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From Coherent to Fermionized Microwave Photons in a Superconducting Transmission Line

Alberto Tabarelli de Fatis1,*, Stephanie Matern1, Gianluca Rastelli1,2, and Iacopo Carusotto1,2

  • *Contact author: a.tabarellidefatis-2@unitn.it
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Phys. Rev. Lett. 137, 193601 – Published 3 November, 2026

DOI: https://doi.org/10.1103/g262-dlhf

Abstract

We investigate superconducting transmission lines as a novel platform for realizing a quantum fluid of microwave photons in a propagating geometry. We anticipate that the strong photon-photon interactions provided by the intrinsic nonlinearity of Josephson junctions are sufficient to enter a regime of strongly interacting photons for realistic parameters. To prove the potential of this platform, we show that a suitable tapering of the transmission line parameters allows for the adiabatic conversion of an incident coherent field into a cold Tonks-Girardeau gas of fermionized photons close to its ground state. Signatures of the strong correlations are visible in the correlation properties of the transmitted light.

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References (59)

  1. I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013).
  2. I. Carusotto, A. A. Houck, A. J. Kollár, P. Roushan, D. I. Schuster, and J. Simon, Photonic materials in circuit quantum electrodynamics, Nat. Phys. 16, 268 (2020).
  3. R. Ma, B. Saxberg, C. Owens, N. Leung, Y. Lu, J. Simon, and D. I. Schuster, A dissipatively stabilized Mott insulator of photons, Nature (London) 566, 51 (2019).
  4. G. P. Fedorov, S. V. Remizov, D. S. Shapiro, W. V. Pogosov, E. Egorova, I. Tsitsilin, M. Andronik, A. A. Dobronosova, I. A. Rodionov, O. V. Astafiev, and A. V. Ustinov, Photon transport in a Bose-Hubbard chain of superconducting artificial atoms, Phys. Rev. Lett. 126, 180503 (2021).
  5. L. W. Clark, N. Schine, C. Baum, N. Jia, and J. Simon, Observation of Laughlin states made of light, Nature (London) 582, 41 (2020).
  6. C. Wang, F.-M. Liu, M.-C. Chen, H. Chen, X.-H. Zhao, C. Ying, Z.-X. Shang, J.-W. Wang, Y.-H. Huo, C.-Z. Peng et al., Realization of fractional quantum Hall state with interacting photons, Science 384, 579 (2024).
  7. Q. Glorieux, C. Piekarski, Q. Schibler, T. Aladjidi, and M. Baker-Rasooli, Chapter four—paraxial fluids of light (Academic Press, 2025), pp. 157–241, 10.1016/bs.aamop.2025.04.002.
  8. Y. Lai and H. A. Haus, Quantum theory of solitons in optical fibers. I. Time-dependent Hartree approximation, Phys. Rev. A 40, 844 (1989).
  9. P.-E. Larré’ and I. Carusotto, Propagation of a quantum fluid of light in a cavityless nonlinear optical medium: General theory and response to quantum quenches, Phys. Rev. A 92, 043802 (2015).
  10. C. Michel, O. Boughdad, M. Albert, P.-É. Larré, and M. Bellec, Superfluid motion and drag-force cancellation in a fluid of light, Nat. Commun. 9, 2108 (2018).
  11. M. Abuzarli, N. Cherroret, T. Bienaimé, and Q. Glorieux, Nonequilibrium prethermal states in a two-dimensional photon fluid, Phys. Rev. Lett. 129, 100602 (2022).
  12. Q. Fontaine, T. Bienaimé, S. Pigeon, E. Giacobino, A. Bramati, and Q. Glorieux, Observation of the Bogoliubov dispersion in a fluid of light, Phys. Rev. Lett. 121, 183604 (2018).
  13. T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, Quantum nonlinear optics with single photons enabled by strongly interacting atoms, Nature (London) 488, 57 (2012).
  14. Q.-Y. Liang, A. V. Venkatramani, S. H. Cantu, T. L. Nicholson, M. J. Gullans, A. V. Gorshkov, J. D. Thompson, C. Chin, M. D. Lukin, and V. Vuletić, Observation of three-photon bound states in a quantum nonlinear medium, Science 359, 783 (2018).
  15. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  16. M. Esposito, A. Ranadive, L. Planat, and N. Roch, Perspective on traveling wave microwave parametric amplifiers, Appl. Phys. Lett. 119, 120501 (2021).
  17. L. Zhong, E. P. Menzel, R. Di Candia, P. Eder, M. Ihmig, A. Baust, M. Haeberlein, E. Hoffmann, K. Inomata, T. Yamamoto, Y. Nakamura, E. Solano, F. Deppe, A. Marx, and R. Gross, Squeezing with a flux-driven Josephson parametric amplifier, New J. Phys. 15, 125013 (2013).
  18. B. Josephson, Possible new effects in superconductive tunnelling, Phys. Lett. 1, 251 (1962).
  19. L. Tonks, The complete equation of state of one, two and three-dimensional gases of hard elastic spheres, Phys. Rev. 50, 955 (1936).
  20. M. Girardeau, Relationship between systems of impenetrable bosons and fermions in one dimension, J. Math. Phys. (N. Y.) 1, 516 (1960).
  21. T. Kinoshita, T. Wenger, and D. S. Weiss, Observation of a one-dimensional Tonks-Girardeau gas, Science 305, 1125 (2004).
  22. B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G. V. Shlyapnikov, T. W. Hänsch, and I. Bloch, Tonks–Girardeau gas of ultracold atoms in an optical lattice, Nature (London) 429, 277 (2004).
  23. Y. Castin, Simple theoretical tools for low dimension Bose gases, J. Phys. IV France 116, 89 (2004).
  24. J. Steinhauer, M. Abuzarli, T. Aladjidi, T. Bienaimé, C. Piekarski, W. Liu, E. Giacobino, A. Bramati, and Q. Glorieux, Analogue cosmological particle creation in an ultracold quantum fluid of light, Nat. Commun. 13, 1 (2022).
  25. E. H. Lieb and W. Liniger, Exact analysis of an interacting Bose gas. I. The general solution and the ground state, Phys. Rev. 130, 1605 (1963).
  26. E. H. Lieb, Exact analysis of an interacting Bose gas. II. The excitation spectrum, Phys. Rev. 130, 1616 (1963).
  27. S. E. Rasmussen, K. S. Christensen, S. P. Pedersen, L. B. Kristensen, T. Bækkegaard, N. J. S. Loft, and N. T. Zinner, Superconducting circuit companion—an introduction with worked examples, PRX Quantum 2, 040204 (2021).
  28. R. Kleiner, D. Koelle, F. Ludwig, and J. Clarke, Superconducting quantum interference devices: State of the art and applications, Proc. IEEE 92, 1534 (2004).
  29. N. Frattini, U. Vool, S. Shankar, A. Narla, K. Sliwa, and M. Devoret, 3-wave mixing Josephson dipole element, Appl. Phys. Lett. 110, 222603 (2017).
  30. W. Zhang, W. Huang, M. E. Gershenson, and M. T. Bell, Josephson metamaterial with a widely tunable positive or negative Kerr constant, Phys. Rev. Appl. 8, 051001(R) (2017).
  31. 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).
  32. See Supplemental Material at http://link.aps.org/supplemental/10.1103/g262-dlhf for the derivation of the action, a comment on the numerical methods, and results on other correlation functions not considered in the main text, which includes Refs. [33–35].
  33. G. Vidal, Classical simulation of infinite-size quantum lattice systems in one spatial dimension, Phys. Rev. Lett. 98, 070201 (2007).
  34. R. Orús and G. Vidal, Infinite time-evolving block decimation algorithm beyond unitary evolution, Phys. Rev. B 78, 155117 (2008).
  35. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases 4 (2022).

  36. The introduction of v¯g is convenient for mapping length into time, though the physical results are independent of it.

  37. The dynamical variable ϕ0 is the only independent degree of freedom as its conjugate momentum is proportional to ϕ0* [38]. Therefore, in Eq. (7) only derivatives of ϕ0 appear.

  38. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics (John Wiley & Sons, New York, 2024).

  39. Higher order corrections to the linear dispersion relation beyond the SVEA would give a momentum dependent mass.

  40. Note that the expansion of the action [Eq. (3)] to the lowest nonlinear order is enough to describe the strongly interacting gas, provided the field amplitude remains weak enough, i.e., ϕ/Φ0≪1. If needed, higher order terms would introduce multibody interaction terms in the Bose gas Hamiltonian.

  41. M. P. da Silva, D. Bozyigit, A. Wallraff, and A. Blais, Schemes for the observation of photon correlation functions in circuit QED with linear detectors, Phys. Rev. A 82, 043804 (2010).
  42. C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. A. Abdumalikov, M. Baur, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, Observation of resonant photon blockade at microwave frequencies using correlation function measurements, Phys. Rev. Lett. 106, 243601 (2011).
  43. D. Bozyigit, C. Lang, L. Steffen, J. M. Fink, C. Eichler, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors, Nat. Phys. 7, 154 (2011).
  44. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (John Wiley & Sons, New York, 2024).
  45. A. Polkovnikov and V. Gritsev, Breakdown of the adiabatic limit in low-dimensional gapless systems, Nat. Phys. 4, 477 (2008).
  46. 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).
  47. R. Behr, O. Kieler, J. Kohlmann, F. Müller, and L. Palafox, Development and metrological applications of Josephson arrays at ptb, Meas. Sci. Technol. 23, 124002 (2012).
  48. T. Langen, R. Geiger, M. Kuhnert, B. Rauer, and J. Schmiedmayer, Local emergence of thermal correlations in an isolated quantum many-body system, Nat. Phys. 9, 640 (2013).
  49. P. Calabrese and J. Cardy, Time dependence of correlation functions following a quantum quench, Phys. Rev. Lett. 96, 136801 (2006).
  50. S. Frasca, C. Roy, G. Beaulieu, and P. Scarlino, Three-wave-mixing quantum-limited kinetic inductance parametric amplifier operating at 6 T near 1 K, Phys. Rev. Appl. 21, 024011 (2024).
  51. P. M. Walker, L. Tinkler, M. Durska, D. M. Whittaker, I. J. Luxmoore, B. Royall, D. N. Krizhanovskii, M. S. Skolnick, I. Farrer, and D. A. Ritchie, Exciton polaritons in semiconductor waveguides, Appl. Phys. Lett. 102, 012109 (2013).
  52. D. G. Suárez-Forero, F. Riminucci, V. Ardizzone, N. Karpowicz, E. Maggiolini, G. Macorini, G. Lerario, F. Todisco, M. De Giorgi, L. Dominici, D. Ballarini, G. Gigli, A. S. Lanotte, K. West, K. Baldwin, L. Pfeiffer, and D. Sanvitto, Enhancement of parametric effects in polariton waveguides induced by dipolar interactions, Phys. Rev. Lett. 126, 137401 (2021).
  53. I. Rosenberg, D. Liran, Y. Mazuz-Harpaz, K. West, L. Pfeiffer, and R. Rapaport, Strongly interacting dipolar-polaritons, Sci. Adv. 4, eaat8880 (2018).
  54. M. Horvath, A. Bastianello, S. Dhar, R. Koch, Y. Guo, J.-S. Caux, M. Landini, and H.-C. Nägerl, Observing Bethe strings in an attractive Bose gas far from equilibrium, arXiv:2505.10550.
  55. C. Oliver, S. Mukherjee, M. C. Rechstman, I. Carusotto, and H. M. Price, Artificial gauge fields in the t-z mapping for optical pulses: Spatiotemporal wave packet control and quantum Hall physics, Sci. Adv. 9, eadj0360 (2023).
  56. J. Monroe, D. Kowsari, K. Zheng, C. Gaikwad, J. Brewster, D. Wisbey, and K. Murch, Optical direct write of Dolan–Niemeyer-bridge junctions for transmon qubits, Appl. Phys. Lett. 119, 062601 (2021).
  57. R. Zhao, S. Park, T. Zhao, M. Bal, C. R. J. McRae, J. Long, and D. P. Pappas, Merged-element transmon, Phys. Rev. Appl. 14, 064006 (2020).
  58. P. Manset, J. Palomo, A. Schmitt, K. Gerashchenko, R. Rousseau, H. Patange, P. Abgrall, E. Flurin, S. Deléglise, T. Jacqmin, and L. Balembois, Hyperinductance based on stacked Josephson junctions, arXiv:2505.02764.
  59. L. Planat, A. Ranadive, R. Dassonneville, J. Puertas Martínez, S. Léger, C. Naud, O. Buisson, W. Hasch-Guichard, D. M. Basko, and N. Roch, Photonic-crystal Josephson traveling-wave parametric amplifier, Phys. Rev. X 10, 021021 (2020).

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Phys. Rev. Lett. 137, 193601– Published 3 November, 2026
  • Received 19 January 2026
  • Revised 12 May 2026
  • Accepted 9 October 2026
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