Kotelnikov Institute of Radio Engineering and Electronics of RAS Русский Sign in Submit a paper
Journal of Radio Electronics Online scientific journal · eISSN 1684-1719
2026, № 5 · NONLINEAR WAVE DYNAMICS IN RADIO ELECTRONICS

Bistable states in metamaterial of RF-SQUIDs

A.S. Averkin1, L.V. Filippenko2, M.V. Fistul1

1 National University of Science and Technology MISIS, Moscow, Russia
2 Kotelnikov IRE RAS, Moscow, Russia
Full text DOI: 10.30898/1684-1719.2026.5.1 UDC 538.945 EDN KUGAJK

Abstract

The nonlinear response of a one-dimensional superconducting metamaterial based on 54 non-hysteretic radiofrequency superconducting quantum interference devices (RF-SQUIDs) was experimentally studied. The dependences of the system's resonant frequency on the pump tone power were measured in a two-tone excitation mode both in the absence and with the application of an external constant magnetic field. The metamaterial exhibits bistable behavior over a wide range of pump powers, indicating its potential for use in quantum electronic devices and superconducting parametric amplifiers.

  • superconductivity
  • rf-SQUID
  • Josephson junction
  • microwave measurements
  • Two-tone spectroscopy
Аннотация (на русском)

Бистабильные состояния в метаматериале из ВЧ-СКВИДов

Экспериментально исследован нелинейный отклик одномерного сверхпроводящего метаматериала, изготовленного на основе 54 безгистерезисных высокочастотных сверхпроводящих квантовых интерферометров (ВЧ-СКВИДов). Проведены измерения зависимостей резонансной частоты системы от мощности тона накачки в двух-тоновом режиме возбуждения как в отсутствие, так и при приложении внешнего постоянного магнитного поля. Метаматериал демонстрирует бистабильное поведение в широком диапазоне мощностей накачки, что указывает на возможность его применения в устройствах квантовой электроники и сверхпроводящих параметрических усилителях.

For citation

Averkin A.S., Filippenko L.V., Fistul M.V. Bistable states in metamaterial of RF-SQUIDs // Journal of Radio Electronics. – 2026. – No. 5. https://doi.org/10.30898/1684-1719.2026.5.1

References

  1. B. Josephson, "Possible new effects in superconductive tunnelling", Physics Letters, vol. 1, no. 7, pp. 251-253, 1962. https://doi.org/10.1016/0031-9163(62)91369-0
  2. P. W. Anderson and J. M. Rowell, "Probable observation of the Josephson superconducting tunneling effect", Phys. Rev. Lett., vol. 10, pp. 230-232, Mar 1963. https://doi.org/10.1103/PhysRevLett.10.230
  3. C. C. GRIMES and S. SHAPIRO, "Millimeter-wave mixing with josephson junctions", Phys. Rev., vol. 169, May 1968. https://doi.org/10.1103/PhysRev.169.397
  4. Y.-F. Chen, "Microwave Photon Counter Based on Josephson Junctions", Phys. Rev. Lett. 107, 217401 Published 14 November, 2011, https://doi.org/10.1103/PhysRevLett.107.217401
  5. R. Vijay, M. H. Devoret, I. Siddiqi; Invited Review Article: The Josephson bifurcation amplifier. Rev. Sci. Instrum. 1 November 2009; 80 (11): 111101. https://doi.org/10.1063/1.3224703
  6. N. Boulant, G. Ithier, P. Meeson, F. Nguyen, D. Vion, D. Esteve, I. Siddiqi, R. Vijay, C. Rigetti, F. Pierre, and M. Devoret, Phys. Rev. B 76, 014525 (2007). https://doi.org/10.1103/PhysRevB.76.014525
  7. J. Hizanidis, N. Lazarides, and G. P. Tsironis, "Robust chimera states in squid metamaterials with local interactions", Phys. Rev. E, vol. 94, p. 032219, Sep 2016. https://doi.org/10.1103/PhysRevE.94.032219
  8. P. Jung, S. Butz, M. Marthaler, M. V. Fistul, J. Lepp¨akangas, V. P. Koshelets, and A. V. Ustinov, "Multistability and switching in a superconducting metamaterial", Nature Communications, vol. 5, p. 174507, Apr 2014. https://doi.org/10.1038/ncomms4730
  9. Tsironis, G.P., Lazarides, N. & Margaris, I. Wide-band tuneability, nonlinear transmission, and dynamic multistability in SQUID metamaterials. Appl. Phys. A 117, 579-588 (2014). https://doi.org/10.1007/s00339-014-8706-7
  10. N. Lazarides and G. Tsironis, "Superconducting metamaterials", Physics Reports, vol. 752, pp. 1-67, 2018. Superconducting Metamaterials. https://doi.org/10.1016/j.physrep.2018.06.005
  11. P. Jung, A. V. Ustinov, and S. M. Anlage, "Progress in superconducting metamaterials", Superconductor Science and Technology, vol. 27, p. 073001, may 2014. https://doi.org/10.1088/0953-2048/27/7/073001
  12. O.A. Mukhanov, S. Sarwana, D. Gupta, A.F. Kirichenko, S.V. Rylov, "Rapid single flux quantum technology for SQUID applications",Physica C: Superconductivity, Vol. 368, Issues 1-4,2002,Pages 196-202,ISSN 0921-4534. https://doi.org/10.1016/S0921-4534(01)01166-2
  13. D. Zhang, M. Trepanier, T. Antonsen, E. Ott, and S. M. Anlage, "Intermodulation in nonlinear squid metamaterials: Experiment and theory", Phys. Rev. B, vol. 94, p. 174507, Nov 2016. https://doi.org/10.1103/PhysRevB.94.174507
  14. P. Jung, S. Butz, S. V. Shitov, and A. V. Ustinov, "Low-loss tunable metamaterials using superconducting circuits with Josephson junctions", Applied Physics Letters, vol. 102, p. 062601, 02 2013. https://doi.org/10.1063/1.4791697
  15. S. Butz, P. Jung, L. V. Filippenko, V. P. Koshelets, and A. V. Ustinov, "A one-dimensional tunable magnetic metamaterial: erratum", Opt. Express, vol. 22, pp. 13041-13042, Jun 2014. https://doi.org/10.1364/OE.22.013041
  16. M. Trepanier, D. Zhang, O. Mukhanov, and S. M. Anlage, "Realization and modeling of metamaterials made of rf superconducting quantum-interference devices", Phys. Rev. X, vol. 3, p. 041029, Dec 2013. https://doi.org/10.1103/PhysRevX.3.041029
  17. A. S. Averkin, A. P. Zhuravel, P. Jung, N. Maleeva, V. P. Koshelets, L. V. Filippenko, A. Karpov, and A. V. Ustinov, "Imaging coherent response of superconducting metasurface, "IEEE Transactions on Applied Superconductivity, vol. 26, no. 3, pp. 1-3, 2016. https://doi.org/10.1109/TASC.2016.2516246
  18. M. Trepanier, D. Zhang, O. Mukhanov, V. P. Koshelets, P. Jung, S. Butz, E. Ott, T. M. Antonsen, A. V. Ustinov, and S. M. Anlage, "Coherent oscillations of driven rf squid metamaterials", Phys. Rev. E, vol. 95, p. 050201, May 2017. https://doi.org/10.1103/PhysRevE.95.050201
  19. M. A. Castellanos-Beltran, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehnert, "Amplification and squeezing of quantum noise with a tunable josephsonmetamaterial", Nature Physics, vol. 4, pp. 929-931, Dec 2008. https://doi.org/10.1038/nphys1090
  20. B. Ho Eom, P. K. Day, H. G. LeDuc, and J. Zmuidzinas, "A wideband, low-noise superconducting amplifier with high dynamic range", Nature Physics, vol. 8, pp. 623-627, Aug 2012. https://doi.org/10.1038/nphys2356
  21. K. O'Brien, C. Macklin, I. Siddiqi, and X. Zhang, "Resonant phase matching of josephson junction traveling wave parametric amplifiers", Phys. Rev. Lett., vol. 113, p. 157001, Oct 2014. https://doi.org/10.1103/PhysRevLett.113.157001
  22. N. E. Frattini, U. Vool, S. Shankar, A. Narla, K. M. Sliwa, and M. H. Devoret, "3-wave mixing josephson dipole element", Applied Physics Letters, vol. 110, p. 222603, 05 2017. https://doi.org/10.1063/1.4984142
  23. O. Yaakobi, L. Friedland, C. Macklin, and I. Siddiqi, "Parametric amplification in josephson junction embedded transmission lines", Phys. Rev. B, vol. 87, p. 144301, Apr 2013. https://doi.org/10.1103/PhysRevB.87.144301
  24. A. B. Zorin, "Josephson traveling-wave parametric amplifier with three-wave mixing", Phys. Rev. Appl.,vol. 6, p. 034006, Sep 2016. https://doi.org/10.1103/PhysRevApplied.6.034006
  25. V. Gaydamachenko, C. Kissling, and L. Grunhaupt,"rf-squid-based traveling-wave parametric amplifier with input saturation power of -84 dbm across more than one octave in bandwidth", Phys. Rev. Appl., vol. 23, p. 064053, Jun 2025. https://doi.org/10.1103/1qk4-fzkq
  26. E. I. Kiselev, A. S. Averkin, M. V. Fistul, V. P. Koshelets, and A. V. Ustinov, "Two-tone spectroscopy of a squid metamaterial in the nonlinear regime", Phys. Rev. Res., vol. 1, p. 033096, Nov 2019. https://doi.org/10.1103/PhysRevResearch.1.033096
  27. Аверкин А.С., Филиппенко Л.В. Эффективная джозефсоновская индуктивность ВЧ-СКВИДа как функция мощности микроволнового облучения // Журнал Радиоэлектроники. - 2026. - №. 1. https://doi.org/10.30898/1684-1719.2026.1.9
  28. УНУ "Криоинтеграл" - "Технологический и измерительный комплекс для создания сверхпроводниковых наносистем на основе новых материалов". http://www.cplire.ru/rus/kriointegral/index.html; http://ckp-rf.ru/usu/352529
  29. M. Tinkham, Introduction to superconductivity 2d ed. //McGraw-Hill international editions, -1996. с. 202.