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Refrigeration of a one-dimensional gas of microwave photons

Lukas Schamriß*, Louis Garbe, and Peter Rabl

  • *Contact author: lukas.schamriss@tum.de
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Phys. Rev. A 114, 022604 – Published 5 August, 2026

DOI: https://doi.org/10.1103/7n7h-6w2p

Abstract

We discuss a conceptually simple scheme for cooling a one-dimensional gas of microwave photons in a superconducting transmission line. By shunting one end of the transmission line by a nonlinear Josephson element, we show how a cooling mechanism can be engineered that transfers photons from high- into low-frequency modes, while preserving their total number. We evaluate the resulting nonequilibrium steady state of the photon gas, which arises from a competition between this engineered cooling process and the natural, number nonconserving thermalization with the surrounding bath. Our analysis predicts that for realistic experimental parameters, this mechanism can be used to prepare photonic gases at submillikelvin temperatures, considerably below the typical base temperature of a dilution refrigerator. In addition, the system exhibits a new type of condensation transition that does not occur in the corresponding equilibrium scenario. As an outlook, we discuss potential applications of this cooling approach for quantum simulation schemes with interacting microwave photons.

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References (63)

  1. A. A. Houck, H. E. Türeci, and J. Koch, On-chip quantum simulation with superconducting circuits, Nat. Phys. 8, 292 (2012).
  2. M. Hartmann, Quantum simulation with interacting photons, J. Opt. 18, 104005 (2016).
  3. M. Kjaergaard, M. E. Schwartz, J. Braumüller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annu. Rev. Condens. Matter Phys. 11, 369 (2020).
  4. S. Greenaway, A. Smith, F. Mintert, and D. Malz, Analogue quantum simulation with fixed-frequency transmon qubits, Quantum 8, 1263 (2024).
  5. T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, Circuit quantum electrodynamics in the ultrastrong-coupling regime, Nat. Phys. 6, 772 (2010).
  6. P. Forn-Díaz, J. García-Ripoll, B. Peropadre, J.-L. Orgiazzi, M. Yurtalan, R. Belyansky, C. Wilson, and A. Lupascu, Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime, Nat. Phys. 13, 39 (2017).
  7. F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime, Nat. Phys. 13, 44 (2017).
  8. A. J. Kollár, M. Fitzpatrick, and A. A. Houck, Hyperbolic lattices in circuit quantum electrodynamics, Nature (London) 571, 45 (2019).
  9. X. Zhang, E. Kim, D. K. Mark, S. Choi, and O. Painter, A superconducting quantum simulator based on a photonic-bandgap metamaterial, Science 379, 278 (2023).
  10. P. Roushan, C. Neill, A. Megrant, Y. Chen, R. Babbush, R. Barends, B. Campbell, Z. Chen, B. Chiaro, et al., Chiral ground-state currents of interacting photons in a synthetic magnetic field, Nat. Phys. 13, 146 (2017).
  11. C. Owens, A. LaChapelle, B. Saxberg, B. M. Anderson, R. Ma, J. Simon, and D. I. Schuster, Quarter-flux Hofstadter lattice in a qubit-compatible microwave cavity array, Phys. Rev. A 97, 013818 (2018).
  12. I. T. Rosen, S. Muschinske, C. N. Barrett, A. Chatterjee, M. Hays, M. A. DeMarco, A. H. Karamlou, D. A. Rower, R. Das, D. K. Kim, et al., A synthetic magnetic vector potential in a 2D superconducting qubit array, Nat. Phys. 20, 1881 (2024).
  13. 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, X. Zhu, C.-Y. Lu, and J.-W. Pan, Realization of fractional quantum Hall state with interacting photons, Science 384, 579 (2024).
  14. J. J. García-Ripoll, E. Solano, and M. A. Martin-Delgado, Quantum simulation of Anderson and Kondo lattices with superconducting qubits, Phys. Rev. B 77, 024522 (2008).
  15. J. Koch and K. Le Hur, Superfluid–Mott-insulator transition of light in the Jaynes-Cummings lattice, Phys. Rev. A 80, 023811 (2009).
  16. M. Leib and M. J. Hartmann, Bose–Hubbard dynamics of polaritons in a chain of circuit quantum electrodynamics cavities, New J. Phys. 12, 093031 (2010).
  17. J.-M. Reiner, M. Marthaler, J. Braumüller, M. Weides, and G. Schön, Emulating the one-dimensional Fermi-Hubbard model by a double chain of qubits, Phys. Rev. A 94, 032338 (2016).
  18. 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).
  19. A. H. Karamlou, I. T. Rosen, S. E. Muschinske, C. N. Barrett, A. Di Paolo, L. Ding, P. M. Harrington, M. Hays, R. Das, D. K. Kim, et al., Probing entanglement in a 2d hard-core bose–hubbard lattice, Nature (London) 629, 561 (2024).
  20. T.-M. Li, Z.-H. Sun, Y.-H. Shi, Z.-T. Bao, Y.-Y. Wang, J.-C. Zhang, Y. Liu, C.-L. Deng, Y.-H. Yu, Z.-H. Liu, et al., Many-body delocalization with a two-dimensional 70-qubit superconducting quantum simulator, arXiv:2507.16882.
  21. B. Du, Q. Guo, S. López, and R. Ma, Tunneling spectroscopy in superconducting circuit lattices, Phys. Rev. Res. 7, L022038 (2025).
  22. D. Marcos, P. Rabl, E. Rico, and P. Zoller, Superconducting circuits for quantum simulation of dynamical gauge fields, Phys. Rev. Lett. 111, 110504 (2013).
  23. D. Marcos, P. Widmer, E. Rico, M. Hafezi, P. Rabl, U.-J. Wiese, and P. Zoller, Two-dimensional lattice gauge theories with superconducting quantum circuits, Ann. Phys. (NY) 351, 634 (2014).
  24. J. H. Busnaina, Z. Shi, J. M. Alcaine-Cuervo, C. X. Yang, I. Nsanzineza, E. Rico, and C. M. Wilson, Native three-body interactions in a superconducting lattice gauge quantum simulator, Phys. Rev. B 112, 134514 (2025).
  25. Y.-H. Shi, R.-Q. Yang, Z. Xiang, Z.-Y. Ge, H. Li, Y.-Y. Wang, K. Huang, Y. Tian, X. Song, D. Zheng, K. Xu, R.-G. Cai, and H. Fan, Quantum simulation of Hawking radiation and curved spacetime with a superconducting on-chip black hole, Nat. Commun. 14, 3263 (2023).
  26. M. A. Javed, D. Kruti, A. Kenawy, T. Herrig, C. Koliofoti, O. Kashuba, and R.-P. Riwar, On-demand analog space-time in superconducting networks: Grey holes, dynamical instability and exceptional points, SciPost Phys. 20, 047 (2024).
  27. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  28. A. Imamoglu, R. J. Ram, S. Pau, and Y. Yamamoto, Nonequilibrium condensates and lasers without inversion: Exciton-polariton lasers, Phys. Rev. A 53, 4250 (1996).
  29. H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, Condensation of semiconductor microcavity exciton polaritons, Science 298, 199 (2002).
  30. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, Bose–Einstein condensation of exciton polaritons, Nature (London) 443, 409 (2006).
  31. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, Bose-Einstein condensation of microcavity polaritons in a trap, Science 316, 1007 (2007).
  32. J. Keeling, F. M. Marchetti, M. H. Szymańska, and P. B. Littlewood, Collective coherence in planar semiconductor microcavities, Semicond. Sci. Technol. 22, R1 (2007).
  33. H. Deng, H. Haug, and Y. Yamamoto, Exciton-polariton Bose-Einstein condensation, Rev. Mod. Phys. 82, 1489 (2010).
  34. J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, Bose-Einstein condensation of photons in an optical microcavity, Nature (London) 468, 545 (2010).
  35. D. Marcos, A. Tomadin, S. Diehl, and P. Rabl, Photon condensation in circuit quantum electrodynamics by engineered dissipation, New J. Phys. 14, 055005 (2012).
  36. M. Hafezi, P. Adhikari, and J. M. Taylor, Chemical potential for light by parametric coupling, Phys. Rev. B 92, 174305 (2015).
  37. S. Hacohen-Gourgy, V. V. Ramasesh, C. De Grandi, I. Siddiqi, and S. M. Girvin, Cooling and autonomous feedback in a Bose-Hubbard chain with attractive interactions, Phys. Rev. Lett. 115, 240501 (2015).
  38. X. Cao, M. Mucci, G. Liu, D. Pekker, and M. Hatridge, Engineering a multilevel bath for transmons with three-wave mixing and parametric drives, Phys. Rev. Lett. 135, 230403 (2025).
  39. S. Polla, Y. Herasymenko, and T. E. O'Brien, Quantum digital cooling, Phys. Rev. A 104, 012414 (2021).
  40. L. Marti, R. Mansuroglu, and M. Hartmann, Efficient quantum cooling algorithm for fermionic systems, Quantum 9, 1635 (2025).
  41. R. Lescanne, S. Deléglise, E. Albertinale, U. Réglade, T. Capelle, E. Ivanov, T. Jacqmin, Z. Leghtas, and E. Flurin, Irreversible qubit-photon coupling for the detection of itinerant microwave photons, Phys. Rev. X 10, 021038 (2020).
  42. Y. Nojiri, K. E. Honasoge, A. Marx, K. G. Fedorov, and R. Gross, Onset of transmon ionization in microwave single-photon detection, Phys. Rev. B 109, 174312 (2024).
  43. P. Kirton and J. Keeling, Nonequilibrium model of photon condensation, Phys. Rev. Lett. 111, 100404 (2013).
  44. P. Kirton and J. Keeling, Thermalization and breakdown of thermalization in photon condensates, Phys. Rev. A 91, 033826 (2015).
  45. S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. Büchler, and P. Zoller, Quantum states and phases in driven open quantum systems with cold atoms, Nat. Phys. 4, 878 (2008).
  46. T. C. H. Liew, M. M. Glazov, K. V. Kavokin, I. A. Shelykh, M. A. Kaliteevski, and A. V. Kavokin, Proposal for a bosonic cascade laser, Phys. Rev. Lett. 110, 047402 (2013).
  47. M. Kaliteevskii and K. Ivanov, Double-boson stimulated terahertz emission in a polariton cascade laser, Tech. Phys. Lett. 39, 91 (2013).
  48. A. Kavokin, T. Liew, C. Schneider, and S. Höfling, Bosonic lasers: The state of the art (review article), J. Low Temp. Phys. 42, 323 (2016).
  49. T. Haga, M. Nakagawa, R. Hamazaki, and M. Ueda, Liouvillian skin effect: Slowing down of relaxation processes without gap closing, Phys. Rev. Lett. 127, 070402 (2021).
  50. L. Garbe, Y. Minoguchi, J. Huber, and P. Rabl, The bosonic skin effect: Boundary condensation in asymmetric transport, SciPost Phys. 16, 029 (2024).
  51. Y. Minoguchi, J. Huber, L. Garbe, A. Gambassi, and P. Rabl, Unified interface model for dissipative transport of bosons and fermions, Phys. Rev. Lett. 134, 207102 (2025).
  52. D. Bernard, T. Jin, S. Scopa, and S. Wei, Large deviations of density fluctuations in the boundary-driven quantum symmetric simple inclusion process, Phys. Rev. E 112, 034106 (2025).
  53. The mpmath development team, Mpmath: A Python library for arbitrary-precision floating-point arithmetic (version 1.3.0), http://mpmath.org/.
  54. L. Schamriß, L. Garbe, and P. Rabl, Code for publication: Refrigeration of a 1D gas of microwave photons [Computer software], Zenodo, 2026, https://doi.org/10.5281/zenodo.19865660.
  55. J.-H. Yeh, J. LeFebvre, S. Premaratne, F. C. Wellstood, and B. S. Palmer, Microwave attenuators for use with quantum devices below 100 mK, J. Appl. Phys. 121, 224501 (2017).
  56. Z. Wang, S. Shankar, Z. K. Minev, P. Campagne-Ibarcq, A. Narla, and M. H. Devoret, Cavity attenuators for superconducting qubits, Phys. Rev. Appl. 11, 014031 (2019).
  57. V. C. Aguilera-Navarro, M. d. Llano, and M. A. Solís, Bose-Einstein condensation for general dispersion relations, Eur. J. Phys. 20, 177 (1999).
  58. N. E. Frattini, V. V. Sivak, A. Lingenfelter, S. Shankar, and M. H. Devoret, Optimizing the nonlinearity and dissipation of a SNAIL parametric amplifier for dynamic range, Phys. Rev. Appl. 10, 054020 (2018).
  59. J. J. García Ripoll, Quantum Information and Quantum Optics with Superconducting Circuits (Cambridge University Press, Cambridge, UK, 2022).
  60. X. You, J. A. Sauls, and J. Koch, Circuit quantization in the presence of time-dependent external flux, Phys. Rev. B 99, 174512 (2019).
  61. A. M. Eriksson, T. Sépulcre, M. Kervinen, T. Hillmann, M. Kudra, S. Dupouy, Y. Lu, M. Khanahmadi, J. Yang, C. Castillo-Moreno, P. Delsing, and S. Gasparinetti, Universal control of a bosonic mode via drive-activated native cubic interactions, Nat. Commun. 15, 2512 (2024).
  62. M. Haider, A black-box quantum model for superconducting traveling-wave parametric amplifiers, IEEE Trans. Microwave Theory Techn. 72, 2143 (2024).
  63. D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem. 81, 2340 (1977).

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Phys. Rev. A 114, 022604– Published 5 August, 2026
  • Received 8 January 2026
  • Revised 30 April 2026
  • Accepted 1 July 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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