- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Revisiting Dissipation-Driven Phase Transition in a Josephson Junction

Diego Subero*, Yu-Cheng Chang, Miguel Monteiro, Ze-Yan Chen, and Jukka P. Pekola

  • *Contact author: suberoda123@gmail.com
PDF

Phys. Rev. Lett. 136, 116301 – Published 20 March, 2026

DOI: https://doi.org/10.1103/4f3c-jv43

Abstract

Despite extensive experimental and theoretical work over several decades, Schmid-Bulgadaev quantum phase transition remains a subject of debate. Here we revisit this problem by performing systematic experiments on low-frequency current-voltage characteristics of Josephson junctions over a wide range of parameters. The experiments are conducted in a true resistive environment formed by a metallic on-chip resistor located near the junction. Over the parameter range of the experiment, we find that the transition occurs when the resistance crosses the quantum value h/(4e2)≃6.5  kΩ for Cooper pairs, as originally predicted. The temperature T of the experiment is naturally nonzero, but our basic theoretical modeling corroborates that the observations under these conditions can serve as the basis for the conclusions made, in particular, the crossover resistance from superconducting to insulating regime is the same as that at T=0.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (39)

  1. A. Schmid, Diffusion and localization in a dissipative quantum system, Phys. Rev. Lett. 51, 1506 (1983).
  2. S. Bulgadaev, Phase diagram of a dissipative quantum system, JETP Lett. 39, 264 (1984).
  3. D. Subero, O. Maillet, D. S. Golubev, G. Thomas, J. T. Peltonen, B. Karimi, M. Marín-Suárez, A. L. Yeyati, R. Sánchez, S. Park et al., Bolometric detection of Josephson inductance in a highly resistive environment, Nat. Commun. 14, 7924 (2023).
  4. A. Murani, N. Bourlet, H. Le Sueur, F. Portier, C. Altimiras, D. Esteve, H. Grabert, J. Stockburger, J. Ankerhold, and P. Joyez, Absence of a dissipative quantum phase transition in Josephson junctions, Phys. Rev. X 10, 021003 (2020).
  5. 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).
  6. M. Houzet and L. I. Glazman, Critical fluorescence of a transmon at the Schmid transition, Phys. Rev. Lett. 125, 267701 (2020).
  7. A. Burshtein, R. Kuzmin, V. E. Manucharyan, and M. Goldstein, Photon-instanton collider implemented by a superconducting circuit, Phys. Rev. Lett. 126, 137701 (2021).
  8. T. Morel and C. Mora, Double-periodic Josephson junctions in a quantum dissipative environment, Phys. Rev. B 104, 245417 (2021).
  9. M. Houzet, T. Yamamoto, and L. I. Glazman, Microwave spectroscopy of the Schmid transition, Phys. Rev. B 109, 155431 (2024).
  10. K. Masuki, H. Sudo, M. Oshikawa, and Y. Ashida, Absence versus presence of dissipative quantum phase transition in Josephson junctions, Phys. Rev. Lett. 129, 087001 (2022).
  11. T. Sépulcre, S. Florens, and I. Snyman, Comment on “absence versus presence of dissipative quantum phase transition in Josephson junctions”, Phys. Rev. Lett. 131, 199701 (2023).
  12. K. Masuki, H. Sudo, M. Oshikawa, and Y. Ashida, Reply to comment on “absence versus presence of dissipative quantum phase transition in Josephson junctions,” Phys. Rev. Lett. 131, 199702 (2023).
  13. A. Burshtein and M. Goldstein, Inelastic decay from integrability, PRX Quantum 5, 020323 (2024).
  14. S. Léger, T. Sépulcre, D. Fraudet, O. Buisson, C. Naud, W. Hasch-Guichard, S. Florens, I. Snyman, D. M. Basko, and N. Roch, Revealing the finite-frequency response of a bosonic quantum impurity, SciPost Phys. 14, 130 (2023).
  15. T. Yokota, K. Masuki, and Y. Ashida, Functional-renormalization-group approach to circuit quantum electrodynamics, Phys. Rev. A 107, 043709 (2023).
  16. R. Daviet and N. Dupuis, Nature of the Schmid transition in a resistively shunted Josephson junction, Phys. Rev. B 108, 184514 (2023).
  17. A. L. Yeyati, D. Subero, J. P. Pekola, and R. Sánchez, Photonic heat transport through a Josephson junction in a resistive environment, Phys. Rev. B 110, L220502 (2024).
  18. N. Paris, L. Giacomelli, R. Daviet, C. Ciuti, N. Dupuis, and C. Mora, Resilience of the quantum critical line in the Schmid transition, Phys. Rev. B 111, 064509 (2025).
  19. L. Giacomelli and C. Ciuti, Emergent quantum phase transition of a Josephson junction coupled to a high-impedance multimode resonator, Nat. Commun. 15, 5455 (2024).
  20. L. Giacomelli, M. H. Devoret, and C. Ciuti, Exact duality at low energy in a Josephson tunnel junction coupled to a transmission line, arXiv:2504.14651.
  21. O. Kashuba and R.-P. Riwar, Limitations of Caldeira-Leggett model for description of phase transitions in superconducting circuits, Phys. Rev. B 110, 184505 (2024).
  22. B. Remez, V. D. Kurilovich, M. Rieger, and L. I. Glazman, Bloch oscillations in a transmon embedded in a resonant electromagnetic environment, Phys. Rev. B 110, 054508 (2024).
  23. V. D. Kurilovich, B. Remez, and L. I. Glazman, Quantum theory of Bloch oscillations in a resistively shunted transmon, Nat. Commun. 16, 1384 (2025).
  24. R. Yagi, S.-i. Kobayashi, and Y. Ootuka, Phase diagram for superconductor-insulator transition in single small Josephson junctions with shunt resistor, J. Phys. Soc. Jpn. 66, 3722 (1997).
  25. J. S. Penttilä, Ü. Parts, P. J. Hakonen, M. A. Paalanen, and E. B. Sonin, “Superconductor-insulator transition” in a single Josephson junction, Phys. Rev. Lett. 82, 1004 (1999).
  26. J. S. Penttilä, P. Hakonen, E. Sonin, and M. Paalanen, Experiments on dissipative dynamics of single Josephson junctions, J. Low Temp. Phys. 125, 89 (2001).
  27. P. J. Hakonen and E. B. Sonin, Comment on “absence of a dissipative quantum phase transition in Josephson junctions,” Phys. Rev. X 11, 018001 (2021).
  28. A. Murani, N. Bourlet, H. le Sueur, F. Portier, C. Altimiras, D. Esteve, H. Grabert, J. Stockburger, J. Ankerhold, and P. Joyez, Reply to Comment on “absence of a dissipative quantum phase transition in Josephson junctions”, Phys. Rev. X 11, 018002 (2021).
  29. J. P. Pekola and B. Karimi, Heat bath in a quantum circuit, Entropy 26, 429 (2024).
  30. Y. P. Zhong, H.-S. Chang, K. J. Satzinger, M.-H. Chou, A. Bienfait, C. Conner, É. Dumur, J. Grebel, G. A. Peairs, R. G. Povey et al., Violating Bell’s inequality with remotely connected superconducting qubits, Nat. Phys. 15, 741 (2019).
  31. See Supplemental Material at http://link.aps.org/supplemental/10.1103/4f3c-jv43 for additional details on sample fabrication, Al/Cr contact characterization, and impedance estimates.
  32. G. J. Dolan, Offset masks for lift-off photoprocessing, Appl. Phys. Lett. 31, 337 (1977).
  33. P. Wahlgren, P. Delsing, and D. B. Haviland, Crossover from global to local rule for the Coulomb blockade in small tunnel junctions, Phys. Rev. B 52, R2293 (1995).
  34. G.-L. Ingold and Y. V. Nazarov, Charge tunneling rates in ultrasmall junctions, in Single Charge Tunneling (Springer, New York, 1992), pp. 21–107.
  35. H. Grabert, G.-L. Ingold, and B. Paul, Phase diffusion and charging effects in Josephson junctions, Europhys. Lett. 44, 360 (1998).
  36. H. Grabert and G.-L. Ingold, Mesoscopic Josephson effect, Superlattices Microstruct. 25, 915 (1999).
  37. C. P. Herrero and A. D. Zaikin, Superconductor-insulator quantum phase transition in a single Josephson junction, Phys. Rev. B 65, 104516 (2002).
  38. N. Kimura and T. Kato, Temperature dependence of zero-bias resistances of a single resistance-shunted Josephson junction, Phys. Rev. B 69, 012504 (2004).
  39. S. Léger, J. Puertas-Martínez, K. Bharadwaj, R. Dassonneville, J. Delaforce, F. Foroughi, V. Milchakov, L. Planat, O. Buisson, C. Naud et al., Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits, Nat. Commun. 10, 5259 (2019).

Outline

Information

Phys. Rev. Lett. 136, 116301– Published 20 March, 2026
  • Received 11 October 2025
  • Accepted 12 February 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation