, 10 (2021).

    Article  ADS  Google Scholar 

  21. 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 

  22. Albrecht, A., Henriet, L., Asenjo-Garcia, A., Dieterle, P. B., Painter, O. & Chang, D. E. Subradiant states of quantum bits coupled to a one-dimensional waveguide. New J. Phys. 21, 025003 (2019).

    Article  MathSciNet  ADS  Google Scholar 

  23. Orell, T., Michailidis, A. A., Serbyn, M. & Silveri, M. Probing the many-body localization phase transition with superconducting circuits. Phys. Rev. B 100, 134504 (2019).

    Article  ADS  Google Scholar 

  24. Fayard, N., Henriet, L., Asenjo-Garcia, A. & Chang, D. E. Many-body localization in waveguide quantum electrodynamics. Phys. Rev. Research 3, 033233 (2021).

    Article  ADS  Google Scholar 

  25. 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  MATH  ADS  Google Scholar 

  26. Hacohen-Gourgy, S., Ramasesh, V. V., De Grandi, C., Siddiqi, I. & Girvin, S. M. Cooling and autonomous feedback in a Bose-Hubbard chain with attractive interactions. Phys. Rev. Lett. 115, 240501 (2015).

    Article  ADS  Google Scholar 

  27. Lu, Y. et al. Characterizing decoherence rates of a superconducting qubit by direct microwave scattering. npj Quantum Inf. 7, 35 (2021).

    Article  ADS  Google Scholar 

  28. Burnett, J. J. et al. Decoherence benchmarking of superconducting qubits. npj Quantum Inf. 5, 54 (2019).

    Article  Google Scholar 

  29. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Phys. Rev. B 92, 035442 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Pozar, D. M. Microwave Engineering 4th edn (Wiley, 2012).

  32. Dalmonte, M. et al. Realizing dipolar spin models with arrays of superconducting qubits. Phys. Rev. B 92, 174507 (2015).

    Article  ADS  Google Scholar 

  33. Probst, S., Song, F. B., Bushev, P. A., Ustinov, A. V. & Weides, M. Efficient and robust analysis of complex scattering data under noise in microwave resonators. Rev. Sci. Instrum. 86, 024706 (2015).

    Article  ADS  Google Scholar 

  34. Leek, P. J. et al. Cavity quantum electrodynamics with separate photon storage and qubit readout modes. Phys. Rev. Lett. 104, 100504 (2010).

    Article  ADS  Google Scholar 

  35. Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281 (2003).

    Article  ADS  Google Scholar 

  36. Roushan, P. et al. Spectroscopic signatures of localization with interacting photons in superconducting qubits. Science 358, 1175–1179 (2017).

    Article  MathSciNet  Google Scholar 

  37. Ma, R., Saxberg, B., Owens, C., Leung, N., Lu, Y., Simon, J. & Schuster, D. I. A dissipatively stabilized Mott insulator of photons. Nature 566, 51–57 (2019).

    Article  Google Scholar 

  38. Orell, T. et al. Collective bosonic effects in an array of transmon devices. Preprint at https://arxiv.org/abs/2112.08134 (2021).

  39. Reiter, F. & Sørensen, A. S. Effective operator formalism for open quantum systems. Phys. Rev. A 85, 032111 (2012).

    Article  ADS  Google Scholar 

  40. Besse, J.-C. et al. Realizing a deterministic source of multipartite-entangled photonic qubits. Nat. Commun. 11, 4877 (2020).

    Article  ADS  Google Scholar 

  41. Ke, Y., Poshakinskiy, A. V., Lee, C., Kivshar, Y. S. & Poddubny, A. N. Inelastic scattering of photon pairs in qubit arrays with subradiant states. Phys. Rev. Lett. 123, 253601 (2019).

    Article  ADS  Google Scholar 

  42. Scigliuzzo, M. et al. Primary thermometry of propagating microwaves in the quantum regime. Phys. Rev. X 10, 041054 (2020).

    Google Scholar 

  43. Hoi, I.-C. et al. Demonstration of a single-photon router in the microwave regime. Phys. Rev. Lett. 107, 073601 (2011).

    Article  ADS  Google Scholar 

  44. Brody, D. C. Biorthogonal quantum mechanics. J. Phys. A: Math. Theor. 47, 035305 (2013).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  45. Autler, S. H. & Townes, C. H. Stark effect in rapidly varying fields. Phys. Rev. 100, 703 (1955).

    Article  ADS  Google Scholar 

  46. Barnett, S. and Radmore, P. M. Methods in Theoretical Quantum Optics (Oxford Univ. Press, 2002).

Download references

Acknowledgements

We thank A. Strasser for fabricating the waveguide sample. We would like to thank E. I. Rosenthal for valuable comments on the manuscript. M.Z. and S.O. acknowledge funding by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (714235). M.Z. and C.M.F.S. acknowledge support by the Austrian Science Fund FWF within the DK-ALM (W1259-N27). R.A. acknowledges support from the Austrian Science Fund FWF within the SFB-BeyondC (F7106-N38). T.O. and M.S. acknowledge funding by the Emil Aaltonen Foundation and by the Academy of Finland (316619 and 320086). M.L.J. acknowledges funding from the Canada First Research Excellence Fund.

Author information

Authors and Affiliations

  1. Institute for Experimental Physics, University of Innsbruck, Innsbruck, Austria

    Maximilian Zanner, Christian M. F. Schneider, Romain Albert, Stefan Oleschko & Gerhard Kirchmair

  2. Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria

    Maximilian Zanner, Christian M. F. Schneider, Romain Albert, Stefan Oleschko & Gerhard Kirchmair

  3. Nano and Molecular Systems Research Unit, University of Oulu, Oulu, Finland

    Tuure Orell & Matti Silveri

  4. Institut Quantique and Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada

    Mathieu L. Juan

Authors
  1. Maximilian Zanner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tuure Orell
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christian M. F. Schneider
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Romain Albert
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Stefan Oleschko
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mathieu L. Juan
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Matti Silveri
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Gerhard Kirchmair
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.Z. and G.K. conceived and designed the experiment. M.Z. simulated and fabricated the devices and also conducted the measurements. M.Z. and C.M.F.S. analysed the data. T.O. and M.S. developed the theoretical model and performed the simulations. M.Z. and G.K. wrote the manuscript. All the authors discussed the results and contributed to the writing of the manuscript.

Corresponding author

Correspondence to Maximilian Zanner.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–8, Tables 1–3, Sections 1–6 and refs. 1–10.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zanner, M., Orell, T., Schneider, C.M.F. et al. Coherent control of a multi-qubit dark state in waveguide quantum electrodynamics. Nat. Phys. 18, 538–543 (2022). https://doi.org/10.1038/s41567-022-01527-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-022-01527-w

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing