Skip to main content
SpringerLink
Log in

Parametric Amplifier and Oscillator Based on Josephson Junction Circuitry

  • Chapter
Principles and Methods of Quantum Information Technologies

Part of the book series: Lecture Notes in Physics ((LNP,volume 911))

Abstract

While the demand for low-noise amplification is ubiquitous, applications where the quantum-limited noise performance is indispensable are not very common. Microwave parametric amplifiers with near quantum-limited noise performance were first demonstrated more than 20 years ago. However, there had been little effort until recently to improve the performance or the ease of use of these amplifiers, partly because of a lack of any urgent motivation. The emergence of the field of quantum information processing in superconducting systems has changed this situation dramatically. The need to reliably read out the state of a given qubit using a very weak microwave probe within a very short time has led to renewed interest in these quantum-limited microwave amplifiers, which are already widely used as tools in this field. Here, we describe the quantum mechanical theory for one particular parametric amplifier design, called the flux-driven Josephson parametric amplifier, which we developed in 2008. The theory predicts the performance of this parametric amplifier, including its gain, bandwidth, and noise temperature. We also present the phase detection capability of this amplifier when it is operated with a pump power that is above the threshold, i.e., as a parametric phase-locked oscillator or parametron.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. H. Takahashi, in Advances in Communication Systems, ed. by A.V. Balakrishnan (Academic, New York, 1965), p. 227

    Google Scholar 

  2. C.M. Caves, Phys. Rev. D 26, 1817 (1982)

    Article  ADS  Google Scholar 

  3. A. Barone, G. Paterno, Physics and Applications of the Josephson Effect (Wiley, New York, 1982), chap. 11

    Book  Google Scholar 

  4. B. Yurke, P.G. Kaminsky, R.E. Miller, E.A. Whittaker, A.D. Smith, A.H. Silver, R.W. Simon, Phys. Rev. Lett. 60, 764 (1988)

    Article  ADS  Google Scholar 

  5. B. Yurke, L.R. Corruccini, P.G. Kaminsky, L.W. Rupp, A.D. Smith, A.H. Silver, R.W. Simon, E.A. Whittaker, Phys. Rev. A 39, 2519 (1989)

    Article  ADS  Google Scholar 

  6. R. Movshovich, B. Yurke, P.G. Kaminsky, A.D. Smith, A.H. Silver, R.W. Simon, M.V. Schneider, Phys. Rev. Lett. 65, 1419 (1990)

    Article  ADS  Google Scholar 

  7. Y. Nakamura, Y.A. Pashkin, J.S. Tsai, Nature 398, 786 (1999)

    Article  ADS  Google Scholar 

  8. A. Blais, R.S. Huang, A. Wallraff, S.M. Girvin, R.J. Schoelkopf, Phys. Rev. A 69, 062320 (2004)

    Article  ADS  Google Scholar 

  9. E.A. Tholén, A. Ergül, E.M. Doherty, F.M. Weber, F. Grégis, D.B. Haviland, Appl. Phys. Lett. 90, 253509 (2007)

    Article  ADS  Google Scholar 

  10. M.A. Castellanos-Beltran, K.W. Lehnert, Appl. Phys. Lett. 91, 083509 (2007)

    Article  ADS  Google Scholar 

  11. T. Yamamoto, K. Inomata, M. Watanabe, K. Matsuba, T. Miyazaki, W.D. Oliver, Y. Nakamura, J.S. Tsai, Appl. Phys. Lett. 93, 042510 (2008)

    Article  ADS  Google Scholar 

  12. N. Bergeal, R. Vijay, V.E. Manucharyan, I. Siddiqi, R.J. Schoelkopf, S.M. Girvin, M.H. Devoret, Nat. Phys. 6, 296 (2010)

    Article  Google Scholar 

  13. M.A. Castellanos-Beltran, K.D. Irwin, G.C. Hilton, L.R. Vale, K.W. Lehnert, Nat. Phys. 4, 928 (2008)

    Article  Google Scholar 

  14. J.D. Teufel, T. Donner, M.A. Castellanos-Beltran, J.W. Harlow, K.W. Lehnert, Nat. Nanotech. 4, 820 (2009)

    Article  ADS  Google Scholar 

  15. R. Vijay, D.H. Slichter, I. Siddiqi, Phys. Rev. Lett. 106, 110502 (2011)

    Article  ADS  Google Scholar 

  16. A. Wallraff, D.I. Schuster, A. Blais, L. Frunzio, R.S. Huang, J. Majer, S. Kumar, S.M. Girvin, R.J. Schoelkopf, Nature 431, 162 (2004)

    Article  ADS  Google Scholar 

  17. F. Mallet, M.A. Castellanos-Beltran, H.S. Ku, S. Glancy, E. Knill, K.D. Irwin, G.C. Hilton, L.R. Vale, K.W. Lehnert, Phys. Rev. Lett. 106, 220502 (2011)

    Article  ADS  Google Scholar 

  18. C. Eichler, D. Bozyigit, C. Lang, M. Baur, L. Steffen, J.M. Fink, S. Filipp, A. Wallraff, Phys. Rev. Lett. 107, 113601 (2011)

    Article  ADS  Google Scholar 

  19. E. Flurin, N. Roch, F. Mallet, M.H. Devoret, B. Huard, Phys. Rev. Lett. 109, 183901 (2012)

    Article  ADS  Google Scholar 

  20. E.P. Menzel, R. Di Candia, F. Deppe, P. Eder, L. Zhong, M. Ihmig, M. Haeberlein, A. Baust, E. Hoffmann, D. Ballester, K. Inomata, T. Yamamoto, Y. Nakamura, E. Solano, A. Marx, R. Gross, Phys. Rev. Lett. 109, 250502 (2012)

    Article  ADS  Google Scholar 

  21. A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations (Wiley-Interscience, New York, 1995)

    Book  Google Scholar 

  22. C.M. Wilson, T. Duty, M. Sandberg, F. Persson, V. Shumeiko, P. Delsing, Phys. Rev. Lett. 105, 233907 (2010)

    Article  ADS  Google Scholar 

  23. C.W. Wilson, T. Duty, P. Delsing, in Fluctuating Nonlinear Oscillators: From Nanomechanics to Quantum Superconducting Circuits, ed. by M. Dykman (Oxford University Press, Oxford, 2012), chap. 15

    Google Scholar 

  24. C.M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J.R. Johansson, T. Duty, F. Nori, P. Delsing, Nature 376, 479 (2011)

    Google Scholar 

  25. E. Goto, Proc. Inst. Radio Eng. 47, 1304 (1959)

    Google Scholar 

  26. L.S. Onyshkevych, W.F. Kosonocky, A.W. Lo, Trans. Inst. Radio Engrs. EC-8, 277 (1959)

    Google Scholar 

  27. Z.R. Lin, K. Inomata, K. Koshino, W.D. Oliver, Y. Nakamura, J.S. Tsai, T. Yamamoto, Nat. Commun. 5, 4480 (2014)

    ADS  Google Scholar 

  28. D.F. Walls, G.J. Milburn, Quantum Optics (Springer, Berlin/Tokyo, 1994)

    Book  MATH  Google Scholar 

  29. M. Wallquist, V.S. Shumeiko, G. Wendin, Phys. Rev. B 74, 224506 (2006)

    Article  ADS  Google Scholar 

  30. T. Ojanen, J. Salo, Phys. Rev. B 75, 184508 (2007)

    Article  ADS  Google Scholar 

  31. M. Hatridge, R. Vijay, D.H. Slichter, J. Clarke, I. Siddiqi, Phys. Rev. B 83, 134501 (2011)

    Article  ADS  Google Scholar 

  32. J.Y. Mutus, T.C. White, E. Jeffrey, D. Sank, R. Barends, J. Bochmann, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, J. Kelly, A. Megrant, C. Neill, P.J.J. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, I. Siddiqi, R. Vijay, A.N. Cleland, J.M. Martinis, Appl. Phys. Lett. 103, 122602 (2013)

    Article  ADS  Google Scholar 

  33. E. Jeffrey, D. Sank, J.Y. Mutus, T.C. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P.J.J. O’Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A.N. Cleland, J.M. Martinis, Phys. Rev. Lett. 112, 190504 (2014)

    Article  ADS  Google Scholar 

  34. Z.R. Lin, K. Inomata, W.D. Oliver, K. Koshino, Y. Nakamura, J.S. Tsai, T. Yamamoto, Appl. Phys. Lett. 103, 132602 (2013)

    Article  ADS  Google Scholar 

  35. L. Zhong, E.P. Menzel, R.D. Candia, P. Eder, M. Ihmig, A. Baust, M. Haeberlein, E. Hoffmann, K. Inomata, T. Yamamoto, Y. Nakamura, E. Solano, F. Deppe, A. Marx, R. Gross, New J. Phys. 15, 125013 (2013)

    Article  ADS  Google Scholar 

  36. B. Abdo, A. Kamal, M. Devoret, Phys. Rev. B 87, 014508 (2013)

    Article  ADS  Google Scholar 

  37. B. Yurke, in Quantum Squeezing, ed. by P.D. Drummond, Z. Ficek (Springer, Berlin/New York, 2004)

    Google Scholar 

  38. B. Yurke, E. Buks, J. Lightwave Tech. 24, 5054 (2006)

    Article  ADS  Google Scholar 

  39. J. Johansson, P. Nation, F. Nori, Comput. Phys. Commun. 184, 1234 (2013)

    Article  ADS  Google Scholar 

  40. K. Beer, Radio Electron. Eng. 25, 432 (1963)

    Article  Google Scholar 

  41. R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T.C. White, J. Mutus, A.G. Fowler, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A.N. Korotkov, A.N. Cleland, J.M. Martinis, Nature 508, 500 (2014)

    Article  ADS  Google Scholar 

  42. B.H. Eom, P.K. Day, H.G. LeDuc, J. Zmuidzinas, Nat. Phys. 8, 623 (2012)

    Article  Google Scholar 

  43. O. Yaakobi, L. Friedland, C. Macklin, I. Siddiqi, Phys. Rev. B 87, 144301 (2013)

    Article  ADS  Google Scholar 

  44. B. Abdo, K. Sliwa, L. Frunzio, M. Devoret, Phys. Rev. X 3, 031001 (2013)

    Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support of the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST). This work was also supported in part by the Project for Developing Innovation Systems of MEXT, MEXT KAKENHI (grant nos. 21102002 and 25400417), SCOPE (111507004) and the National Institute of Information and Communications Technology (NICT).

Author information

Authors and Affiliations

  1. NEC Smart Energy Research Laboratories, Tsukuba, Ibaraki, 305-8501, Japan

    T. Yamamoto

  2. College of Liberal Arts and Sciences, Tokyo Medical and Dental University, 2-8-30 Konodai, Ichikawa, Chiba, 272-0827, Japan

    K. Koshino

  3. Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo, 153-8904, Japan

    Y. Nakamura

  4. RIKEN Center for Emergent Matter Science (CEMS), 2-1 Hirosawa, Wako, Saitama, 351-0198, Japan

    Y. Nakamura

Authors
  1. T. Yamamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Koshino
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Nakamura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Yamamoto .

Editor information

Editors and Affiliations

  1. ImPACT Program, Council for Science Technology and Innovation, Tokyo, Japan

    Yoshihisa Yamamoto

  2. National Institute of Information and Communications Technology, Koganei, Tokyo, Japan

    Kouichi Semba

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Japan

About this chapter

Cite this chapter

Yamamoto, T., Koshino, K., Nakamura, Y. (2016). Parametric Amplifier and Oscillator Based on Josephson Junction Circuitry. In: Yamamoto, Y., Semba, K. (eds) Principles and Methods of Quantum Information Technologies. Lecture Notes in Physics, vol 911. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55756-2_23

Download citation

Publish with us

Policies and ethics

Search

Navigation