SpringerLink
Log in

Analysis, FPGA implementation of a Josephson junction circuit with topologically nontrivial barrier and its application to ring-based dual entropy core true random number generator

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

The analysis and field programmable gate arrays (FPGA) implementation of a resistive-capacitive-inductive shunted Josephson junction (RCLSJJ) circuit with topologically nontrivial barrier (TNB) are investigated in this paper. The stability analysis of the equilibrium points reveals the presence of a Pitchfork bifurcation. RCLSJJ circuit with TNB can change the spiking, bursting and relaxation oscillations to an excitable mode. The numerical simulations results also point out the existence of periodic attractors and different shapes of hidden chaotic attractors in RCLSJJ circuit with TNB. The FPGA of RCLSJJ circuit with TNB is implemented to ascertain the numerical simulations results. Finally, the dual entropy core (DEC) true random number generator (TRNG) application using Dormand–Prince based on RCLSJJ circuit with TNB and ring oscillators is implemented on FPGA. By synthesizing DEC TRNG for **linx XC7VX485T-2-FFG1761 FPGA chip, 1 Mbit number stream obtained from the design is analyzed using NIST-800-22 test suite and this bit stream acquired from the proposed structure is successfully passed all of the randomness tests.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. J.M. Martinis, M.H. Devoret, J. Clarke, Experimental tests for the quantum behavior of a macroscopic degree of freedom: the phase difference across a Josephson junction. Phys. Rev. B 35, 4682–4698 (1987)

    ADS  Google Scholar 

  2. J. Clarke, N.N. Cleland, M.H. Devoret, D. Esteve, J.M. Martinis, Quantum mechanics of a macroscopic variable: the phase difference of a Josephson junction. Science 239, 992–997 (1988)

    ADS  Google Scholar 

  3. M. Machida, T. Koyama, Localized rotating-modes in capacitively coupled intrinsic Josephson junctions: systematic study of branching structure and collective dynamical instability. Phys. Rev. B 70, 024523–024528 (2004)

    ADS  Google Scholar 

  4. Y.M. Shukrinov, F. Mahfouzi, P. Seidel, Equidistance of branch structure in capacitively coupled Josephson junctions model with diffusion current. Phys. C 449–453, 62–66 (2006)

    ADS  Google Scholar 

  5. M. Suzuki, M. Hayashi, H. Ebisawa, Nonlinear dynamics and resistive transition in intrinsic Josephson junctions. J. Phys. Chem. Solid 69, 3253–3256 (2008)

    ADS  Google Scholar 

  6. R.N. Chitra, V.C. Kuriakose, Phase synchronization in an array of driven Josephson junctions. Chaos 18, 013125–013130 (2008)

    ADS  MATH  Google Scholar 

  7. E.N. Pozzo, D. Domınguez, Fidelity and quantum chaos in the mesoscopic device for the Josephson flux qubit. Phys. Rev. Lett. 98, 057006–057009 (2007)

    ADS  Google Scholar 

  8. K. Inomata, S. Sato, K. Nakajima, A. Tanaka, H.B. Wang, M. Nagao, H. Hatano, S. Kawabata, Macroscopic quantum tunneling in a d-Wave HighT\(_{C}\) Bi\(_{2}\)Sr\(_{2}\)CaCu2O\(_{8+\delta }\) superconductor. Phys. Rev. Lett. 95, 107005–107008 (2005)

    ADS  Google Scholar 

  9. M. Machida, T. Kano, S. Yamada, M. Okumora, T. Imamura, T. Koyama, Quantum effects on capacitively-coupled intrinsic Josephson junctions. J. Phys. Chem. Solids 69, 3221–3224 (2008)

    ADS  Google Scholar 

  10. T. Koyama, M. Machida, Effects of capacitive coupling on the escape rate in Intrinsic Josephson junction stacks. J. Phys. Chem. Solids 69, 3232–3235 (2008)

    ADS  Google Scholar 

  11. M.P. Kennedy, R. Rovatti, G. Setti, B. Raton, Chaotic Electronics in Telecommunications (CRC, Boca Raton, 2000)

    Google Scholar 

  12. T. Sugiura, Y. Yamanashi, N. Yoshikawa, Demonstration of 30 Gbit/s generation of superconductive true random number generator. IEEE Trans. Appl. Supercond. 21, 843–846 (2011)

    ADS  Google Scholar 

  13. A. Uchida, P. Davis, S. Itaya, Generation of information theoretic secure keys using a chaotic semiconductor laser. Appl. Phys. Lett. 83, 3213–3215 (2003)

    ADS  Google Scholar 

  14. R.L. Kautz, Chaotic states of RF-biased Josephson junctions. J. Appl. Phys. 52, 6241–6246 (1981)

    ADS  Google Scholar 

  15. S.K. Dana, Spiking and bursting in Josephson junction. IEEE Trans. Circuits Syst. II Express Briefs 53, 1031–1034 (2006)

    Google Scholar 

  16. A. Mishra, S. Ghosh, S.K. Dana, T. Kapitaniak, C. Hens, Neuron-like spiking and bursting in Josephson junctions: a review. Chaos 31, 052101–052108 (2021)

    ADS  MathSciNet  Google Scholar 

  17. C. Hens, P. Pal, S.K. Dana, Bursting dynamics in a population of oscillatory and excitable Josephson junctions. Phys. Rev. E 92, 022915–022918 (2015)

    ADS  MathSciNet  Google Scholar 

  18. S.K. Dana, D.C. Sengupta, K.D. Edoh, Chaotic dynamics in Josephson Junction. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48, 990–996 (2001)

    Google Scholar 

  19. C.B. Whan, C.J. Lobb, Complex dynamical behavior in RCL-shunted Josephson tunnel junctions. Phys. Rev. E 53, 405–413 (1996)

    ADS  Google Scholar 

  20. A.B. Cawthorne, C.B. Whan, C.J. Lobb, Complex dynamics of resistively and inductively shunted Josephson junctions. J. Appl. Phys. 84, 1126–1132 (1998)

    ADS  Google Scholar 

  21. S.T. Kingni, G.F. Kuiate, R. Kengne, R. Tchitnga, P. Woafo, Analysis of a no equilibrium linear resistive-capacitive-inductance shunted junction model, dynamics, synchronization and application to digital cryptography in its fractional-order form. Complexity 2017, Article ID 4107358 (2017). https://doi.org/10.1155/2017/4107358

    Article  MathSciNet  MATH  Google Scholar 

  22. U.E. Vincent, A. Ucar, J.A. Laoye, S.O. Kareem, Control and synchronization of chaos in RCL-shunted Josephson junction using backstep** design. Phys. C 468, 374–382 (2008)

    ADS  Google Scholar 

  23. A.N. Njah, K.S. Ojo, G.A. Adebayo, A.O. Obawole, Generalized control and synchronization of chaos in RCL-shunted Josephson junction using backstep** design. Phys. C 470, 558–564 (2010)

    ADS  Google Scholar 

  24. S.K. Dana, P.K. Roy, G.C. Sethia, A. Sen, D.C. Sengupta, Taming of chaos and synchronisation in RCL-shunted Josephson junctions by external forcing. In: IEEE Proc. Circuits, Devices and Systems, vol. 153, pp. 453–460 (2006)

  25. E. Il’ichev, M. Grajcar, R. Hlubina, R.P.J. IJsselsteijn, H.E. Hoenig, H.-G. Meyer, A. Golubov, M.H.S. Amin, A.M. Zagoskin, A.N. Omelyanchouk, et al.: Anomalous periodicity of the current phase relationship of grain-boundary Josephson junctions in high Tc superconductors. Phys. Rev. Lett. 86, 5369–5373 (2001)

  26. G. Testa, E. Sarnelli, A. Monaco, E. Esposito, M. Ejrnaes, D.-J. Kang, S.H. Mennema, E.J. Tarte, M.G. Blamire, A class of high Tc YBa2Cu3O7\(-\)x grain boundary junctions with high-TcRn products. Phys. Rev. B. 71, 7–9 (2005)

    Google Scholar 

  27. M. Canturk, I. Askerzade, Numerical study of I–V characteristics of externally shunted Josephson junctions with unharmonic current-phase relation. IEEE Trans. Appl. Supercond. 22, 1400106–1400111 (2012)

    ADS  Google Scholar 

  28. M. Canturk, I. Askerzade, Numerical study Josephson junction qubits with an unharmonic current phase relation. IEEE Trans. Appl. Supercond. 21, 3541–3544 (2011)

    ADS  Google Scholar 

  29. S. Yu Barash, Interfacial pair breaking and planar weak links with an unharrnonic current-phase relation. JETP Lett. 100, 205–215 (2014)

    Google Scholar 

  30. S.T. Kingni, G. Fautso Kuiate, V. Kamdoum Tamba, A.V. Monwanou, J. Bio Chabi, Analysis of a fractal Josephson junction with unharmonic current-phase relation. J. Supercond. Novel Magn. 32, 2295–2301 (2019)

  31. M. Canturk, I.N. Askerzade, Numerical study Josephson junction qubits with an unharmonic current phase relation. IEEE Trans. Appl. Supercond. 21, 3541–3544 (2011)

    ADS  Google Scholar 

  32. M. Canturk, I. Askerzade, Chaotic dynamics of externally shunted Josephson junction with unharmonic CPR. J. Supercond. Novel Magn. 26, 839–843 (2013)

    Google Scholar 

  33. S. T. Kingni, K. Rajagopal, S. Çiçek, A. Cheukem, V. Kamdoum Tamba and J. G. Fautso Kuiate, Dynamical analysis, FPGA implementation and its application to chaos based random number generator of a fractal Josephson junction with unharmonic current-phase relation. Eur. Phys. J. B 93, 44–55 (2020)

  34. L. Fu, C.L. Kane, Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407–096411 (2008)

    ADS  Google Scholar 

  35. Y. Tanaka, T. Yokoyama, N. Nagaosa, Manipulation of the majorana fermion, Andreev reflection and Josephson current on topological insulators. Phys. Rev. Lett. 103, 107002–107005 (2009)

    ADS  Google Scholar 

  36. M. Veldhorst, C.G. Molenaar, C.J.M. Verwijs, H. Hilgenkamp, A. Brinkman, Optimizing the Majorana character of SQUIDs with topologically nontrivial barriers. Phys. Rev. B 86, 024509–024513 (2012)

    ADS  Google Scholar 

  37. I.R. Rahmonov, Yu.M. Shukrinov, R. Dawood, H. El Samman, Determination of Cooper pairs and Majorana fermions currents ratio in dc SQUID with topologically nontrivial barriers. Low Temp. Phys. 43, 824–828 (2017)

  38. I.N. Askerzade, Effects of thermal fluctuations on dynamics of Josephson junction with unconventional current-phase relation. J. Supercond. Novel Magn. 32, 3149–3154 (2019)

    Google Scholar 

  39. M.Z. Hasan, C.L. Kane, Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010)

    ADS  Google Scholar 

  40. L. Fu, C.L. Kane, Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction. Phys. Rev. B 79, 161408(R)-161411(R) (2009)

    ADS  Google Scholar 

  41. S.T. Kingni, A. Cheukem, A. Chéagé Chamgoué, F. Togue Kamga, Analysis of Josephson junction with topologically nontrivial barrier. Eur. Phys. J. B 93, 143–147 (2020)

  42. M. Tuna, A. Karthikeyan, K. Rajagopal, M. Alcin, I. Koyuncu, Hyperjerk multiscroll oscillators with megastability: analysis, FPGA implementation and a novel ANN-ring-based true random number generator. AEU Int. J. Electron. Commun. 112, 152941 (2019)

    Google Scholar 

  43. M. Alcin, I. Koyuncu, M. Tuna, M. Varan, I. Pehlivan, A novel high speed Artificial Neural Network-based chaotic true random number generator on field programmable gate array. Int. J. Circuit Theory Appl. 47, 365–378 (2019)

    Google Scholar 

  44. A. Akgul, C. Li, I. Pehlivan, Amplitude control analysis of a four-wing chaotic attractor, its electronic circuit designs and microcontroller-based random number generator. J. Circuits Syst. Comput. 26, 1750190 (2017)

    Google Scholar 

  45. I. Koyuncu, M. Tuna, I. Pehlivan, C.B. Fidan, M. Alçın, Design, FPGA implementation and statistical analysis of chaos-ring based dual entropy core true random number generator. Analog. Integr. Circ. Sig. Process. 102, 445–456 (2020)

    Google Scholar 

  46. M. Alçın, I. Pehlivan, I. Koyuncu, Hardware design and implementation of a novel ANN-based chaotic generator in FPGA. Optik 127, 5500–5505 (2016)

    ADS  Google Scholar 

  47. P. Prakash, K. Rajagopal, I. Koyuncu, J.P. Singh, M. Alcin, B.K. Roy, M. Tuna, A novel simple 4-D hyperchaotic system with a saddle-point index-2 equilibrium point and multistability: design and FPGA-based applications. Circuits Syst. Signal Process. 39, 4259–4280 (2020)

    Google Scholar 

  48. E. Tlelo-Cuautle, J.J. Rangel-Magdaleno, A.D. Pano-Azucena, P.J. Obeso-Rodelo, J.C. Nunez-Perez, FPGA realization of multi-scroll chaotic oscillators. Commun. Nonlinear Sci. Numer. Simul. 27, 66–80 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  49. E. Dong, Z. Liang, S. Du, Z. Chen, Topological horseshoe analysis on a four-wing chaotic attractor and its FPGA implement. Nonlinear Dyn. 83, 623–630 (2016)

    MathSciNet  Google Scholar 

  50. K. Rajagopal, A. Karthikeyan, A.K. Srinivasan, FPGA implementation of novel fractional-order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization. Nonlinear Dyn. 87, 2281–2304 (2017)

    Google Scholar 

Download references

Acknowledgements

This work is partially funded by the Center for Nonlinear Systems, Chennai Institute of Technology, India via funding number CIT/CNS/2021/RD/064. A.A.O. is grateful to Prof. Alidou Mohamadou (University of Maroua, Cameroon) and Prof. Betchewe Gambo (University of Maroua, Cameroon) for their valuable teachings and fruitful advices.

Author information

Authors and Affiliations

  1. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, 600069, India

    Balamurali Ramakrishnan & Karthikeyan Rajagopal

  2. Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon

    Alhadji Abba Oumate

  3. Department of Electrical, Technical Sciences Vocational School, Kirklareli University, Harmanlik Mevkii, 39100, Kirklareli, Turkey

    Murat Tuna

  4. Department of Electrical Electronics Engineering, Technology Faculty, Afyon Kocatepe University, ANS Campus, 03200, Afyonkarahisar, Turkey

    İsmail Koyuncu

  5. Department of Mechanical, Petroleum and Gas Engineering, Faculty of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon

    Sifeu Takougang Kingni

Authors
  1. Balamurali Ramakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alhadji Abba Oumate
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Murat Tuna
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. İsmail Koyuncu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sifeu Takougang Kingni
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Karthikeyan Rajagopal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sifeu Takougang Kingni.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramakrishnan, B., Oumate, A.A., Tuna, M. et al. Analysis, FPGA implementation of a Josephson junction circuit with topologically nontrivial barrier and its application to ring-based dual entropy core true random number generator. Eur. Phys. J. Spec. Top. 231, 1049–1059 (2022). https://doi.org/10.1140/epjs/s11734-021-00324-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00324-5

Search

Navigation