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  • Letter
  • Open Access

Analog black-white hole solitons in traveling wave parametric amplifiers with superconducting nonlinear asymmetric inductive elements

Haruna Katayama1,2,*, Noriyuki Hatakenaka2, Toshiyuki Fujii3, and Miles P. Blencowe1

  • 1Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA
  • 2Graduate School of Advanced Science and Engineering, Hiroshima University, Higashihiroshima 739-8521, Japan
  • 3Department of Physics, Asahikawa Medical University, Midorigaoka-higashi, Asahikawa 078-8510, Japan

  • *halna496@gmail.com
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Phys. Rev. Research 5, L022055 – Published 20 June, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L022055

Abstract

We show that existing traveling wave parametric amplifier (TWPA) setups, using superconducting nonlinear asymmetric inductive elements (SNAILs), admit soliton solutions that act as analog event horizons. The SNAIL-TWPA circuit dynamics are described by the Korteweg–de Vries or modified Korteweg–de Vries equations in the continuum field approximation, depending on the external magnetic flux bias, and validated numerically. The soliton spatially modulates the velocity for weak probes, resulting in the effective realization of analog black hole and white hole event horizon pairs. The SNAIL external magnetic flux bias tunability facilitates a three-wave mixing process, which enhances the prospects for observing Hawking photon radiation.

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References (42)

  1. S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975).
  2. W. G. Unruh, Experimental Black-Hole Evaporation? Phys. Rev. Lett. 46, 1351 (1981).
  3. S. Weinfurtner, E. W. Tedford, M. C. J. Penrice, W. G. Unruh, and G. A. Lawrence, Measurement of Stimulated Hawking Emission in an Analogue System, Phys. Rev. Lett. 106, 021302 (2011).
  4. L.-P. Euvé, F. Michel, R. Parentani, T. G. Philbin, and G. Rousseaux, Observation of Noise Correlated by the Hawking Effect in a Water Tank, Phys. Rev. Lett. 117, 121301 (2016).
  5. J. Steinhauer, Observation of self-amplifying Hawking radiation in an analogue black-hole laser, Nat. Phys. 10, 864 (2014).
  6. J. Steinhauer, Observation of quantum Hawking radiation and its entanglement in an analogue black hole, Nat. Phys. 12, 959 (2016).
  7. T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, Fiber-optical analog of the event horizon, Science 319, 1367 (2008).
  8. A. Choudhary and F. König, Efficient frequency shifting of dispersive waves at solitons, Opt. Express 20, 5538 (2012).
  9. J. Drori, Y. Rosenberg, D. Bermudez, Y. Silberberg, and U. Leonhardt, Observation of Stimulated Hawking Radiation in an Optical Analogue, Phys. Rev. Lett. 122, 010404 (2019).
  10. H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaître, I. Sagnes, J. Bloch, and A. Amo, Acoustic Black Hole in a Stationary Hydrodynamic Flow of Microcavity Polaritons, Phys. Rev. Lett. 114, 036402 (2015).
  11. M. J. Jacquet, T. Boulier, F. Claude, A. Maître, E. Cancellieri, C. Adrados, A. Amo, S. Pigeon, Q. Glorieux, A. Bramati, and E. Giacobino, Polariton fluids for analogue gravity physics, Philos. Trans. R. Soc. A 378, 20190225 (2020).
  12. P. D. Nation, J. R. Johansson, M. P. Blencowe, and F. Nori, Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits, Rev. Mod. Phys. 84, 1 (2012).
  13. C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature (London) 479, 376 (2011).
  14. P. Lähteenmäki, G. S. Paraoanu, J. Hassel, and P. J. Hakonen, Dynamical Casimir effect in a Josephson metamaterial, Proc. Natl. Acad. Sci. USA 110, 4234 (2013).
  15. R. Schützhold and W. G. Unruh, Hawking Radiation in an Electromagnetic Waveguide? Phys. Rev. Lett. 95, 031301 (2005).
  16. P. D. Nation, M. P. Blencowe, A. J. Rimberg, and E. Buks, Analogue Hawking Radiation in a dc-SQUID Array Transmission Line, Phys. Rev. Lett. 103, 087004 (2009).
  17. H. Katayama, N. Hatakenaka, and T. Fujii, Analogue Hawking radiation from black hole solitons in quantum Josephson transmission lines, Phys. Rev. D 102, 086018 (2020).
  18. H. Katayama, S. Ishizaka, N. Hatakenaka, and T. Fujii, Solitonic black holes induced by magnetic solitons in a dc-SQUID array transmission line coupled with a magnetic chain, Phys. Rev. D 103, 066025 (2021).
  19. H. Katayama, Designed analogue black hole solitons in Josephson transmission Lines, IEEE Trans. Appl. Supercond. 31, 1800305 (2021).
  20. H. Katayama, N. Hatakenaka, and K.-i. Matsuda, Analogue Hawking radiation in nonlinear LC transmission lines, Universe 7, 334 (2021).
  21. E. Kogan, The kinks, the solitons and the shocks in series-connected discrete Josephson transmission lines, Phys. Status Solidi B 259, 2200160 (2022).
  22. S. Boutin, D. M. Toyli, A. V. Venkatramani, A. W. Eddins, I. Siddiqi, and A. Blais, Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers, Phys. Rev. Appl. 8, 054030 (2017).
  23. K. Peng, M. Naghiloo, J. Wang, G. D. Cunningham, Y. Ye, and K. P. O'Brien, Floquet-mode traveling-wave parametric amplifiers, PRX Quantum 3, 020306 (2022).
  24. N. E. Frattini, U. Vool, S. Shankar, A. Narla, K. M. Sliwa, and M. H. Devoret, 3-wave mixing Josephson dipole element, Appl. Phys. Lett. 110, 222603 (2017).
  25. M. Esposito, A. Ranadive, L. Planat, S. Leger, D. Fraudet, V. Jouanny, O. Buisson, W. Guichard, C. Naud, J. Aumentado, F. Lecocq, and N. Roch, Observation of Two-Mode Squeezing in a Traveling Wave Parametric Amplifier, Phys. Rev. Lett. 128, 153603 (2022).
  26. M. R. Perelshtein, K. V. Petrovnin, V. Vesterinen, S. Hamedani Raja, I. Lilja, M. Will, A. Savin, S. Simbierowicz, R. N. Jabdaraghi, J. S. Lehtinen, L. Grönberg, J. Hassel, M. P. Prunnila, J. Govenius, G. S. Paraoanu, and P. J. Hakonen, Broadband Continuous-Variable Entanglement Generation Using a Kerr-Free Josephson Metamaterial, Phys. Rev. Appl. 18, 024063 (2022).
  27. A. Ranadive, M. Esposito, L. Planat, E. Bonet, C. Naud, O. Buisson, W. Guichard, and N. Roch, Kerr reversal in Josephson meta-material and traveling wave parametric amplification, Nat. Commun. 13, 1737 (2022).
  28. T. Taniuti and C.-C. Wei, Reductive perturbation method in nonlinear wave propagation. I, J. Phys. Soc. Jpn. 24, 941 (1968).
  29. T. Taniuti and N. Yajima, Perturbation method for a nonlinear wave modulation. I, J. Math. Phys. 10, 1369 (1969).
  30. T. Taniuti, Reductive perturbation method and far fields of wave equations, Prog. Theor. Phys. Suppl. 55, 1 (1974).
  31. D. D. J. Korteweg and D. G. de Vries, XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, London Edinburgh Dublin Philos. Mag. J. Sci. 39, 422 (1895).
  32. Y. S. Kivshar and B. A. Malomed, Dynamics of solitons in nearly integrable systems, Rev. Mod. Phys. 61, 763 (1989).
  33. C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method for Solving the Korteweg-deVries Equation, Phys. Rev. Lett. 19, 1095 (1967).
  34. R. M. Miura, Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation, J. Math. Phys. 9, 1202 (1968).
  35. T. Perelman, A. Fridman, and M. El'Yashevich, On the relationship between the N-soliton solution of the modified Korteweg-de Vries equation and the KdV equation solution, Phys. Lett. A 47, 321 (1974).
  36. G. Chanteur and M. Raadu, Formation of shocklike modified Korteweg-de Vries solitons: Application to double layers, Phys. Fluids 30, 2708 (1987).
  37. N. J. Zabusky and M. D. Kruskal, Interaction of “Solitons” in a Collisionless Plasma and the Recurrence of Initial States, Phys. Rev. Lett. 15, 240 (1965).
  38. F. Bass, Y. Kivshar, V. Konotop, and Y. Sinitsyn, Dynamics of solitons under random perturbations, Phys. Rep. 157, 63 (1988).
  39. M. P. Blencowe and H. Wang, Analogue gravity on a superconducting chip, Philos. Trans. R. Soc. London, Ser. A 378, 20190224 (2020).
  40. S. Corley and T. Jacobson, Black hole lasers, Phys. Rev. D 59, 124011 (1999).
  41. H. Katayama, Quantum-circuit black hole lasers, Sci. Rep. 11, 19137 (2021).
  42. D. Cattiaux, I. Golokolenov, S. Kumar, M. Sillanpää, L. Mercier de Lépinay, R. R. Gazizulin, X. Zhou, A. D. Armour, O. Bourgeois, A. Fefferman, and E. Collin, A macroscopic object passively cooled into its quantum ground state of motion beyond single-mode cooling, Nat. Commun. 12, 6182 (2021).

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Phys. Rev. Research 5, L022055– Published 20 June, 2023
  • Received 30 January 2023
  • Accepted 23 May 2023
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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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