No Access Submitted: 27 October 2010 Accepted: 09 March 2011 Published Online: 12 May 2011
Journal of Applied Physics 109, 093915 (2011); https://doi.org/10.1063/1.3581139
We have studied both theoretically and experimentally how an LC series circuit connected in parallel to a Josephson junction influences the Josephson dynamics. The presence of the shell circuit introduces two energy scales, which in specific cases, can strongly differ from the plasma frequency of the isolated junction. Josephson junctions were manufactured using the Nb/Al-AlOx/Nb fabrication technology with various on-chip LC shunt circuits. Spectroscopic measurements in the quantum limit show excellent agreement with theory taking into account the shunt inductance and capacitance in the resistively and capacitively shunted junction model. The results clearly show that the dynamics of the system are two-dimensional, resulting in two resonant modes of the system. These findings have important implications for the design and operation of Josephson junction based quantum bits.
This work was partly supported by the Deutsche Forschungsgemeinschaft Center for Functional Nanostructures (Project No. B3.4), the Swedish Research Council (VR), EU STREP project MIDAS, and the Knut and Alice Wallenberg Foundation. F.L. was supported by a grant from the Knut and Alice Wallenberg Foundation. Furthermore, we would like to thank M. Birk for help with inductor simulation, D. Bruch for the design of the printed circuit board, and J. Czolk and T. Wienhold for help with LC circuit characterization.
  1. 1. T. van Duzer, Principles of Superconductive Devices and Circuits, 2nd ed. (Prentice Hall, Upper Saddle River, NJ, 1999). Google Scholar
  2. 2. Y. Makhlin, G. Schön, and A. Shnirman, Rev. Mod. Phys. 73, 357 (2001). https://doi.org/10.1103/RevModPhys.73.357 , Google ScholarCrossref
  3. 3. W. C. Stewart, Appl. Phys. Lett. 12, 277 (1968). https://doi.org/10.1063/1.1651991 , Google ScholarScitation, ISI
  4. 4. D. E. McCumber, J. Appl. Phys. 39, 3113 (1968). https://doi.org/10.1063/1.1656743 , Google ScholarScitation, ISI
  5. 5. C. C. Tsuei and J. R. Kirtley, Rev. Mod. Phys. 72, 969 (2000). https://doi.org/10.1103/RevModPhys.72.969 , Google ScholarCrossref
  6. 6. T. Bauch, T. Lindström, F. Tafuri, G. Rotoli, P. Delsing, T. Claeson and F. Lombardi, Science 311, 57 (2006). https://doi.org/10.1126/science.1120793 , Google ScholarCrossref
  7. 7. G. Rotoli, T. Bauch, T. Lindström, D. Stornaiuolo, F. Tafuri, and F. Lombardi, Phys. Rev. B 75, 144501 (2007). https://doi.org/10.1103/PhysRevB.75.144501 , Google ScholarCrossref
  8. 8. M. Steffen, M. Ansmann, R. McDermott, N. Katz, R. C. Bialczak, E. Lucero, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, Phys. Rev. Lett. 97, 050502 (2006). https://doi.org/10.1103/PhysRevLett.97.050502 , Google ScholarCrossref
  9. 9. A. Lupascu, C. J. M. Verwijs, R. N. Schouten, C. J. P. M. Harmans, and J. E. Mooij, Phys. Rev. Lett. 93, 177006 (2004). https://doi.org/10.1103/PhysRevLett.93.177006 , Google ScholarCrossref
  10. 10. A. J. Berkley, H. Xu, M. A. Gubrud, R. C. Ramos, J. R. Anderson, C. J. Lobb, and F. C. Wellstood, Phys. Rev. B 68, 060502 (2003). https://doi.org/10.1103/PhysRevB.68.060502 , Google ScholarCrossref
  11. 11. J. Claudon, F. Balestro, F. K. J. Hekking, and O. Buisson, Phys. Rev. Lett. 93, 187003 (2004). https://doi.org/10.1103/PhysRevLett.93.187003 , Google ScholarCrossref
  12. 12. M. Tinkham, Introduction to Superconductivity, 2nd ed. (McGraw-Hill, New York, 2004). Google Scholar
  13. 13. A. O. Caldeira and A. J. Leggett, Phys. Rev. Lett. 46, 211 (1981). https://doi.org/10.1103/PhysRevLett.46.211 , Google ScholarCrossref
  14. 14. M. H. Devoret, D. Esteve, C. Urbina, J. Martinis, A. Creland, and J. Clarke, in Quantum Tunneling in Condensed Media, edited by Y. Kagan and A. J. Leggett (North-Holland, Amsterdam, 1992). Google Scholar
  15. 15. V. Ambegaokar and A. Baratoff, Phys. Rev. Lett. 10, 486 (1963). https://doi.org/10.1103/PhysRevLett.10.486 , Google ScholarCrossref
  16. 16. Sonnet Software Inc., 1020 Seventh North Street, Suite 210, Liverpool, NY 13088, USA . Google Scholar
  17. 17. T. Bauch, F. Lombardi, F. Tafuri, A. Barone, G. Rotoli, P. Delsing, and T. Claeson, Phys. Rev. Lett. 94, 087003 (2005). https://doi.org/10.1103/PhysRevLett.94.087003 , Google ScholarCrossref
  18. 18. A. Wallraff, T. Duty, A. Lukashenko, and A. V. Ustinov, Phys. Rev. Lett. 90, 037003 (2003). https://doi.org/10.1103/PhysRevLett.90.037003 , Google ScholarCrossref
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