Applied Physics B

, 123:116 | Cite as

Double-electron ionization driven by inhomogeneous fields

  • A. Chacón
  • L. Ortmann
  • F. Cucchietti
  • N. Suárez
  • J. A. Pérez-Hernández
  • M. F. Ciappina
  • A. S. Landsman
  • M. Lewenstein
Part of the following topical collections:
  1. “Enlightening the World with the Laser” - Honoring T. W. Hänsch


Electron–electron correlation effects play a crucial role in our understanding of sequential (SDI) and non-sequential double ionization (NSDI) mechanisms. Here, we present a theoretical study of NSDI driven by plasmonic-enhanced spatial inhomogeneous fields. By numerically solving the time-dependent Schrödinger equation for a linear reduced model of He and a double-electron time-evolution probability analysis, we provide evidence for enhancement effects in NSDI showing that the double ionization yield at lower laser peak intensities is increased due to the spatial inhomogeneous character of plasmonic-enhanced field. The change in the emission direction of the double-ion as a function of the field inhomogeneity degree demonstrates that plasmonic-enhanced fields could configure a reliable instrument to control the ion emission. Furthermore, our quantum mechanical model, as well as classical trajectory Monte Carlo simulations, show that inhomogeneous fields are as well as a useful tool for splitting the binary and recoil processes in the rescattering scenario.


Laser Field Inhomogeneous Field Double Ionization Carrier Envelope Phase Laser Peak Intensity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by the project ELI-Extreme Light Infrastructure-phase 2 (Project No. CZ.02.1.01/0.0/0.0/15_008/0000162) from European Regional Development Fund, Spanish MINECO (National Plan grants FIS2011-30465-C02-01, FOQUS No. FIS2013-46768-P, FISICATEAMO FIS2016-79508-P and Severo Ochoa Excellence Grant No. SEV-2015-0522), the Generalitat de Catalunya (SGR 874 and CERCA/Program) and Fundació Privada Cellex Barcelona. N.S. was supported by the Erasmus Mundus Doctorate Program Europhotonics (Grant No. 159224-1-2009-1-FR-ERA MUNDUS-EMJD). N.S., A.C., and M.L. acknowledge ERC AdG OSYRIS, EU FETPRO QUIC and National Science Centre, Poland—Symfonia Grant 2016/20/W/ST4/00314. A. S. L. acknowledges Max Planck Center for Attosecond Science (MPC-AS). J. A. P.-H. acknowledges to the Spanish Ministerio de Economía y Competitividad (FURIAM Project No. FIS2013-47741-R and PALMA project FIS2016- 81056-R) and Laserlab-Europe (EU-H2020 654148). L.O. acknowledges valuable input from Andre Staudte. The authors thankfully acknowledge the computer resources at MareNostrum, technical expertise and assistance provided by the Barcelona Supercomputing Center and the Red Española de Supercomputación (RES).


  1. 1.
    A. L’Huillier, L.A. Lompre, G. Mainfray, C. Manus, Multiply charged ious formed by multiphoton absorption processes in the continuum. Phys. Rev. Lett. 48(26), 1814–1817 (1982)ADSCrossRefGoogle Scholar
  2. 2.
    P. Lambropoulos, X. Tang, P. Agostini, G. Petite, A. L’Huillier, Multiphoton spectroscopy of doubly excited, bound, and autoionizing states of strontium. Phys. Rev. A 38(12), 6165–6179 (1988)ADSCrossRefGoogle Scholar
  3. 3.
    B. Bergues, M. Kübel, N.G. Kling, C. Burger, M.F. Kling, Single-cycle non-sequential double ionization. IEEE J. Sel. Top. Quantum Electron. 21(5), 8701009–8701009 (2015)CrossRefGoogle Scholar
  4. 4.
    B. Bergues, M. Kübel, N.G. Johnson, B. Fischer, N. Camus, K.J. Betsch, O. Herrwerth, A. Senftleben, A.M. Sayler, T. Rathje, T. Pfeifer, I. Ben-Itzhak, R.R. Jones, G.G. Paulus, F. Krausz, R. Moshammer, J. Ullrich, M.F. Kling, Attosecond tracing of correlated electron-emission in non-sequential double ionization. Nat. Comm. 3(813), 1–6 (2012)Google Scholar
  5. 5.
    M. G. Pullen, B. Wolter, X. Wang, X.-M. Tong, M. Sclafani, M. Baudisch, H. Pires, C.D. Schröter, J. Ullrich, T. Pfeifer, R. Moshammer, J.H. Eberly, J. Biegert, Transition from non-sequential to sequential double ionisation in many-electron systems. ArXiv:1602.07840 (2016)
  6. 6.
    B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, K.C. Kulander, Precision measurement of strong field double ionization of helium. Phys. Rev. Lett. 73(9), 1227–1230 (1994)ADSCrossRefGoogle Scholar
  7. 7.
    Th Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, R. Dörner, Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields. Phys. Rev. Lett. 84(3), 443–446 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    Th Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, R. Dörner, Correlated electron emission in multiphoton double ionization. Nature 405(6787), 658–661 (2000)ADSCrossRefGoogle Scholar
  9. 9.
    W. Becker, X.J. Liu, P.J. Ho, J.H. Eberly, Theories of photoelectron correlation in laser-driven multiple atomic ionization. Rev. Mod. Phys. 84(3), 1011–1043 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    P.B. Corkum, Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 71(13), 1994–1997 (1993)ADSCrossRefGoogle Scholar
  11. 11.
    A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th Weber, M. Meckel, D.M. Villeneuve, P.B. Corkum, A. Becker, R. Dörner, Binary and recoil collisions in strong field double ionization of helium. Phys. Rev. Lett. 99(26), 263002 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    R. Kopold, W. Becker, H. Rottke, W. Sandner, Routes to nonsequential double ionization. Phys. Rev. Lett. 85(18), 3781–3784 (2000)ADSCrossRefGoogle Scholar
  13. 13.
    E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G.G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, J. Ullrich, Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization. J. Phys. B: At. Mol. Phys 36(15), 3269–3280 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    A. Chacón, M.F. Ciappina, M. Lewenstein, Double-electron recombination in high-order-harmonic generation driven by spatially inhomogeneous fields. Phys. Rev. A 94(4), 043407 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    M.F. Ciappina, J.A. Pérez-Hernández, A.S. Landsman, W. Okell, S. Zherebtsov, B. Förg, J. Schötz, L. Seiffert, T. Fennel, T. Shaaran, T. Zimmermann, R. Guichard A. Chacón, A. Zaïr, J.W.G. Tisch, J.P. Marangos, T. Witting, A. Braun, S.A. Maier, L. Roso, M. Krüger, P. Hommelhoff, M.F. Kling, F. Krausz, M. Lewenstein. Attosecond physics at the nanoscale. Rep. Prog. Phys. 80(5), 054401 (2017)Google Scholar
  16. 16.
    D. Bauer, Two-dimensional, two-electron model atom in a laser pulse: Exact treatment, single-active-electron analysis, time-dependent density-functional theory, classical calculations, and nonsequential ionization. Phys. Rev. A 56(4), 3028–3039 (1997)ADSCrossRefGoogle Scholar
  17. 17.
    D.G. Lappas, R. van Leeuwen, Electron correlation effects in the double ionization of he. J. Phys. B 31(6), L249–L256 (1998)CrossRefGoogle Scholar
  18. 18.
    D.G. Lappas, A. Sanpera, J.B. Watson, K. Burnett, P.L. Knight, R. Grobe, J.H. Eberly, Two-electron effects in harmonic generation and ionization from a model he atom. J. Phys. B: At. Mol. Phys 29(16), L619 (1996)ADSCrossRefGoogle Scholar
  19. 19.
    M. Lein, E.K.U. Gross, V. Engel, Intense-field double ionization of helium: Identifying the mechanism. Phys. Rev. Lett. 85(22), 4707–4710 (2000)ADSCrossRefGoogle Scholar
  20. 20.
    S.E. Harris, J.J. Macklin, T.W. Hänsch, Atomic scale temporal structure inherent to high-order harmonic generation. Opt. Comm. 100(5–6), 487–490 (1993)ADSCrossRefGoogle Scholar
  21. 21.
    C.G. Wahlström, M.B. Gaarde, A. L’Huillier, C. Lyngå, I. Mercer, E. Mevel, R. Zerne, Ph Antoine, M. Bellini, T.W. Hänsch, Manipulations of high-order harmonics, in Multiphoton Processes 1996, ed. by P. Lambropoulos, H. Walther (Institute of Physics Publishing, Bristol, 1997), p. 160Google Scholar
  22. 22.
    R. Zerne, C. Altucci, M. Bellini, M.B. Gaarde, T.W. Hänsch, A. L’Huillier, C. Lyngå, C.-G. Wahlström, Phase-locked high-order harmonic sources. Phys. Rev. Lett. 79(6), 1006–1009 (1997)ADSCrossRefGoogle Scholar
  23. 23.
    J.B. Watson, A. Sanpera, D.G. Lappas, P.L. Knight, K. Burnett, Nonsequential double ionization of helium. Phys. Rev. Lett. 78(10), 1884–1887 (1997)ADSCrossRefGoogle Scholar
  24. 24.
    A. Chacón, M.F. Ciappina, M. Lewenstein, Numerical studies of light-matter interaction driven by plasmonic fields: The velocity gauge. Phys. Rev. A 92(6), 063834 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    M.F. Ciappina, J. Biegert, R. Quidant, M. Lewenstein, High-order-harmonic generation from inhomogeneous fields. Phys. Rev. A 85(3), 033828 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    M.D. Feit, J.A. Fleck, A. Steiger, Solution of the schrdinger equation by a spectral method. J. Comput. Phys. 47(3), 412–433 (1982)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    C. Ruiz, A. Chacón, QFISHBOWL library (2008).
  28. 28.
    M. Frigo, S.G. Johnson. FFTW library (1998).
  29. 29.
    R. Grobe, J.H. Eberly, One-dimensional model of a negative ion and its interaction with laser fields. Phys. Rev. A 48(6), 4664–4681 (1993)ADSCrossRefGoogle Scholar
  30. 30.
    M.V. Ammosov, N.B. Delone, V.P. Krainov, Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field. Sov. Phys.-JETP, 64(6), 1191–1194 (1986)Google Scholar
  31. 31.
    N.B. Delone, V.P. Krainov, Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation. J. Opt. Soc. Am. B 8(6), 1207–1211 (1991)ADSCrossRefGoogle Scholar
  32. 32.
    L. Arissian, C. Smeenk, F. Turner, C. Trallero, A.V. Sokolov, D.M. Villeneuve, A. Staudte, P.B. Corkum, Direct test of laser tunneling with electron momentum imaging. Phys. Rev. Lett. 105(13), 133002 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    A.S. Landsman, A.N. Pfeiffer, C. Hofmann, M. Smolarski, C. Cirelli, U. Keller, Rydberg state creation by tunnel ionization. New J. Phys. 15(1), 013001 (2013)ADSCrossRefGoogle Scholar
  34. 34.
    A.S. Landsman, U. Keller, Tunnelling time in strong field ionisation. J. Phys. B: At. Mol. Phys 47(20), 204024 (2014)ADSCrossRefGoogle Scholar
  35. 35.
    T. Nubbemeyer, K. Gorling, A. Saenz, U. Eichmann, W. Sandner, Strong-field tunneling without ionization. Phys. Rev. Lett. 101(23), 233001 (2008)ADSCrossRefGoogle Scholar
  36. 36.
    C. Hofmann, A.S. Landsman, C. Cirelli, A.N. Pfeiffer, U. Keller, Comparison of different approaches to the longitudinal momentum spread after tunnel ionization. J. Phys. B: At. Mol. Phys 46(12), 125601 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    S.P. Goreslavski, G.G. Paulus, S.V. Popruzhenko, N.I. Shvetsov-Shilovski, Coulomb asymmetry in above-threshold ionization. Phys. Rev. Lett. 93(2), 233002 (2004)ADSCrossRefGoogle Scholar
  38. 38.
    Y. Liu, S. Tschuch, A. Rudenko, M. Dürr, M. Siegel, U. Morgner, R. Moshammer, J. Ullrich, Strong-field double ionization of ar below the recollision threshold. Phys. Rev. Lett. 101(5), 053001 (2008)ADSCrossRefGoogle Scholar
  39. 39.
    A. Rudenko, K. Zrost, B. Feuerstein, V.L.B. de Jesus, C.D. Schröter, R. Moshammer, J. Ullrich, Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms. Phys. Rev. Lett. 93(25), 253001 (2004)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • A. Chacón
    • 1
  • L. Ortmann
    • 2
  • F. Cucchietti
    • 3
  • N. Suárez
    • 1
  • J. A. Pérez-Hernández
    • 4
  • M. F. Ciappina
    • 5
  • A. S. Landsman
    • 2
    • 6
  • M. Lewenstein
    • 1
    • 7
  1. 1.ICFO-Institut de Ciencies FotoniquesThe Barcelona Institute of Science and TechnologyCastelldefelsSpain
  2. 2.Max Planck Institute for the Physics of Complex SystemsDresdenGermany
  3. 3.Barcelona Supercomputing Center (BSC)BarcelonaSpain
  4. 4.Centro de Láseres Pulsados (CLPU), Parque CientíficoVillamayorSpain
  5. 5.Institute of Physics of the ASCRELI-BeamlinesPragueCzech Republic
  6. 6.Max Planck Postech/Department of PhysicsPohangRepublic of Korea
  7. 7.ICREABarcelonaSpain

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