Fano resonances in scattering: an alternative perspective

  • Lukas Schwarz
  • Holger Cartarius
  • Günter Wunner
  • Walter Dieter Heiss
  • Jörg Main
Regular Article

Abstract

In a previous paper it has been shown that the interference of the first and second order pole of the Green’s function at an exceptional point, as well as the interference of the first order poles in the vicinity of the exceptional point, gives rise to asymmetric scattering cross section profiles. In the present paper we demonstrate that these line profiles are indeed well described by the Beutler-Fano formula, and thus are genuine Fano resonances. Also further away from the exceptional points excellent agreement can be found by introducing energy dependent Fano parameters.

Graphical abstract

Keywords

Atomic Physics 

References

  1. 1.
    H. Beutler, Z. Phys. 93, 177 (1935)ADSCrossRefGoogle Scholar
  2. 2.
    U. Fano, Nuovo Cim. 12, 154 (1935)CrossRefMATHGoogle Scholar
  3. 3.
    H. Feshbach, Ann. Phys. (N.Y.) 5, 357 (1958)MathSciNetADSCrossRefMATHGoogle Scholar
  4. 4.
    J.M. Blatt, V.F. Weisskopf, Theoretical Nuclear Physics (Springer-Verlag, New York, 1979)Google Scholar
  5. 5.
    U. Fano, Phys. Rev. 124, 1866 (1961)ADSCrossRefMATHGoogle Scholar
  6. 6.
    U. Fano, J.W. Cooper, Rev. Mod. Phys. 40, 441 (1968)ADSCrossRefGoogle Scholar
  7. 7.
    U. Fano, A.R.P. Rau, Atomic collisions and spectra (Academic Press, New York, 1986)Google Scholar
  8. 8.
    A.R.P. Rau, Phys. Scripta 69, C10 (2004)CrossRefMATHGoogle Scholar
  9. 9.
    M.I. Tribelsky, S. Flach, A.E. Miroshnichenko, A.V. Gorbach, Y.S. Kivshar, Phys. Rev. Lett. 100, 043903 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    A.E. Miroshnichenko, S. Flach, Y.S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, H.-J. Stöckmann, Phys. Rev. Lett. 105, 056801 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    C. Ott, A. Kaldun, P. Raith, K. Meyer, M. Laux, J. Evers, C.H. Keitel, C. Greene, T. Pfeifer, Science 340, 716 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    C.D. Lin, W.-C. Chu, Science 340, 694 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    B. Lukyanchuk, N.I. Zheludev, S.A. Maier, N.J. Halas, P. Nordlander, H. Giessen, C.T. Chong, Nat. Mater. 9, 707 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    J. Zhao, C. Zhang, P.V. Braun, H. Giessen, Adv. Mat 24, 247 (2012)CrossRefGoogle Scholar
  16. 16.
    A. Lovera, B. Gallinet, P. Nordlander, O.J. Martin, ACS Nano 7, 4527 (2011)CrossRefGoogle Scholar
  17. 17.
    J. Butet, O.J.F. Martin, Opt. Express 22, 29693 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    T. Kato, Perturbation theory for linear operators (Springer, Berlin, 1966)Google Scholar
  19. 19.
    N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, Cambridge, 2011)Google Scholar
  20. 20.
    W.D. Heiss, J. Phys. A 45, 444016 (2012)MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    W.D. Heiss, G. Wunner, Eur. Phys. J. D 68, 284 (2014)ADSCrossRefGoogle Scholar
  22. 22.
    I. Rotter, J. Phys. A 42, 153001 (2009)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    R. Gutöhrlein, J. Main, H. Cartarius, G. Wunner, J. Phys. A 46, 305001 (2013)MathSciNetCrossRefGoogle Scholar
  24. 24.
    M. Am-Shallem, R. Kosloff, N. Moiseyev, e-prints arXiv:1406.6364v2Google Scholar
  25. 25.
    A.I. Magunov, I. Rotter, S.I. Strakhova, Phys. Rev. B 68, 245305 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    Y.S. Joe, A.M. Satanin, Ch.S. Kim, Phys. Scripta 74, 259 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    D.M. Riffe, Phys. Rev. B 84, 064308 (2011)ADSCrossRefGoogle Scholar
  28. 28.
    A. Satpathy, A. Roy, A. Mohapatra, Eur. J. Phys. 33, 863 (2012)CrossRefGoogle Scholar
  29. 29.
    J.P. Connerade, A.M. Lane, J. Phys. B 20, 1757 (1987)ADSCrossRefGoogle Scholar
  30. 30.
    J.P. Connerade, A.M. Lane, J. Phys. B 20 L363 (1987)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Lukas Schwarz
    • 1
  • Holger Cartarius
    • 1
  • Günter Wunner
    • 1
  • Walter Dieter Heiss
    • 2
    • 3
  • Jörg Main
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgartGermany
  2. 2.Department of PhysicsUniversity of StellenboschMatielandSouth Africa
  3. 3.National Institute for Theoretical Physics (NITheP)Western CapeSouth Africa

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