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Quantum electrodynamics of a superconductor–insulator phase transition

Nature Physics volume 15, pages 930–934 (2019)Cite this article

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Abstract

A chain of Josephson junctions represents one of the simplest many-body models undergoing a superconductor–insulator quantum phase transition1,2. Apart from zero resistance, the superconducting state is necessarily accompanied by a sound-like mode due to collective oscillations of the phase of the complex-valued order parameter3,4. Little is known about the fate of this mode on entering the insulating state, where the order parameter’s amplitude remains non-zero, but the phase ordering is ‘melted’ by quantum fluctuations5. Here, we show that the phase mode survives far into the insulating regime, such that megaohm-resistance chains can carry gigahertz-frequency alternating currents as nearly ideal superconductors. The insulator reveals itself through interaction-induced broadening and random frequency shifts of collective mode resonances. Our spectroscopic experiment puts forward the problem of quantum electrodynamics of a Bose glass for both theory and experiment6,7,8. By pushing the chain parameters deeper into the insulating state, we achieved a wave impedance of the phase mode exceeding the predicted critical value by an order of magnitude9,10,11,12,13,14. The effective fine structure constant of such a one-dimensional electromagnetic vacuum exceeds unity, promising transformative applications to quantum science and technology.

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Fig. 1: The Josephson transmission line and wireless radio-frequency spectroscopy set-up.
Fig. 2: Collective modes in the Josephson transmission line.
Fig. 3: Broadening and random frequency shifts of collective mode resonances.
Fig. 4: The reversible transition in the Q-factor frequency dependence.

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Data availability

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

References

  1. Sachdev, S. Quantum Phase Transitions (Cambridge University Press, 2011).

  2. Bradley, R. M. & Doniach, S. Quantum fluctuations in chains of Josephson junctions. Phys. Rev. B 30, 1138–1147 (1984).

    Article  ADS  Google Scholar 

  3. Fazio, R., Wagenblast, K.-H., Winkelholz, C. & Schön, G. Tunneling into one-dimensional Josephson chains and Luttinger liquids. Phys. B 222, 364–369 (1996).

    Article  ADS  Google Scholar 

  4. Basko, D. M. & Hekking, F. W. J. Disordered Josephson junction chains: Anderson localization of normal modes and impedance fluctuations. Phys. Rev. B 88, 094507 (2013).

    Article  ADS  Google Scholar 

  5. Sondhi, S., Girvin, S., Carini, J. & Shahar, D. Continuous quantum phase transitions. Rev. Mod. Phys. 69, 315–333 (1997).

    Article  ADS  Google Scholar 

  6. Wu, H.-K. & Sau, J. D. Theory of coherent phase modes in insulating Josephson junction arrays. Preprint at https://arxiv.org/abs/1811.07941 (2018).

  7. Bard, M., Protopopov, I. & Mirlin, A. Decay of plasmonic waves in Josephson junction chains. Phys. Rev. B 98, 224513 (2018).

    Article  ADS  Google Scholar 

  8. Houzet, M. & Glazman, L. I. Microwave spectroscopy of a weakly-pinned charge density wave in a superinductor. Preprint at https://arxiv.org/abs/1901.01515 (2019).

  9. Giamarchi, T. & Schulz, H. J. Anderson localization and interactions in one-dimensional metals. Phys. Rev. B 37, 325–340 (1988).

    Article  ADS  Google Scholar 

  10. Korshunov, S. Effect of dissipation on the low-temperature properties of a tunnel-junction chain. Zh. Eksp. Teor. Fiz. 95, 1058–1075 (1989).

    Google Scholar 

  11. Choi, M.-S., Yi, J., Choi, M. Y., Choi, J. & Lee, S.-I. Quantum phase transitions in Josephson-junction chains. Phys. Rev. B 57, 716–719 (1998).

    Article  ADS  Google Scholar 

  12. Giamarchi, T. Quantum Physics In One Dimension (Oxford University Press, 2004).

  13. Bard, M., Protopopov, I., Gornyi, I., Shnirman, A. & Mirlin, A. Superconductor–insulator transition in disordered Josephson-junction chains. Phys. Rev. B 96, 064514 (2017).

    Article  ADS  Google Scholar 

  14. Cedergren, K. et al. Insulating Josephson junction chains as pinned Luttinger liquids. Phys. Rev. Lett. 119, 167701 (2017).

    Article  ADS  Google Scholar 

  15. Devoret, M. H. Quantum fluctuations in electrical circuits. In Fluctuations Quantiques/Quantum Fluctuations: Les Houches Session LXIII (ed. Reynaud, S. et al.) 351–386 (Elsevier, 1997).

  16. Lin, Y.-H., Nelson, J. & Goldman, A. M. Superconductivity of very thin films: the superconductor–insulator transition. Phys. C 514, 130–141 (2015).

    Article  ADS  Google Scholar 

  17. Chow, E., Delsing, P. & Haviland, D. B. Length-scale dependence of the superconductor-to-insulator quantum phase transition in one dimension. Phys. Rev. Lett. 81, 204–207 (1998).

    Article  ADS  Google Scholar 

  18. Haviland, D. B., Andersson, K. & Ågren, P. Superconducting and insulating behavior in one-dimensional Josephson junction arrays. J. Low Temp. Phys. 118, 733–749 (2000).

    Article  ADS  Google Scholar 

  19. Ergül, A. et al. Localizing quantum phase slips in one-dimensional Josephson junction chains. New J. Phys. 15, 095014 (2013).

    Article  ADS  Google Scholar 

  20. Choi, M.-S., Choi, M., Choi, T. & Lee, S.-I. Cotunneling transport and quantum phase transitions in coupled Josephson-junction chains with charge frustration. Phys. Rev. Lett. 81, 4240–4243 (1998).

    Article  ADS  Google Scholar 

  21. Weißl, T. et al. Kerr coefficients of plasma resonances in Josephson junction chains. Phys. Rev. B 92, 104508 (2015).

    Article  ADS  Google Scholar 

  22. Fukuyama, H. & Lee, P. A. Dynamics of the charge-density wave. I. Impurity pinning in a single chain. Phys. Rev. B 17, 535–541 (1978).

    Article  ADS  Google Scholar 

  23. Vogt, N. et al. One-dimensional Josephson junction arrays: lifting the Coulomb blockade by depinning. Phys. Rev. B 92, 045435 (2015).

    Article  ADS  Google Scholar 

  24. Matveev, K. A., Larkin, A. I. & Glazman, L. I. Persistent current in superconducting nanorings. Phys. Rev. Lett. 89, 096802 (2002).

    Article  ADS  Google Scholar 

  25. Rastelli, G., Pop, I. M. & Hekking, F. W. J. Quantum phase slips in Josephson junction rings. Phys. Rev. B 87, 174513 (2013).

    Article  ADS  Google Scholar 

  26. Crane, R. et al. Survival of superconducting correlations across the two-dimensional superconductor–insulator transition: a finite-frequency study. Phys. Rev. B 75, 184530 (2007).

    Article  ADS  Google Scholar 

  27. Arutyunov, K. Y., Golubev, D. S. & Zaikin, A. D. Superconductivity in one dimension. Phys. Rep. 464, 1–70 (2008).

    Article  ADS  Google Scholar 

  28. Sacépé, B. et al. Localization of preformed Cooper pairs in disordered superconductors. Nat. Phys. 7, 239–244 (2011).

    Article  Google Scholar 

  29. André, A. et al. A coherent all-electrical interface between polar molecules and mesoscopic superconducting resonators. Nat. Phys. 2, 636–642 (2006).

    Article  Google Scholar 

  30. Schuster, D., Fragner, A., Dykman, M., Lyon, S. & Schoelkopf, R. Proposal for manipulating and detecting spin and orbital states of trapped electrons on helium using cavity quantum electrodynamics. Phys. Rev. Lett. 105, 040503 (2010).

    Article  ADS  Google Scholar 

  31. Stockklauser, A. et al. Strong coupling cavity QED with gate-defined double quantum dots enabled by a high impedance resonator. Phys. Rev. X 7, 011030 (2017).

    Google Scholar 

  32. Samkharadze, N. et al. Strong spin–photon coupling in silicon. Science 359, 1123–1127 (2018).

    Article  ADS  Google Scholar 

  33. Arrangoiz-Arriola, P. et al. Coupling a superconducting quantum circuit to a phononic crystal defect cavity. Phys. Rev. X 8, 031007 (2018).

    Google Scholar 

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Acknowledgements

We acknowledge discussions with L. Glazman, M. Goldstein, M. Houzet, I. Protopopov, J. Sau and A. Shnirman. The work was supported by US NSF (DMR 1455261), US-Israel BSF (2016224), NSF PFC at JQI (1430094), and ARO-MURI (W911NF-15-1-0397) ‘Exotic states of light in superconducting circuits’.

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Authors and Affiliations

  1. Department of Physics, Joint Quantum Institute, and Center for Nanophysics and Advanced Materials, University of Maryland, College Park, MD, USA

    R. Kuzmin, R. Mencia, N. Grabon, N. Mehta, Y.-H. Lin & V. E. Manucharyan

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  1. R. Kuzmin
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  2. R. Mencia
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  3. N. Grabon
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Contributions

R.K., aided by N.G. and N.M., performed measurements and data analysis. R.M. and N.G. fabricated devices, Y.-H.L. developed the wireless waveguide interface. V.E.M. managed the project. All authors participated in extensive discussions of the experimental results and contributed to writing the manuscript.

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Correspondence to V. E. Manucharyan.

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Supplementary Figs. 1–7, Table 1 and refs. 1–3.

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Kuzmin, R., Mencia, R., Grabon, N. et al. Quantum electrodynamics of a superconductor–insulator phase transition. Nat. Phys. 15, 930–934 (2019). https://doi.org/10.1038/s41567-019-0553-1

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