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Pseudo PT symmetric lattice

  • Cem YuceEmail author
Regular Article

Abstract

We study pseudo \(\mathcal{P}\mathcal{T}\)symmetry for a tight binding lattice with a general form of the modulation. Using high-frequency Floquet method, we show that the critical non-Hermitian degree for the reality of the spectrum can be manipulated by varying the parameters of the modulation. We study the effect of periodical and quasi-periodical nature of the modulation on the pseudo \(\mathcal{P}\mathcal{T}\) symmetry.

Keywords

Quantum Optics 

References

  1. 1.
    C.M. Bender, S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    C.E. Ruter, K.G. Makris, R. El-Ganainy, D.N. Christodoulides, M. Segev, D. Kip, Nat. Phys. 6, 192 (2010)CrossRefGoogle Scholar
  3. 3.
    A. Guo, G.J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G.A. Siviloglou, D.N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    A. Regensburger, C. Bersch, M.A. Miri, G. Onishchukov, D.N. Christodoulides, U. Peschel, Nature 488, 167 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    K.G. Makris, R. El-Ganainy, D.N. Christodoulides, Z.H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    J. Ctyroky, V. Kuzmiak, S. Eyderman, Optics Express 18, 21585 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    S. Longhi, Phys. Rev. Lett. 103, 123601 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, D.N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    A.E. Miroshnichenko, B.A. Malomed, Yu. S. Kivshar, Phys. Rev. A 84, 012123 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    C.T. West, T. Kottos, T. Prosen, Phys. Rev. Lett. 104, 054102 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    O. Bendix, R. Fleischmann, T. Kottos, B. Shapiro, J. Phys. A 43 265305 (2010)ADSCrossRefMathSciNetGoogle Scholar
  12. 12.
    X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Y.S. Kivshar, C. Lee, Phys. Rev. Lett. 110, 243902 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    X. Lian, H. Zhong, Q. Xie, X. Zhou, Y. Wu, W. Liao, Eur. Phys. J. D 68, 189 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    A.A. Sukhorukov, S.V. Dmitriev, S.V. Suchkov, Yu.S. Kivshar, Opt. Lett. 37, 2148 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    O. Bendix, R. Fleischmann, T. Kottos, B. Shapiro, Phys. Rev. Lett. 103, 030402 (2009)ADSCrossRefMathSciNetGoogle Scholar
  16. 16.
    S. Longhi, Phys. Rev. A 88, 052102 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    C. Yuce, Phys. Lett. A 378, 2024 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    Y.N. Joglekar, D. Scott, M. Babbey, A. Saxena, Phys. Rev. A 82, 030103(R) (2010)ADSCrossRefGoogle Scholar
  19. 19.
    M.C. Zheng, D.N. Christodoulides, R. Fleischmann, T. Kottos, Phys. Rev. A 82, 010103R (2010)ADSCrossRefGoogle Scholar
  20. 20.
    W.H. Hu, L. Jin, Y. Li, Z. Song, Phys. Rev. A 86, 042110 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    X.Z. Zhang, L. Jin, Z. Song, Phys. Rev. A 85, 012106 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    L. Jin, Z. Song, Phys. Rev. A 80, 052107 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    S. Kalish, Z. Lin, T. Kottos, Phys. Rev. A 85, 055802 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    H. Vemuri, V. Vavilala, T. Bhamidipati, Y.N. Joglekar, Phys. Rev. A 84, 043826 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    C.T. West, T. Kottos, T. Prosen, Phys. Rev. Lett. 104, 054102 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    J. Wu, X.-T. Xie, Phys. Rev. A 86, 032112 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    S. Longhi, Phys. Rev. B 80, 235102 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    R. El-Ganainy, K.G. Makris, D.N. Christodoulides, Phys. Rev. A 86, 033813 (2012)ADSCrossRefGoogle Scholar
  29. 29.
    G. DellaValle, S. Longhi, Phys. Rev. A 87, 022119 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    A. Eckardt, C. Weiss, M. Holthaus, Phys. Rev. Lett. 95, 260404 (2005)ADSCrossRefGoogle Scholar
  31. 31.
    A. Hemmerich, Phys. Rev. A 81, 063626 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    C. Yuce, Europhys. Lett. 103, 30011 (2013)ADSCrossRefGoogle Scholar
  33. 33.
    M.C. Zheng, D.N. Christodoulides, R. Fleischmann, T. Kottos, Phys. Rev. A 82, 010103 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    H. Ramezani, D.N. Christodoulides, V. Kovanis, I. Vitebskiy, T. Kottos, Phys. Rev. Lett. 109, 033902 (2012)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Physics DepartmentAnadolu UniversityEskişehirTurkey

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