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Plasmon decay and nonequilibrium steady states in Josephson junction chains

Lucia Vigliotti1,*, Andrew P. Higginbotham2, and Maksym Serbyn1

  • *Contact author: lucia.vigliotti@ist.ac.at
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Phys. Rev. B 114, 194501 – Published 1 October, 2026

DOI: https://doi.org/10.1103/cw3m-thsw

Abstract

Josephson junction (JJ) chains combine the coherence of superconductivity with the controllability of microwave-frequency circuits, making them a powerful platform for circuit quantum electrodynamics. In this work, we consider a long JJ chain that effectively realizes a multimode cavity with nonlinear dispersion and additional multimode interactions. Individual modes appearing due to the finite size of the chain can be experimentally probed via microwave spectroscopy, both in equilibrium and in driven far-from-equilibrium settings. We study the role of multimode interactions in degrading internal coherence—observable as excess linewidth—in both equilibrium and driven regimes. Focusing on two-into-two mode scattering as the leading relaxation process, we classify the relevant scattering processes and derive their expected temperature- and frequency-scaling under equilibrium conditions. For experimentally relevant parameters, we show that the equilibrium decay rate is dominated by nonresonant processes, however, weakly driving a particular set of modes out of equilibrium enhances resonant scattering, leading to observable signatures in the distribution function and linewidth. Finally, in the strong nonequilibrium regime, we report a crossover to a qualitatively different nonequilibrium steady state.

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References (62)

  1. A. J. Leggett, Macroscopic quantum systems and the quantum theory of measurement, Prog. Theor. Phys. Suppl. 69, 80 (1980).
  2. A. J. Leggett, Quantum tunneling in the presence of an arbitrary linear dissipation mechanism, Phys. Rev. B 30, 1208 (1984).
  3. O. G. Turutanov, Chronicle: “Foot of the iceberg” of Nobel Prize in Physics 2025: ILTPE and LTP contribution, Low Temp. Phys. 51, 1522 (2025).
  4. M. H. Devoret, J. M. Martinis, and J. Clarke, Measurements of macroscopic quantum tunneling out of the zero-voltage state of a current-biased Josephson junction, Phys. Rev. Lett. 55, 1908 (1985).
  5. J. Clarke, A. N. Cleland, M. H. Devoret, D. Esteve, and J. M. Martinis, Quantum mechanics of a macroscopic variable: The phase difference of a Josephson junction, Science 239, 992 (1988).
  6. M. H. Devoret, A. Wallraff, and J. M. Martinis, Superconducting qubits: A short review, arXiv:cond-mat/0411174.
  7. A. R. Matanin, K. I. Gerasimov, E. S. Moiseev, N. S. Smirnov, A. I. Ivanov, E. I. Malevannaya, V. I. Polozov, E. V. Zikiy, A. A. Samoilov, I. A. Rodionov, and S. A. Moiseev, Toward highly efficient multimode superconducting quantum memory, Phys. Rev. Appl. 19, 034011 (2023).
  8. R. Naik, N. Leung, S. Chakram, P. Groszkowski, Y. Lu, N. Earnest, D. C. McKay, J. Koch, and D. I. Schuster, Random access quantum information processors using multimode circuit quantum electrodynamics, Nat. Commun. 8, 1904 (2017).
  9. J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007).
  10. I. M. Pop, K. Geerlings, G. Catelani, R. J. Schoelkopf, L. I. Glazman, and M. H. Devoret, Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles, Nature (London) 508, 369 (2014).
  11. V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Fluxonium: Single Cooper-pair circuit free of charge offsets, Science 326, 113 (2009).
  12. N. A. Masluk, I. M. Pop, A. Kamal, Z. K. Minev, and M. H. Devoret, Microwave characterization of Josephson junction arrays: Implementing a low loss superinductance, Phys. Rev. Lett. 109, 137002 (2012).
  13. E. Chow, P. Delsing, and D. B. Haviland, Length-scale dependence of the superconductor-to-insulator quantum phase transition in one dimension, Phys. Rev. Lett. 81, 204 (1998).
  14. R. Kuzmin, R. Mencia, N. Grabon, N. Mehta, Y.-H. Lin, and V. E. Manucharyan, Quantum electrodynamics of a superconductor–insulator phase transition, Nat. Phys. 15, 930 (2019).
  15. S. Mukhopadhyay, J. Senior, J. Saez-Mollejo, D. Puglia, M. Zemlicka, J. M. Fink, and A. P. Higginbotham, Superconductivity from a melted insulator in Josephson junction arrays, Nat. Phys. 19, 1630 (2023).
  16. A. van Otterlo, K.-H. Wagenblast, R. Fazio, and G. Schön, Response of Josephson-junction arrays near the quantum phase transition, Phys. Rev. B 48, 3316 (1993).
  17. B. J. P. Pernack, M. V. Fistul, and I. M. Eremin, Quantum dynamics of frustrated Josephson junction arrays embedded in a transmission line: An effective XX spin chain with long-range interaction, Phys. Rev. B 110, 184502 (2024).
  18. R. Fazio and H. van der Zant, Quantum phase transitions and vortex dynamics in superconducting networks, Phys. Rep. 355, 235 (2001).
  19. G. Rastelli, I. M. Pop, and F. W. J. Hekking, Quantum phase slips in Josephson junction rings, Phys. Rev. B 87, 174513 (2013).
  20. I. M. Pop, I. Protopopov, F. Lecocq, Z. Peng, B. Pannetier, O. Buisson, and W. Guichard, Measurement of the effect of quantum phase slips in a Josephson junction chain, Nat. Phys. 6, 589 (2010).
  21. A. Ergül, J. Lidmar, J. Johansson, Y. Azizoğlu, D. Schaeffer, and D. B. Haviland, Localizing quantum phase slips in one-dimensional Josephson junction chains, New J. Phys. 15, 095014 (2013).
  22. A. Ergül, T. Weißl, J. Johansson, J. Lidmar, and D. B. Haviland, Spatial and temporal distribution of phase slips in Josephson junction chains, Sci. Rep. 7, 11447 (2017).
  23. B. J. van Wees, H. S. J. van der Zant, and J. E. Mooij, Phase transitions of Josephson-tunnel-junction arrays at zero and full frustration, Phys. Rev. B 35, 7291 (1987).
  24. P. Chandra, L. B. Ioffe, and D. Sherrington, Possible glassiness in a periodic long-range Josephson array, Phys. Rev. Lett. 75, 713 (1995).
  25. C. Chamon, D. Green, and Z.-C. Yang, Constructing quantum spin liquids using combinatorial gauge symmetry, Phys. Rev. Lett. 125, 067203 (2020).
  26. R. Kuzmin, N. Grabon, N. Mehta, A. Burshtein, M. Goldstein, M. Houzet, L. I. Glazman, and V. E. Manucharyan, Inelastic scattering of a photon by a quantum phase slip, Phys. Rev. Lett. 126, 197701 (2021).
  27. A. Burshtein, R. Kuzmin, V. E. Manucharyan, and M. Goldstein, Photon-instanton collider implemented by a superconducting circuit, Phys. Rev. Lett. 126, 137701 (2021).
  28. N. Mehta, R. Kuzmin, C. Ciuti, and V. E. Manucharyan, Down-conversion of a single photon as a probe of many-body localization, Nature (London) 613, 650 (2023).
  29. A. V. Bubis, L. Vigliotti, M. Serbyn, and A. P. Higginbotham, Non-equilibrium plasmon liquid in a Josephson junction chain, Sci. Adv. 12, eady7222 (2026).
  30. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  31. J. Lin, K. A. Matveev, and M. Pustilnik, Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid, Phys. Rev. Lett. 110, 016401 (2013).
  32. M. Bard, I. V. Protopopov, and A. D. Mirlin, Decay of plasmonic waves in Josephson junction chains, Phys. Rev. B 98, 224513 (2018).
  33. N. Crescini, S. Cailleaux, W. Guichard, C. Naud, O. Buisson, K. W. Murch, and N. Roch, Evidence of dual Shapiro steps in a Josephson junctions array, Nat. Phys. 19, 851 (2023).
  34. R. Kuzmin, N. Mehta, N. Grabon, R. A. Mencia, A. Burshtein, M. Goldstein, and V. E. Manucharyan, Observation of the Schmid–Bulgadaev dissipative quantum phase transition, Nat. Phys. 21, 132 (2025).
  35. J. Bourassa, F. Beaudoin, J. M. Gambetta, and A. Blais, Josephson-junction-embedded transmission-line resonators: From Kerr medium to in-line transmon, Phys. Rev. A 86, 013814 (2012).
  36. A. Imamoğlu, H. Schmidt, G. Woods, and M. Deutsch, Strongly interacting photons in a nonlinear cavity, Phys. Rev. Lett. 79, 1467 (1997).
  37. S. I. Mukhin and M. V. Fistul, Generation of non-classical photon states in superconducting quantum metamaterials, Supercond. Sci. Technol. 26, 084003 (2013).
  38. Yu. Krupko, V. D. Nguyen, T. Weißl, É. Dumur, J. Puertas, R. Dassonneville, C. Naud, F. W. J. Hekking, D. M. Basko, O. Buisson, N. Roch, and W. Hasch-Guichard, Kerr nonlinearity in a superconducting Josephson metamaterial, Phys. Rev. B 98, 094516 (2018).
  39. D. M. Basko, F. Pfeiffer, P. Adamus, M. Holzmann, and F. W. J. Hekking, Superconductor-insulator transition in Josephson junction chains by quantum Monte Carlo calculations, Phys. Rev. B 101, 024518 (2020).
  40. P. R. Muppalla, Josephson junction array resonators in the mesoscopic regime: Design, characterization and application, Ph.D. thesis, Leopold-Franzens University of Innsbruck, 2020.
  41. B. I. Halperin, G. Refael, and E. Demler, Resistance in superconductors, Int. J. Mod. Phys. B 24, 4039 (2010).
  42. D. Haviland, Quantum phase slips, Nat. Phys. 6, 565 (2010).
  43. M. Bard, I. V. Protopopov, I. V. Gornyi, A. Shnirman, and A. D. Mirlin, Superconductor-insulator transition in disordered Josephson-junction chains, Phys. Rev. B 96, 064514 (2017).
  44. M. Houzet and L. I. Glazman, Microwave spectroscopy of a weakly pinned charge density wave in a superinductor, Phys. Rev. Lett. 122, 237701 (2019).
  45. A. Imambekov, T. L. Schmidt, and L. I. Glazman, One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm, Rev. Mod. Phys. 84, 1253 (2012).
  46. T. Weißl, B. Küng, E. Dumur, A. K. Feofanov, I. Matei, C. Naud, O. Buisson, F. W. J. Hekking, and W. Guichard, Kerr coefficients of plasma resonances in Josephson junction chains, Phys. Rev. B 92, 104508 (2015).
  47. Y. Krupko, V. D. Nguyen, T. Weißl, E. Dumur, J. Puertas, R. Dassonneville, C. Naud, F. W. J. Hekking, D. M. Basko, O. Buisson, N. Roch, and W. Hasch-Guichard, Erratum: Kerr nonlinearity in a superconducting Josephson metamaterial [Phys. Rev. B 98, 094516 (2018)], Phys. Rev. B 108, 219904(E) (2023).
  48. S. Apostolov, D. E. Liu, Z. Maizelis, and A. Levchenko, Thermal transport and quench relaxation in nonlinear Luttinger liquids, Phys. Rev. B 88, 045435 (2013).
  49. I. V. Protopopov, D. B. Gutman, and A. D. Mirlin, Relaxation in Luttinger liquids: Bose-Fermi duality, Phys. Rev. B 90, 125113 (2014).
  50. M. Bard, I. V. Protopopov, and A. D. Mirlin, Plasmon localization, plasmon relaxation, and thermal transport in one-dimensional conductors, Phys. Rev. B 100, 115153 (2019).
  51. S. Bhattacharyya, J. F. Rodriguez-Nieva, and E. Demler, Universal prethermal dynamics in Heisenberg ferromagnets, Phys. Rev. Lett. 125, 230601 (2020).
  52. R. Fazio, F. W. J. Hekking, and D. E. Khmelnitskii, Anomalous thermal transport in quantum wires, Phys. Rev. Lett. 80, 5611 (1998).
  53. R. Sawant and S. A. Rangwala, Lasing by driven atoms-cavity system in collective strong coupling regime, Sci. Rep. 7, 11432 (2017).
  54. A. Bahuleyan, V. R. Thakar, V. I. Gokul, S. P. Dinesh, B. P. Venkatesh, and S. A. Rangwala, Gain, amplification, and lasing in a driven atom-cavity system, Opt. Continuum 4, 888 (2025).
  55. J. Hauss, A. Fedorov, C. Hutter, A. Shnirman, and G. Schön, Single-qubit lasing and cooling at the Rabi frequency, Phys. Rev. Lett. 100, 037003 (2008).
  56. C. Eichler and A. Wallraff, Controlling the dynamic range of a Josephson parametric amplifier, EPJ Quantum Technol. 1, 2 (2014).
  57. J. Berges, A. Rothkopf, and J. Schmidt, Nonthermal fixed points: Effective weak coupling for strongly correlated systems far from equilibrium, Phys. Rev. Lett. 101, 041603 (2008).
  58. S. Nazarenko, Wave Turbulence (Springer Berlin, Heidelberg, 2011).
  59. A. A. Houck, H. E. Türeci, and J. Koch, On-chip quantum simulation with superconducting circuits, Nat. Phys. 8, 292 (2012).
  60. L. Vigliotti, A. P. Higginbotham, and M. Serbyn, Numerical simulation data and code for “Plasmon decay and non-equilibrium steady states in Josephson junction chains”, Zenodo, 2026, doi:https://doi.org/10.5281/zenodo.19456426.
  61. D. M. Basko and F. W. J. Hekking, Disordered Josephson junction chains: Anderson localization of normal modes and impedance fluctuations, Phys. Rev. B 88, 094507 (2013).
  62. A. E. Svetogorov and D. M. Basko, Effect of disorder on coherent quantum phase slips in Josephson junction chains, Phys. Rev. B 98, 054513 (2018).

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Phys. Rev. B 114, 194501– Published 1 October, 2026
  • Received 9 April 2026
  • Accepted 17 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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