Strong field approximation within a Faddeev-like formalism for laser-matter interactions

  • Yuri Popov
  • Alexander Galstyan
  • Francisca Mota-Furtado
  • Patrick F. O’Mahony
  • Bernard Piraux
Regular Article
Part of the following topical collections:
  1. Topical Issue: Many Particle Spectroscopy of Atoms, Molecules, Clusters and Surfaces


We consider the interaction of atomic hydrogen with an intense laser field within the strong-field approximation. By using a Faddeev-like formalism, we introduce a new perturbative series in the binding potential of the atom. As a first test of this new approach, we calculate the electron energy spectrum in the very simple case of a photon energy higher than the ionisation potential. We show that by contrast to the standard perturbative series in the binding potential obtained within the strong field approximation, the first terms of the new series converge rapidly towards the results we get by solving the corresponding time-dependent Schrödinger equation.

Graphical abstract


  1. 1.
    L.V. Keldysh, Sov. Phys. J. Exp. Theor. Phys. 20, 1307 (1965)MathSciNetGoogle Scholar
  2. 2.
    F.H.M. Faisal, J. Phys. B 6, L89 (1973)ADSCrossRefGoogle Scholar
  3. 3.
    H.R. Reiss, Phys. Rev. A 22, 1786 (1980)ADSCrossRefGoogle Scholar
  4. 4.
    G.G. Paulus, D. Bauer, in Time in Quantum Mechanics, edited by J.G. Muga, A. Ruschhaupt, A. del Campo (Springer-Verlag, Berlin, Heidelberg, 2009), Vol. 2, pp. 303–337Google Scholar
  5. 5.
    M. Lewenstein, K.C. Kulander, K.J. Schafer, Ph. Bucksbaum, Phys. Rev. A 51, 1495 (1995)ADSCrossRefGoogle Scholar
  6. 6.
    M. Lewenstein, Ph. Balcou, M.Yu. Ivanov, A. L’Huillier, P.B. Corkum, Phys. Rev. A 49, 2117 (1994)ADSCrossRefGoogle Scholar
  7. 7.
    F. Krausz, M. Ivanov, Rev. Mod. Phys. 81, 163 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    A. Galstyan, O. Chuluunbaatar, A. Hamido, Yu.V. Popov, F. Mota-Furtado, P.F. O’Mahony, N. Janssens, F. Catoire, B. Piraux, Phys. Rev. A 93, 023422 (2016)ADSCrossRefGoogle Scholar
  9. 9.
    F.H.M. Faisal, J. Phys. B 40, F145 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    F.H.M. Faisal, Phys. Rev. A 75, 063412 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    A.M. Perelomov, V.S. Popov, Sov. Phys. J. Exp. Theor. Phys. 25, 336 (1967)ADSGoogle Scholar
  12. 12.
    V.P. Krainov, J. Opt. Soc. Am. B 14, 425 (1997)ADSCrossRefGoogle Scholar
  13. 13.
    M. Klaiber, E. Yakaboylu, K.Z. Hatsargortsyan, Phys. Rev. A 87, 023417 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    S.V. Popruzhenko, G.G. Paulus, D. Bauer, Phys. Rev. A 77, 053409 (2008)ADSCrossRefGoogle Scholar
  15. 15.
    T.-M. Yan, S.V. Popruzhenko, M.J.J. Vrakking, D. Bauer, Phys. Rev. Lett. 105, 253002 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    X.-Y. Lai, C. Poli, H. Schomerus, C.F. de Morisson Faria, Phys. Rev. A 92, 043407 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    L. Torlina, O. Smirnova, Phys. Rev. A 86, 043408 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    A.M. Perelomov, V.S. Popov, M.V. Terent’ev, Sov. Phys. J. Exp. Theor. Phys. 23, 924 (1966)ADSGoogle Scholar
  19. 19.
    F.H.M. Faisal, Phys. Rev. A 94, 031401 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    A.M. Perelomov, V.S. Popov, M.V. Terent’ev, Sov. Phys. J. Exp. Theor. Phys. 24, 207 (1967)ADSGoogle Scholar
  21. 21.
    E.E. Serebryannikov, A.M. Zheltikov, Phys. Rev. Lett. 116, 123901 (2016)ADSCrossRefGoogle Scholar
  22. 22.
    T. Nubbemeyer, K. Gorling, A. Saenz, U. Eichmann, W. Sandner, Phys. Rev. Lett. 101, 233001 (2008)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Yuri Popov
    • 1
    • 2
  • Alexander Galstyan
    • 3
  • Francisca Mota-Furtado
    • 4
  • Patrick F. O’Mahony
    • 4
  • Bernard Piraux
    • 3
  1. 1.Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Joint Institute for Nuclear ResearchDubnaRussia
  3. 3.Institute of Condensed Matter and Nanosciences, Université catholique de LouvainLouvain-la-NeuveBelgium
  4. 4.Department of MathematicsRoyal Holloway, University of LondonSurreyUK

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