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Effects of Thermal and Lévy Noise Sources on the Switching Current Distributions of a Josephson Junction

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13th Chaotic Modeling and Simulation International Conference (CHAOS 2020)

Part of the book series: Springer Proceedings in Complexity ((SPCOM))

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Abstract

We discuss the combined effect of Gaussian and \(\alpha \)-stable Lévy noise sources on the switching current distribution of a short tunnel Josephson junction, while an external bias current flowing through the junction is linearly swept. At a fixed temperature, if the bias current is repeatedly ramped up from zero, and the value of the bias current at which the system switches to the finite voltage state is recorded, we obtain the distribution of the current values associated to escape events, i.e., the probability distribution of the bias currents at which the junction switches to the finite voltage state from the superconducting zero-voltage state. This information content is promptly available in experiments on Josephson junctions. We demonstrate that a Lévy noise current added to the linearly increased bias current clearly modifies the switching current distribution due to the sole Gaussian-distributed thermal fluctuations. Albeit both Gaussian and Lévy components contribute to the overall noise level, they do not interfere, because they produce switching at different bias levels: the Lévy noise in the lower-current portion of the distribution, the Gaussian noise when the energy barrier becomes comparable to the noise energy. Finally, the analytical expression of the cumulative distribution function of Josephson switching currents can be compared with an analytical estimate.

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References

  1. J.P. Pekola, Josephson junction as a detector of Poissonian charge injection. Phys. Rev. Lett. 93, 206601 (2004)

    Google Scholar 

  2. J. Ankerhold, Detecting charge noise with a Josephson junction: a problem of thermal escape in presence of non-Gaussian fluctuations. Phys. Rev. Lett. 98, 036601 (2007)

    Google Scholar 

  3. J.T. Peltonen, A.V. Timofeev, M. Meschke, T.T. Heikkilä, J.P. Pekola, Detecting non-Gaussian current fluctuations using a Josephson threshold detector. Phys. E 40, 111 (2007)

    Article  Google Scholar 

  4. B. Huard, H. Pothier, N.O. Birge, D. Esteve, X. Waintal, J. Ankerhold, Josephson junctions as detectors for non-Gaussian noise. Ann. Phys. 16, 736 (2007)

    Article  Google Scholar 

  5. H. Grabert, Theory of a Josephson junction detector of non-Gaussian noise. Phys. Rev. B 77, 205315 (2008)

    Google Scholar 

  6. T. Novotnỳ, Josephson junctions as threshold detectors of full counting statistics: open issues. J. Stat. Mech. P01050(2009)

    Google Scholar 

  7. T. Peacock, P. Verhoeve, N. Rando, C. Erd, M. Bavdaz, B.G. Taylor, D. Perez, Recent developments in superconducting tunnel junctions for ultraviolet, optical & near infrared astronomy. Astron. Astrophys. Suppl. Ser. 127, 497 (1998)

    Article  Google Scholar 

  8. J.N. Ullom, D.A. Bennett, Review of superconducting transition-edge sensors for X-ray and gamma-ray spectroscopy. Supercond. Sci. Technol. 28, 084003 (2015)

    Google Scholar 

  9. E.D. Walsh, D.K. Efetov, G.-H. Lee, M. Heuck, J. Crossno, T.A. Ohki, P. Kim, D. Englund, K.C. Fong, Graphene-based Josephson-junction single-photon detector. Phys. Rev. Appl. 8, 024022 (2017)

    Google Scholar 

  10. L.S. Kuzmin, A.S. Sobolev, C. Gatti, D. Di Gioacchino, N. Crescini, A. Gordeeva, E. Il’ichev, Single photon counter based on a Josephson junction at 14 GHz for searching galactic axions. IEEE Trans. Appl. Supercond. 28(2018)

    Google Scholar 

  11. C. Guarcello, A. Braggio, P. Solinas, F. Giazotto, Nonlinear critical-current thermal response of an asymmetric Josephson tunnel junction. Phys. Rev. Appl. 11, 024002 (2019)

    Google Scholar 

  12. C. Guarcello, A. Braggio, P. Solinas, G.P. Pepe, F. Giazotto, Josephson-threshold calorimeter. Phys. Rev. Appl. 11, 054074 (2019)

    Google Scholar 

  13. L.S. Revin, A.L. Pankratov, A.V. Gordeeva, A.A. Yablokov, I.V. Rakut, V.O. Zbrozhek, L.S. Kuzmin, Microwave photon detection by an Al Josephson junction. Beilstein J. Nanotechnol. 11, 960–965 (2020)

    Article  Google Scholar 

  14. C. Guarcello, D. Valenti, B. Spagnolo, V. Pierro, G. Filatrella, Anomalous transport effects on switching currents of graphene-based Josephson junctions. Nanotechnology 28, 134001 (2017)

    Google Scholar 

  15. C. Guarcello, D. Valenti, B. Spagnolo, V. Pierro, G. Filatrella, Josephson-based threshold detector for Lévy-distributed current fluctuations. Phys. Rev. Appl. 11, 044078 (2019)

    Google Scholar 

  16. C. Guarcello, G. Filatrella, B. Spagnolo, V. Pierro, D. Valenti, Voltage drop across Josephson junctions for Lévy noise detection. Phys. Rev. Res. 2, 043332 (2020)

    Google Scholar 

  17. B.D. Josephson, Possible new effects in superconductive tunnelling. Phys. Lett. 1, 251 (1962)

    Article  Google Scholar 

  18. B.D. Josephson, The discovery of tunnelling supercurrents. Rev. Mod. Phys. 46, 251 (1974)

    Article  Google Scholar 

  19. G. Augello, D. Valenti, B. Spagnolo, Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction. Eur. Phys. J. B 78, 225 (2010)

    Article  Google Scholar 

  20. B. Spagnolo, P. Caldara, A. La Cognata, G. Augello, D. Valenti, A. Fiasconaro, A. Dubkov, G. Falci, Relaxation phenomena in classical and quantum systems. Acta Phys. Pol. B 43, 1169 (2012)

    Article  Google Scholar 

  21. C. Guarcello, D. Valenti, G. Augello, B. Spagnolo, The role of non-Gaussian sources in the transient dynamics of long Josephson junctions. Acta Phys. Pol. B 44, 997 (2013)

    Article  MathSciNet  Google Scholar 

  22. D. Valenti, C. Guarcello, B. Spagnolo, Switching times in long-overlap Josephson junctions subject to thermal fluctuations and non-Gaussian noise sources. Phys. Rev. B 89, 214510 (2014)

    Google Scholar 

  23. C. Guarcello, D. Valenti, A. Carollo, B. Spagnolo, Effects of Lévy noise on the dynamics of sine-Gordon solitons in long Josephson junctions. J. Stat. Mech.: Theory Exp. 054012(2016)

    Google Scholar 

  24. B. Spagnolo, D. Valenti, C. Guarcello, A. Carollo, D. Persano Adorno, S. Spezia, N. Pizzolato, B. Di Paola, Noise-induced effects in nonlinear relaxation of condensed matter systems. Chaos Solitons Fractals 81(Part B), 412 (2015)

    Google Scholar 

  25. C. Guarcello, D. Valenti, B. Spagnolo, Phase dynamics in graphene-based Josephson junctions in the presence of thermal and correlated fluctuations. Phys. Rev. B 92, 174519 (2015)

    Google Scholar 

  26. C. Guarcello, D. Valenti, A. Carollo, B. Spagnolo, Stabilization effects of dichotomous noise on the lifetime of the superconducting state in a long Josephson junction. Entropy 17, 2862 (2015)

    Article  Google Scholar 

  27. R. Parmentier, Fluxons in long Josephson junctions, in Solitons in Action. ed. by K. Lonngren, A.C. Scott (Academic Press, Cambridge, MA, USA, 1978), pp. 173–199

    Google Scholar 

  28. A. Ustinov, Solitons in Josephson junctions. Phys. D: Nonlinear Phenom. 123, 315 (1998)

    Article  Google Scholar 

  29. C. Guarcello, F. Giazotto, P. Solinas, Coherent diffraction of thermal currents in long Josephson tunnel junctions. Phys. Rev. B 94, 054522 (2016)

    Google Scholar 

  30. A. Barone, G. Paternó, Physics and Applications of the Josephson Effect (Wiley, New York, 1982)

    Book  Google Scholar 

  31. B. Spagnolo, C. Guarcello, L. Magazzú, A. Carollo, D. Persano Adorno, D. Valenti, Nonlinear relaxation phenomena in metastable condensed matter systems. Entropy 19 (2017)

    Google Scholar 

  32. A. Dubkov, B. Spagnolo, Fluct. Noise Lett. 5, L267 (2005)

    Google Scholar 

  33. D. Valenti, L. Schimansky-Geier, X. Sailer, B. Spagnolo, Eur. Phys. J. B Condens. Matter Complex Syst. 50, 199 (2006)

    Google Scholar 

  34. D. Valenti, L. Tranchina, M. Brai, A. Caruso, C. Cosentino, B. Spagnolo, Ecol. Model. 213, 449 (2008)

    Article  Google Scholar 

  35. D. Valenti, L. Magazzú, P. Caldara, B. Spagnolo, Phys. Rev. B 91, 235412 (2015)

    Google Scholar 

  36. G. Falci, A. La Cognata, M. Berritta, A. D’Arrigo, E. Paladino, B. Spagnolo, Phys. Rev. B 87, 214515 (2013)

    Google Scholar 

  37. P. Kadanoff, Phys. Today 54, 34 (2001)

    Article  Google Scholar 

  38. N. Scafetta, B.J. West, Phys. Rev. Lett. 90, 248701 (2003)

    Google Scholar 

  39. P. Barthelemy, J. Bertolotti, D.S. Wiersma, Nature 453, 495 (2008)

    Article  Google Scholar 

  40. S. Luryi, A. Subashiev, J. Geophys. Res. 21, 1250001 (2012)

    Google Scholar 

  41. A. Dubkov, B. Spagnolo, Eur. Phys. J. B Condens. Matter Complex Syst. 65, 361 (2008)

    Google Scholar 

  42. A. La Cognata, D. Valenti, A.A. Dubkov, B. Spagnolo, Phys. Rev. E 82, 011121 (2010)

    Google Scholar 

  43. A.A. Dubkov, B. Spagnolo, V.V. Uchaikin, Lévy flight superdiffusion: an introduction. Int. J. Bifurc. Chaos 18, 2649 (2008)

    Article  Google Scholar 

  44. V. Zaburdaev, S. Denisov, J. Klafter, Lévy walks. Rev. Mod. Phys. 87, 483 (2015)

    Article  Google Scholar 

  45. H.A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284 (1940)

    Article  MathSciNet  Google Scholar 

  46. H. Grabert, U. Weiss, Crossover from thermal hopping to quantum tunneling. Phys. Rev. Lett. 53, 1787 (1984)

    Article  Google Scholar 

  47. J.A. Blackburn, M. Cirillo, N. Grønbech-Jensen, A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures. Phys. Rev. B 85, 104501 (2012)

    Google Scholar 

  48. A.V. Chechkin, V.Y. Gonchar, J. Klafter, R. Metzler, Barrier crossing of a Lévy flight. Europhys. Lett. 72, 348 (2005)

    Article  MathSciNet  Google Scholar 

  49. A.V. Chechkin, O.Y. Sliusarenko, R. Metzler, J. Klafter, Barrier crossing driven by Lévy noise: universality and the role of noise intensity. Phys. Rev. E 75, 041101 (2007)

    Google Scholar 

  50. B. Dybiec, E. Gudowska-Nowak, P. Hänggi, Lévy-Brownian motion on finite intervals: mean first passage time analysis. Phys. Rev. E 73, 046104 (2006)

    Google Scholar 

  51. B. Dybiec, E. Gudowska-Nowak, P. Hänggi, Escape driven by \(\alpha \)-stable white noises. Phys. Rev. E 75, 021109 (2007)

    Google Scholar 

  52. A.A. Dubkov, A. La Cognata, B. Spagnolo, The problem of analytical calculation of barrier crossing characteristics for Lévy flights. J. Stat. Mech.: Theory Exp. 2009, P01002 (2009)

    Google Scholar 

  53. T.A. Fulton, L.N. Dunkleberger, Lifetime of the zero-voltage state in Josephson tunnel junctions. Phys. Rev. B 9, 4760 (1974)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy

    Claudio Guarcello

  2. INFN, Sezione di Napoli Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, 80126, Naples, Italy

    Claudio Guarcello & Vincenzo Pierro

  3. Department of Sciences and Technologies and Salerno Unit of CNISM, University of Sannio, Via Port’Arsa 11, 82100, Benevento, Italy

    Giovanni Filatrella

  4. Dipartimento di Fisica e Chimica “Emilio Segrè”, Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Viale delle Scienze, Edificio 18, 90128, Palermo, Italy

    Bernardo Spagnolo & Davide Valenti

  5. Radiophysics Department, Lobachevsky State University, 23 Gagarin Ave., 603950, Nizhny Novgorod, Russia

    Bernardo Spagnolo

  6. Department of Engineering, University of Sannio, Corso Garibaldi 107, 82100, Benevento, Italy

    Vincenzo Pierro

  7. CNR-IRIB, Consiglio Nazionale delle Ricerche - Istituto per la Ricerca e l’Innovazione Biomedica, Via Ugo La Malfa 153, 90146, Palermo, Italy

    Davide Valenti

Authors
  1. Claudio Guarcello
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  2. Giovanni Filatrella
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  3. Bernardo Spagnolo
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  4. Vincenzo Pierro
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Corresponding author

Correspondence to Claudio Guarcello .

Editor information

Editors and Affiliations

  1. ManLab, Technical University of Crete, Chania, Greece

    Christos H. Skiadas

  2. Department of Management Science and Technology, Hellenic Mediterranean University, Agios Nikolaos, Crete, Lasithi, Greece

    Yiannis Dimotikalis

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Guarcello, C., Filatrella, G., Spagnolo, B., Pierro, V., Valenti, D. (2021). Effects of Thermal and Lévy Noise Sources on the Switching Current Distributions of a Josephson Junction. In: Skiadas, C.H., Dimotikalis, Y. (eds) 13th Chaotic Modeling and Simulation International Conference. CHAOS 2020. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-70795-8_20

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