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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
H. Takahashi, in Advances in Communication Systems, ed. by A.V. Balakrishnan (Academic, New York, 1965), p. 227
C.M. Caves, Phys. Rev. D 26, 1817 (1982)
A. Barone, G. Paterno, Physics and Applications of the Josephson Effect (Wiley, New York, 1982), chap. 11
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)
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)
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)
Y. Nakamura, Y.A. Pashkin, J.S. Tsai, Nature 398, 786 (1999)
A. Blais, R.S. Huang, A. Wallraff, S.M. Girvin, R.J. Schoelkopf, Phys. Rev. A 69, 062320 (2004)
E.A. Tholén, A. Ergül, E.M. Doherty, F.M. Weber, F. Grégis, D.B. Haviland, Appl. Phys. Lett. 90, 253509 (2007)
M.A. Castellanos-Beltran, K.W. Lehnert, Appl. Phys. Lett. 91, 083509 (2007)
T. Yamamoto, K. Inomata, M. Watanabe, K. Matsuba, T. Miyazaki, W.D. Oliver, Y. Nakamura, J.S. Tsai, Appl. Phys. Lett. 93, 042510 (2008)
N. Bergeal, R. Vijay, V.E. Manucharyan, I. Siddiqi, R.J. Schoelkopf, S.M. Girvin, M.H. Devoret, Nat. Phys. 6, 296 (2010)
M.A. Castellanos-Beltran, K.D. Irwin, G.C. Hilton, L.R. Vale, K.W. Lehnert, Nat. Phys. 4, 928 (2008)
J.D. Teufel, T. Donner, M.A. Castellanos-Beltran, J.W. Harlow, K.W. Lehnert, Nat. Nanotech. 4, 820 (2009)
R. Vijay, D.H. Slichter, I. Siddiqi, Phys. Rev. Lett. 106, 110502 (2011)
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)
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)
C. Eichler, D. Bozyigit, C. Lang, M. Baur, L. Steffen, J.M. Fink, S. Filipp, A. Wallraff, Phys. Rev. Lett. 107, 113601 (2011)
E. Flurin, N. Roch, F. Mallet, M.H. Devoret, B. Huard, Phys. Rev. Lett. 109, 183901 (2012)
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)
A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations (Wiley-Interscience, New York, 1995)
C.M. Wilson, T. Duty, M. Sandberg, F. Persson, V. Shumeiko, P. Delsing, Phys. Rev. Lett. 105, 233907 (2010)
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
C.M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J.R. Johansson, T. Duty, F. Nori, P. Delsing, Nature 376, 479 (2011)
E. Goto, Proc. Inst. Radio Eng. 47, 1304 (1959)
L.S. Onyshkevych, W.F. Kosonocky, A.W. Lo, Trans. Inst. Radio Engrs. EC-8, 277 (1959)
Z.R. Lin, K. Inomata, K. Koshino, W.D. Oliver, Y. Nakamura, J.S. Tsai, T. Yamamoto, Nat. Commun. 5, 4480 (2014)
D.F. Walls, G.J. Milburn, Quantum Optics (Springer, Berlin/Tokyo, 1994)
M. Wallquist, V.S. Shumeiko, G. Wendin, Phys. Rev. B 74, 224506 (2006)
T. Ojanen, J. Salo, Phys. Rev. B 75, 184508 (2007)
M. Hatridge, R. Vijay, D.H. Slichter, J. Clarke, I. Siddiqi, Phys. Rev. B 83, 134501 (2011)
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)
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)
Z.R. Lin, K. Inomata, W.D. Oliver, K. Koshino, Y. Nakamura, J.S. Tsai, T. Yamamoto, Appl. Phys. Lett. 103, 132602 (2013)
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)
B. Abdo, A. Kamal, M. Devoret, Phys. Rev. B 87, 014508 (2013)
B. Yurke, in Quantum Squeezing, ed. by P.D. Drummond, Z. Ficek (Springer, Berlin/New York, 2004)
B. Yurke, E. Buks, J. Lightwave Tech. 24, 5054 (2006)
J. Johansson, P. Nation, F. Nori, Comput. Phys. Commun. 184, 1234 (2013)
K. Beer, Radio Electron. Eng. 25, 432 (1963)
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)
B.H. Eom, P.K. Day, H.G. LeDuc, J. Zmuidzinas, Nat. Phys. 8, 623 (2012)
O. Yaakobi, L. Friedland, C. Macklin, I. Siddiqi, Phys. Rev. B 87, 144301 (2013)
B. Abdo, K. Sliwa, L. Frunzio, M. Devoret, Phys. Rev. X 3, 031001 (2013)
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
Corresponding author
Editor information
Editors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-4-431-55756-2_23
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55755-5
Online ISBN: 978-4-431-55756-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)