Quadripartite entanglement of microwave photons from separated resonators via concurrent parametric interactions in superconducting quantum circuits

  • Wen-Xue Zhong
  • Guang-Ling Cheng
  • Ai-Xi Chen
Regular Article


We present an alternative scheme for generating quadripartite continuous variable entanglement using the dispersion interactions of four separated resonators with a single driven superconducting qubit. We show that the cluster and Greenberger-Horne-Zeilinger (GHZ) entangled states of four output microwave photons can be created at the presence of quantum relaxations. The physical mechanism is proposed in the dressed-state representation of driving interaction. With the proper choice of the physical parameters, the concurrent parametric down-conversion interactions occur among four microwave modes, which are responsible for the four-mode entanglement generation. In practice, our scheme provides a useful approach for the scalable information processing in the solid-state system.


Quantum Optics 


  1. 1.
    S.L. Braunstein, P. van Loock, Rev. Mod. Phys. 77, 513 (2005)ADSCrossRefMATHGoogle Scholar
  2. 2.
    P. van Loock, S.L. Braunstein, Phys. Rev. Lett. 84, 3482 (2000)ADSCrossRefGoogle Scholar
  3. 3.
    J. Zhang, C.D. Xie, K.C. Peng, P. van Loock, Phys. Rev. A 77, 022316 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    J.T. Jing, J. Zhang, Y. Yan, F.G. Zhao, C.D. Xie, K.C. Peng, Phys. Rev. Lett. 90, 167903 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, P. van Loock, Phys. Rev. Lett. 91, 080404 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    X.L. Su, A.H. Tan, X.J. Jia, J. Zhang, C.D. Xie, K.C. Peng, Phys. Rev. Lett. 98, 070502 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    H.Y. Leng, J.F. Wang, Y.B. Yu, X.Q. Yu, P. Xu, Z.D. Xie, J.S. Zhao, S.N. Zhu, Phys. Rev. A 79, 032337 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    J.F. Wang, J.S. Zhao, H.Y. Leng, X.Q. Yu, Z.D. Xie, Y.L. Yin, P. Xu, S.N. Zhu, Opt. Commun. 282, 3729 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    S.L.W. Midgley, A.S. Bradley, O. Pfister, M.K. Olsen, Phys. Rev. A 81, 063834 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    J.F. Wang, J.T. Sheng, S.N. Zhu, M. Xiao, J. Opt. Soc. Am. B 30, 2130 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    Y.B. Yu, J.T. Sheng, M. Xiao, Phys. Rev. A 83, 012321 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    X.L. Su, Y.P. Zhao, S.H. Hao, X.J. Jia, C.D. Xie, K.C. Peng, Opt. Lett. 37, 5178 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    Y. Gu, G.Q. He, X.F. Wu, Phys. Rev. A 85, 052328 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    H.T. Tan, G.X. Li, Phys. Rev. A 84, 024301 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    Y. Wu, L. Deng, Opt. Lett. 29, 1144 (2004)ADSCrossRefGoogle Scholar
  16. 16.
    X.H. Yang, Y.Y. Zhou, M. Xiao, Phys. Rev. A 85, 052307 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    Y. Wu, M.G. Payne, E.W. Hagley, L. Deng, Phys. Rev. A 69, 063803 (2004)ADSCrossRefGoogle Scholar
  18. 18.
    H. Xiong, M.O. Scully, M.S. Zubairy, Phys. Rev. Lett. 94, 023601 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    X.M. Hu, J.H. Zou, Phys. Rev. A 78, 045801 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    S. Pielawa, G. Morigi, D. Vitali, L. Davidovich, Phys. Rev. Lett. 98, 240401 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    X.Y. Lü, P. Huang, W.X. Yang, X.X. Yang, Phys. Rev. A 80, 032305 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    G.L. Cheng, A.X. Chen, W.X. Zhong, Opt. Commun. 284, 4028 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    R. Guzmán, J.C. Retamal, E. Solano, N. Zagury, Phys. Rev. Lett. 96, 010502 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    X.M. Hu, X. Li, J. Phys. B 43, 055502 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    X. Liang, X.M. Hu, C. He, Phys. Rev. A 85, 032329 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    X. Li, X.M. Hu, J. Phys. B 45, 135503 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    L. Tian, Phys. Rev. Lett. 110, 233602 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    Y. Makhlin, G. Schön, A. Shnirman, Rev. Mod. Phys. 73, 357 (2001)ADSCrossRefGoogle Scholar
  29. 29.
    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)ADSCrossRefGoogle Scholar
  30. 30.
    O. Astafiev, A.M. Zagoskin, A.A. Abdumalikov Jr., Y.A. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, J.S. Tsai, Science 327, 840 (2010)ADSCrossRefGoogle Scholar
  31. 31.
    W.R. Kelly, Z. Dutton, J. Schlafer, B. Mookerji, T.A. Ohki, J.S. Kline, D.P. Pappas, Phys. Rev. Lett. 104, 163601 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    P.M. Leung, B.C. Sanders, Phys. Rev. Lett. 109, 253603 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    S.L. Zhu, Z.D. Wang, P. Zanardi, Phys. Rev. Lett. 94, 100502 (2005)ADSCrossRefMathSciNetGoogle Scholar
  34. 34.
    L. DiCarlo, M.D. Reed, L. Sun, B.R. Johnson, J.M. Chow, J.M. Gambetta, L. Frunzio, S.M. Girvin, M.H. Devoret, R.J. Schoelkopf, Nature 467, 574 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    A.F. Obada, H.A. Hessian, A.A. Mohamed, A.H. Homid, J. Opt. Soc. Am. B 30, 1178 (2013)ADSCrossRefGoogle Scholar
  36. 36.
    F.W. Strauch, K. Jacobs, R.W. Simmonds, Phys. Rev. Lett. 105, 050501 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    F.W. Strauch, D. Onyango, K. Jacobs, R.W. Simmonds, Phys. Rev. A 85, 022335 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    H. Wang, M. Mariantoni, R.C. Bialczak, M. Lenander, E. Lucero, M. Neeley, A.D. O’Connell, D. Sank, M. Weides, J. Wenner, T. Yamamoto, Y. Yin, J. Zhao, J.M. Martinis, A.N. Cleland, Phys. Rev. Lett. 106, 060401 (2011)ADSCrossRefGoogle Scholar
  39. 39.
    C.P. Yang, Q.P. Su, S.Y. Han, Phys. Rev. A 86, 022329 (2012)ADSCrossRefGoogle Scholar
  40. 40.
    C.P. Yang, Q.P. Su, S.B. Zheng, S.Y. Han, Phys. Rev. A 87, 022320 (2013)ADSCrossRefGoogle Scholar
  41. 41.
    D.F.V. James, Fortschr. Phys. 48, 823 (2000)CrossRefGoogle Scholar
  42. 42.
    F. Marquardt, Phys. Rev. B 76, 205416 (2007)ADSCrossRefGoogle Scholar
  43. 43.
    K. Moon, S.M. Girvin, Phys. Rev. Lett. 95, 140504 (2005)ADSCrossRefGoogle Scholar
  44. 44.
    W.Y. Huo, G.L. Long, New J. Phys. 10, 013026 (2008)ADSCrossRefGoogle Scholar
  45. 45.
    P.B. Stiffell, M.J. Everitt, T.D. Clark, C.J. Harland, J.F. Ralph, Phys. Rev. B 72, 014508 (2005)ADSCrossRefGoogle Scholar
  46. 46.
    G.L. Cheng, A.X. Chen, W.X. Zhong, J. Opt. Soc. Am. B 30, 2875 (2013)ADSCrossRefGoogle Scholar
  47. 47.
    M. Sargent III, M.O. Scully, W.E. Lamb Jr., Laser Physics (Addison-Wesley, 1974)Google Scholar
  48. 48.
    P. van Loock, A. Furusawa, Phys. Rev. A 67, 052315 (2003)ADSCrossRefGoogle Scholar
  49. 49.
    H. Wang, M. Hofheinz, M. Ansmann, R.C. Bialczak, E. Lucero, M. Neeley, A.D. O’Connell, D. Sank, J. Wenner, A.N. Cleland, J.M. Martinis, Phys. Rev. Lett. 101, 240401 (2008)ADSCrossRefGoogle Scholar
  50. 50.
    A. Megrant, C. Neill, R. Barends, B. Chiaro, Y. Chen, L. Feigl, J. Kelly, E. Lucero, M. Mariantoni, P.J.J. O’Malley, D. Sank, A. Vainsencher, J. Wenner, T.C. White, Y. Yin, J. Zhao, C.J. Palmstrøm, J.M. Martinis, A.N. Cleland, Appl. Phys. Lett. 100, 113510 (2012)ADSCrossRefGoogle Scholar
  51. 51.
    M. Baur, S. Filipp, R. Bianchetti, J.M. Fink, M. Göppl, L. Steffen, P.J. Leek, A. Blais, A. Wallraff, Phys. Rev. Lett. 102, 243602 (2009)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Applied PhysicsEast China Jiaotong UniversityNanchangP.R. China

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