Skip to main content
SpringerLink
Log in

Chiral behaviour of the wave functions for three wave guides in the vicinity of an exceptional point of third order

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

A matrix model that has been used to describe essential features of a parity-time symmetric set-up of three coupled wave guides is investigated. The emphasis of the study lies on the occurrence of an exceptional point of third order. It is demonstrated that the eigenfunctions in close vicinity of the exceptional point have a distinctive chiral behaviour. Using data describing realistic situations it is argued that such chiral behaviour can be tested experimentally.

Graphical abstract

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C.M. Bender, S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  2. N. Moiseyev, Non-Hermitian quantum mechanics (Cambridge University Press, Cambridge, 2011)

  3. W.D. Heiss, J. Phys. A 45, 444016 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  4. C.M. Bender, M. Gianfreda, P. Peng, S.K. Özdemir, L. Yang, Phys. Rev. A 88, 062111 (2013)

    Article  ADS  Google Scholar 

  5. E.-M. Graefe, U. Günther, H.J. Korsch, A.E. Niederle, J. Phys. A 41, 255206 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  6. W.D. Heiss, J. Phys. A 41, 244010 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  7. G. Demange, E.-M. Graefe, J. Phys. A 45, 025303 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  8. J.-W. Ryu, S.-Y. Lee, S.W Kim, Phys. Rev A 85, 042101 (2012)

    Article  ADS  Google Scholar 

  9. R. Gutöhrlein, J. Main, H. Cartarius, G. Wunner, J. Phys. A 46, 305001 (2013)

    Article  MathSciNet  Google Scholar 

  10. M.H. Teimourpour, R. El-Ganainy, A. Eisfeld, A. Szameit, D.N. Christodoulides, Phys. Rev. A 90, 053817 (2014)

    Article  ADS  Google Scholar 

  11. W.D. Heiss, G. Wunner, J. Phys. A 48, 345203 (2015)

    Article  MathSciNet  Google Scholar 

  12. M. Am-Shallem, R. Kosloff, N. Moiseyev, New J. Phys. 17, 113036 (2015)

    Article  ADS  Google Scholar 

  13. M. Am-Shallem, R. Kosloff, N. Moiseyev, Phys. Rev. A 93, 032116 (2016)

    Article  ADS  Google Scholar 

  14. K. Ding, G. Ma, M. Xiao, Z.Q. Zhang, C.T. Chan, Phys. Rev. X 6, 01200 (2016)

    Google Scholar 

  15. H. Jing, Ş.K. Özdemir, H. Lü, F. Nori, Sci. Rep. 7, 3386 (2017)

    Article  ADS  Google Scholar 

  16. J. Schnabel, H. Cartarius, J. Main, G. Wunner, W.D. Heiss, Phys. Rev. A 95, 053868 (2017)

    Article  ADS  Google Scholar 

  17. J. Schnabel, Physical realization of third-order exceptional points, Master thesis, http://www.itp1.uni-stuttgart.de/publikationen/abschlussarbeiten/schnabel_master_2016.pdf (in German)

  18. J. Schnabel, H. Cartarius, J. Main, G. Wunner, W.D. Heiss, Acta Polytech. (2017), arXiv:1708.03206

  19. C. Dembowski, B. Dietz, H.-D. Gräf, H.-L. Harney, W.D. Heiss, A. Richter, Phys. Rev. E 69, 056216 (2004)

    Article  ADS  Google Scholar 

  20. W.D. Heiss, H.L. Harney, Eur. Phys. J. D 17, 149 (2001)

    Article  ADS  Google Scholar 

  21. T. Stehmann, W.D. Heiss, F.G. Scholtz, J. Phys. A 37, 7813 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  22. B. Dietz, H.L. Harney, O.N. Kirillov, M. Miski-Oglu, A. Richter, F. Schäfer, Phys. Rev. Lett. 106, 150403 (2011)

    Article  ADS  Google Scholar 

  23. W.D. Heiss, G. Wunner, J. Phys. A 49, 495303 (2016)

    Article  MathSciNet  Google Scholar 

  24. Sh. Klaiman, U. Günther, N. Moiseyev, Phys. Rev. Lett. 101, 080402 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  25. J. Doppler, A.A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T.J. Milburn, P. Rabl, N. Moiseyev, S. Rotter, Nature 537, 76 (2016)

    Article  ADS  Google Scholar 

  26. H. Xu, D. Mason, L. Jiang, J.G.E. Harris, Nature 537, 80 (2016)

    Article  ADS  Google Scholar 

  27. Ch.E. Rüter, K.G. Makris, R. El-Ganainy, D.N. Christodoulides, M. Segev, D. Kip, Nat. Phys. 6, 192 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Stellenbosch, 7602, Matieland, South Africa

    Walter Dieter Heiss

  2. National Institute for Theoretical Physics (NITheP), Western Cape, South Africa

    Walter Dieter Heiss

  3. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Günter Wunner

Authors
  1. Walter Dieter Heiss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Günter Wunner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Günter Wunner.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Heiss, W.D., Wunner, G. Chiral behaviour of the wave functions for three wave guides in the vicinity of an exceptional point of third order. Eur. Phys. J. D 71, 312 (2017). https://doi.org/10.1140/epjd/e2017-80473-2

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2017-80473-2

Keywords

Search

Navigation