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Study of Fano Resonance in the Core-Level Absorption Spectrum in Terms of Complex Spectral Analysis

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Fano Resonances in Optics and Microwaves

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 219))

Abstract

We study theoretically the core absorption spectrum of an impurity embedded in a tight-binding chain in terms of complex spectral analysis. The absorption spectral profile associated with the resonance states in principle exhibits an asymmetric Fano-type structure, even without apparent multiple interference transition paths. The asymmetric Fano absorption profile is attributed to the complex-valued oscillator strength of the transition to the resonance state belonging to the extended Hilbert space. The boundary condition on the continuum causes a large energy dependence of the self-energy, so that it enhances the nonlinearity of the eigenvalue problem of the effective Hamiltonian, yielding several non-analytic resonance states. The optical transitions to these resonance states constitute the overall absorption spectrum structure.

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References

  1. R. Loudon, The Quantum Theory of Light (OUP Oxford, Oxford, 2000)

    MATH  Google Scholar 

  2. H. Beautler, Z. Physik A 93, 177 (1935)

    Article  ADS  Google Scholar 

  3. U. Fano, Nuovo Cimento 12, 154 (1935)

    Article  Google Scholar 

  4. U. Fano, Phys. Rev. 124, 1866 (1961)

    Article  ADS  Google Scholar 

  5. C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications. A Wiley-Interscience Publication (Wiley, 1998)

    Google Scholar 

  6. A.E. Miroshnichenko, S. Flach, Y.S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010)

    Article  ADS  Google Scholar 

  7. P. Fan, Z. Yu, S. Fan, M.L. Brongersma, Nat. Mater. 13, 471 EP (2014)

    Google Scholar 

  8. S. Yoshino, G. Oohata, K. Mizoguchi, Phys. Rev. Lett. 15, 157402 (2015)

    Article  ADS  Google Scholar 

  9. N. Hatano, D.R. Nelson, Phys. Rev. Lett. 77, 570 (1996)

    Article  ADS  Google Scholar 

  10. N. Hatano, D.R. Nelson, Phys. Rev. B 56, 8651 (1997)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  12. C.M. Bender, D.C. Brody, H.F. Jones, Am. J. Phys. 71, 1095 (2003)

    Article  ADS  Google Scholar 

  13. W.D. Heiss, J. Phys. A: Math. Gen. 37, 2455 (2004)

    Article  ADS  Google Scholar 

  14. I. Rotter, J. Phys. A: Math. Theor. 42, 153001 (2009)

    Article  ADS  Google Scholar 

  15. I. Rotter, J.P. Bird, Rep. Prog. Phys. 78, 114001 (2015)

    Article  ADS  Google Scholar 

  16. H. Feshbach, Ann. Phys. 19, 287 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  17. C. Jung, M. Müller, I. Rotter, Phys. Rev. E 60, 114 (1999)

    Article  ADS  Google Scholar 

  18. C. Jung, M. Müller, I. Rotter, J. Mod. Phys. 1, 303 (2010)

    Article  Google Scholar 

  19. H. Eleuch, I. Rotter, Eur. Phys. J. D 69, 229 (2015)

    Article  ADS  Google Scholar 

  20. T. Petrosky, I. Prigogine, S. Tasaki, Phys. A: Stat. Mech. Appl. 173, 175 (1991)

    Article  Google Scholar 

  21. T. Petrosky, I. Prigogine, Adv. Chem. Phys. 99, 1 (1997)

    Google Scholar 

  22. T. Petrosky, G. Ordonez, I. Prigogine, Phys. Rev. A. At. Mol. Opt. Phys. 64, 062101/1 (2001)

    Google Scholar 

  23. G. Ordonez, T. Petrosky, I. Prigogine, Phys. Rev. A. At. Mol. Opt. Phys. 63, 521061 (2001)

    Google Scholar 

  24. S. Tanaka, S. Garmon, T. Petrosky, Phys. Rev. B 73, 115340 (2006)

    Article  ADS  Google Scholar 

  25. S. Tanaka, S. Garmon, G. Ordonez, T. Petrosky, Phys. Rev. B 76, 153308 (2007)

    Article  ADS  Google Scholar 

  26. S. Garmon, H. Nakamura, N. Hatano, T. Petrosky, Phys. Rev. B 80, 115318 (2009)

    Article  ADS  Google Scholar 

  27. S. Garmon, I. Rotter, N. Hatano, D. Segal, Int. J. Theor. Phys. 51, 3536 (2012)

    Article  Google Scholar 

  28. S. Tanaka, S. Garmon, K. Kanki, T. Petrosky, Phys. Rev. A 94, 022105 (2016)

    Article  ADS  Google Scholar 

  29. T. Kato, Perturbation Theory for Linear Operators, 2nd edn. (Springer, Berlin, Heidelberg, 1995)

    Book  Google Scholar 

  30. K. Kanki, K. Hashimoto, T. Petrosky, S. Tanaka, Spontaneous Breakdown of a PT-Symmetry in the Liouvillian Dynamics at a Non-Hermitian Degeneracy Point (Springer International Publishing, Cham, 2016), pp. 289–304

    Google Scholar 

  31. N. Hatano, G. Ordonez, J. Math. Phys. 55, 122106 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  32. S. Garmon, M. Gianfreda, N. Hatano, Phys. Rev. A 92, 022125 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  33. S.C.G. Sudarshan, C.B. Chiu, V. Gorini, Phys. Rev. D 18, 2914 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  34. J. von Neumann, E. Wigner, Phys. Z. 30, 465 (1929)

    Google Scholar 

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Acknowledgements

We are very grateful Drs. S. Garmon, K. Noba, and K. Kanki for many valuable discussions. We also thank K. Mizoguchi and Y. Kayanuma for fruitful comments. This work was partially supported by JSPS Grant-in-Aid for Scientific Research No.16H04003, 16K05481, and 17K05585.

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Authors and Affiliations

  1. Department of Physical Science, Osaka Prefecture University, Gakuen-cho 1-1, Sakai, 599-8531, Japan

    Satoshi Tanaka & Taku Fukuta

  2. Center for Complex Quantum System, University of Texas at Austin, Austin, USA

    Tomio Petrosky

  3. Institute of Industrial Science, The University of Tokyo, Tokyo, Japan

    Tomio Petrosky

Authors
  1. Satoshi Tanaka
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  2. Taku Fukuta
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  3. Tomio Petrosky
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Corresponding author

Correspondence to Satoshi Tanaka .

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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beersheba, Israel

    Eugene Kamenetskii

  2. Federal Research Center KSC SB RAS, Kirensky Institute of Physics, Krasnoyarsk, Russia

    Almas Sadreev

  3. School of Engineering and Information Technology, University of New South Wales, Canberra, ACT, Australia

    Andrey Miroshnichenko

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Tanaka, S., Fukuta, T., Petrosky, T. (2018). Study of Fano Resonance in the Core-Level Absorption Spectrum in Terms of Complex Spectral Analysis. In: Kamenetskii, E., Sadreev, A., Miroshnichenko, A. (eds) Fano Resonances in Optics and Microwaves. Springer Series in Optical Sciences, vol 219. Springer, Cham. https://doi.org/10.1007/978-3-319-99731-5_11

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