Abstract

The ab initio investigation of ionization shows the strong regularization of the Coulomb potential by a high-frequency laser field in the stabilization regime, which is characterized with a large energy shift in the first dressed state. The decreasing of the second major ionization burst at the lowering edge of the laser pulse indicates another aspect of three-dimensional effect. Moreover, the modulation in the ionization time profile, previously attributed to the classical drift [Phys. Rev. A 83, 063418 (2011)], is illustrated by a superposition of the two free-electron wave-packets, which have arisen via ionization from the two different Kramers–Henneberger states. This finding is in excellent agreement with the time profile of the current density.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. S. Voronov, and N. B. Delone, “Ionization of the xenon atom by the electric field of ruby laser emission,” JETP 1, 66–68 (1965).
  2. M. Göppert-Mayer, “Über Elementarakte mit zwei Quantensprüngen,” Ann. Phys. 401, 273–294 (1931).
    [CrossRef]
  3. P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
    [CrossRef]
  4. P. Salieres, A. lHuillier, P. Antoine, and M. Lewenstein, “Study of the spatial and temporal coherence of high-order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83–142 (1999).
    [CrossRef]
  5. T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
    [CrossRef]
  6. T. Marchenko, H. G. Muller, K. J. Schafer, and M. J. J. Vrakking, “Wavelength dependence of photoelectron spectra in above-threshold ionization,” J. Phys. B 43, 185001 (2010).
    [CrossRef]
  7. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
    [CrossRef]
  8. K. J. Schafer, K. C. Kulander, and J. L. Krause, in Super-Intense Laser-Atom Physics (SILAP III), B. Piraux, ed. (NATO, Plenum Press, 1993), p. 95.
  9. H. B. van den Heuvell and H. G. Muller, in Multiphoton Processes, S. J. Smith and P. L. Knight, eds. (Cambridge University, 1988), p. 25.
  10. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
    [CrossRef]
  11. J. Henkel, M. Lein, and V. Engel, “Interference in above-threshold-ionization electron distributions from molecules,” Phys. Rev. A 83, 051401 (2011).
    [CrossRef]
  12. F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
    [CrossRef]
  13. G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
    [CrossRef]
  14. J. N. Bardsley, A. Szoke, and M. J. Comella, “Multiphoton ionization from a short-range potential by short-pulse lasers,” J. Phys. B 21, 3899–3916 (1988).
    [CrossRef]
  15. V. C. Reed and K. Burnett, “Role of resonances and quantum-mechanical interference in the generation of above-threshold-ionization spectra,” Phys. Rev. A 43, 6217–6226 (1991).
    [CrossRef]
  16. L. Guo, S. S. Han, and J. Chen, “Time-energy analysis of above-threshold ionization,” Opt. Express 18, 1240–1248 (2010).
    [CrossRef]
  17. W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
    [CrossRef]
  18. C. Liu and K. Z. Hatsagortsyan, “Origin of unexpected low energy structure in photoelectron spectra induced by mid-infrared strong laser fields,” Phys. Rev. Lett. 105, 113003(2010).
    [CrossRef]
  19. D. A. Telnov and S. I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: role of the Coulomb threshold effect,” Phys. Rev. A 83, 063406–063411 (2011).
    [CrossRef]
  20. T. M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, “Low-energy structures in strong field ionization revealed by quantum orbits,” Phys. Rev. Lett. 105, 253002–253005(2010).
    [CrossRef]
  21. M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
    [CrossRef]
  22. A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
    [CrossRef]
  23. http://hasylab.desy.de/facilities/flash/, http://lcls.slac.stanford.edu/, http://www-xfel.spring8.or.jp/.
  24. K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Siegert-state expansion in the Kramers–Henneberger frame: interference substructure of above-threshold ionization peaks in the stabilization regime,” Phys. Rev. A 76, 043418–043425 (2007).
    [CrossRef]
  25. O. Tolstikhin, “Siegert-state expansion for non-stationary systems. IV. Three-dimensional case,” Phys. Rev. A 77, 032712–032721 (2008).
    [CrossRef]
  26. K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Slow electrons generated by intense high-frequency laser pulses,” Phys. Rev. Lett. 103, 153003–153006 (2009).
    [CrossRef]
  27. H. Ebadi, C. H. Keitel, and K. Z. Hatsagortsyan, “Time analysis of above-threshold ionization in extreme-ultraviolet laser pulses,” Phys. Rev. A 83, 063418–063425 (2011).
    [CrossRef]
  28. J. R. Vazquez de Aldana and Luis Roso, “Non-relativistic numerical study of atomic ionization by strong laser fields without the dipole approximation in a flat-atom model,” Phys. Rev. A 61, 043403–043409 (2000).
    [CrossRef]
  29. R. S. Varga, Matrix Iterative Analysis (Prentice-Hall, 1962).
  30. H. G. Muller, “An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge,” Laser Phys. 9, 138–148 (1999).
  31. K. J. Schafer and K. C. Kulander, “Energy analysis of time-dependent wave functions: application to above-threshold ionization,” Phys. Rev. A 42, 5794–5797 (1990).
    [CrossRef]
  32. D. Bauer, “Emergence of classical orbits in few-cycle above-threshold ionization of atomic hydrogen,” Phys. Rev. Lett. 94, 113001–113004 (2005).
    [CrossRef]
  33. H. A. Kramers, Collected Scientific Papers (North-Holland, 1956) p. 272.
  34. W. C. Henneberger, “Perturbation method for atoms in intense light beams,” Phys. Rev. Lett. 21, 838–841 (1968).
    [CrossRef]
  35. M. Gavrila, I. Simbotin, and M. Stroe, “Low-frequency atomic stabilization and dichotomy in super intense laser fields: full Floquet results,” Phys. Rev. A 78, 033404–033414 (2008).
    [CrossRef]
  36. N. V. Bordyug and V. P. Krainov, “Dynamic resonances in ultra-short laser pulses,” Laser Phys. Lett. 4, 418–420 (2007).
    [CrossRef]
  37. Z. Zhou and J. Yuam, “Fine structures of the harmonic and hyper-Raman spectrum of the hydrogen atom in an intense high-frequency laser pulse,” Phys. Rev. A 77, 063411–063416 (2008).
    [CrossRef]
  38. K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamic stabilization of hydrogen in an intense, high-frequency, pulsed laser field,” Phys. Rev. Lett. 66, 2601–2604 (1991).
    [CrossRef]

2011 (3)

J. Henkel, M. Lein, and V. Engel, “Interference in above-threshold-ionization electron distributions from molecules,” Phys. Rev. A 83, 051401 (2011).
[CrossRef]

D. A. Telnov and S. I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: role of the Coulomb threshold effect,” Phys. Rev. A 83, 063406–063411 (2011).
[CrossRef]

H. Ebadi, C. H. Keitel, and K. Z. Hatsagortsyan, “Time analysis of above-threshold ionization in extreme-ultraviolet laser pulses,” Phys. Rev. A 83, 063418–063425 (2011).
[CrossRef]

2010 (5)

T. M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, “Low-energy structures in strong field ionization revealed by quantum orbits,” Phys. Rev. Lett. 105, 253002–253005(2010).
[CrossRef]

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

L. Guo, S. S. Han, and J. Chen, “Time-energy analysis of above-threshold ionization,” Opt. Express 18, 1240–1248 (2010).
[CrossRef]

C. Liu and K. Z. Hatsagortsyan, “Origin of unexpected low energy structure in photoelectron spectra induced by mid-infrared strong laser fields,” Phys. Rev. Lett. 105, 113003(2010).
[CrossRef]

T. Marchenko, H. G. Muller, K. J. Schafer, and M. J. J. Vrakking, “Wavelength dependence of photoelectron spectra in above-threshold ionization,” J. Phys. B 43, 185001 (2010).
[CrossRef]

2009 (4)

T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
[CrossRef]

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Slow electrons generated by intense high-frequency laser pulses,” Phys. Rev. Lett. 103, 153003–153006 (2009).
[CrossRef]

2008 (4)

O. Tolstikhin, “Siegert-state expansion for non-stationary systems. IV. Three-dimensional case,” Phys. Rev. A 77, 032712–032721 (2008).
[CrossRef]

M. Gavrila, I. Simbotin, and M. Stroe, “Low-frequency atomic stabilization and dichotomy in super intense laser fields: full Floquet results,” Phys. Rev. A 78, 033404–033414 (2008).
[CrossRef]

Z. Zhou and J. Yuam, “Fine structures of the harmonic and hyper-Raman spectrum of the hydrogen atom in an intense high-frequency laser pulse,” Phys. Rev. A 77, 063411–063416 (2008).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

2007 (2)

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Siegert-state expansion in the Kramers–Henneberger frame: interference substructure of above-threshold ionization peaks in the stabilization regime,” Phys. Rev. A 76, 043418–043425 (2007).
[CrossRef]

N. V. Bordyug and V. P. Krainov, “Dynamic resonances in ultra-short laser pulses,” Laser Phys. Lett. 4, 418–420 (2007).
[CrossRef]

2005 (3)

D. Bauer, “Emergence of classical orbits in few-cycle above-threshold ionization of atomic hydrogen,” Phys. Rev. Lett. 94, 113001–113004 (2005).
[CrossRef]

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

2000 (1)

J. R. Vazquez de Aldana and Luis Roso, “Non-relativistic numerical study of atomic ionization by strong laser fields without the dipole approximation in a flat-atom model,” Phys. Rev. A 61, 043403–043409 (2000).
[CrossRef]

1999 (2)

H. G. Muller, “An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge,” Laser Phys. 9, 138–148 (1999).

P. Salieres, A. lHuillier, P. Antoine, and M. Lewenstein, “Study of the spatial and temporal coherence of high-order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83–142 (1999).
[CrossRef]

1993 (1)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef]

1991 (2)

V. C. Reed and K. Burnett, “Role of resonances and quantum-mechanical interference in the generation of above-threshold-ionization spectra,” Phys. Rev. A 43, 6217–6226 (1991).
[CrossRef]

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamic stabilization of hydrogen in an intense, high-frequency, pulsed laser field,” Phys. Rev. Lett. 66, 2601–2604 (1991).
[CrossRef]

1990 (1)

K. J. Schafer and K. C. Kulander, “Energy analysis of time-dependent wave functions: application to above-threshold ionization,” Phys. Rev. A 42, 5794–5797 (1990).
[CrossRef]

1988 (1)

J. N. Bardsley, A. Szoke, and M. J. Comella, “Multiphoton ionization from a short-range potential by short-pulse lasers,” J. Phys. B 21, 3899–3916 (1988).
[CrossRef]

1979 (1)

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

1968 (1)

W. C. Henneberger, “Perturbation method for atoms in intense light beams,” Phys. Rev. Lett. 21, 838–841 (1968).
[CrossRef]

1965 (1)

G. S. Voronov, and N. B. Delone, “Ionization of the xenon atom by the electric field of ruby laser emission,” JETP 1, 66–68 (1965).

1931 (1)

M. Göppert-Mayer, “Über Elementarakte mit zwei Quantensprüngen,” Ann. Phys. 401, 273–294 (1931).
[CrossRef]

Agostini, P.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Antoine, P.

P. Salieres, A. lHuillier, P. Antoine, and M. Lewenstein, “Study of the spatial and temporal coherence of high-order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83–142 (1999).
[CrossRef]

Baltuška, A.

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

Bardsley, J. N.

J. N. Bardsley, A. Szoke, and M. J. Comella, “Multiphoton ionization from a short-range potential by short-pulse lasers,” J. Phys. B 21, 3899–3916 (1988).
[CrossRef]

Bauer, D.

T. M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, “Low-energy structures in strong field ionization revealed by quantum orbits,” Phys. Rev. Lett. 105, 253002–253005(2010).
[CrossRef]

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

D. Bauer, “Emergence of classical orbits in few-cycle above-threshold ionization of atomic hydrogen,” Phys. Rev. Lett. 94, 113001–113004 (2005).
[CrossRef]

Becker, W.

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

Belkacem, A.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Benedetti, E.

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

Bordyug, N. V.

N. V. Bordyug and V. P. Krainov, “Dynamic resonances in ultra-short laser pulses,” Laser Phys. Lett. 4, 418–420 (2007).
[CrossRef]

Burgdörfer, J.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Burnett, K.

V. C. Reed and K. Burnett, “Role of resonances and quantum-mechanical interference in the generation of above-threshold-ionization spectra,” Phys. Rev. A 43, 6217–6226 (1991).
[CrossRef]

Caumes, J.-P.

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

Chen, J.

L. Guo, S. S. Han, and J. Chen, “Time-energy analysis of above-threshold ionization,” Opt. Express 18, 1240–1248 (2010).
[CrossRef]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Chen, S. G.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Chen, Z.

T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
[CrossRef]

Cheng, Y.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Chu, S. I.

D. A. Telnov and S. I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: role of the Coulomb threshold effect,” Phys. Rev. A 83, 063406–063411 (2011).
[CrossRef]

Cole, K.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Collins, L. A.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Comella, M. J.

J. N. Bardsley, A. Szoke, and M. J. Comella, “Multiphoton ionization from a short-range potential by short-pulse lasers,” J. Phys. B 21, 3899–3916 (1988).
[CrossRef]

Corkum, P. B.

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef]

De Silvestri, S.

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

Delone, N. B.

G. S. Voronov, and N. B. Delone, “Ionization of the xenon atom by the electric field of ruby laser emission,” JETP 1, 66–68 (1965).

Dörner, R.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Düsterer, S.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Ebadi, H.

H. Ebadi, C. H. Keitel, and K. Z. Hatsagortsyan, “Time analysis of above-threshold ionization in extreme-ultraviolet laser pulses,” Phys. Rev. A 83, 063418–063425 (2011).
[CrossRef]

Engel, V.

J. Henkel, M. Lein, and V. Engel, “Interference in above-threshold-ionization electron distributions from molecules,” Phys. Rev. A 83, 051401 (2011).
[CrossRef]

Ergler, Th.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Fabre, F.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Feist, J.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Foucar, L.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Fu, Y.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Gavrila, M.

M. Gavrila, I. Simbotin, and M. Stroe, “Low-frequency atomic stabilization and dichotomy in super intense laser fields: full Floquet results,” Phys. Rev. A 78, 033404–033414 (2008).
[CrossRef]

Gensch, M.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Göppert-Mayer, M.

M. Göppert-Mayer, “Über Elementarakte mit zwei Quantensprüngen,” Ann. Phys. 401, 273–294 (1931).
[CrossRef]

Goulielmakis, E.

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

Guo, L.

L. Guo, S. S. Han, and J. Chen, “Time-energy analysis of above-threshold ionization,” Opt. Express 18, 1240–1248 (2010).
[CrossRef]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Han, S. S.

Hatsagortsyan, K. Z.

H. Ebadi, C. H. Keitel, and K. Z. Hatsagortsyan, “Time analysis of above-threshold ionization in extreme-ultraviolet laser pulses,” Phys. Rev. A 83, 063418–063425 (2011).
[CrossRef]

C. Liu and K. Z. Hatsagortsyan, “Origin of unexpected low energy structure in photoelectron spectra induced by mid-infrared strong laser fields,” Phys. Rev. Lett. 105, 113003(2010).
[CrossRef]

Havermeier, T.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

He, X. T.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Henkel, J.

J. Henkel, M. Lein, and V. Engel, “Interference in above-threshold-ionization electron distributions from molecules,” Phys. Rev. A 83, 051401 (2011).
[CrossRef]

Henneberger, W. C.

W. C. Henneberger, “Perturbation method for atoms in intense light beams,” Phys. Rev. Lett. 21, 838–841 (1968).
[CrossRef]

Herrwerth, O.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Horner, D. A.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Ivanov, M.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

Jiang, Y. H.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Kang, H.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Keitel, B.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Keitel, C. H.

H. Ebadi, C. H. Keitel, and K. Z. Hatsagortsyan, “Time analysis of above-threshold ionization in extreme-ultraviolet laser pulses,” Phys. Rev. A 83, 063418–063425 (2011).
[CrossRef]

Kheifets, A.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Kling, M. F.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Krainov, V. P.

N. V. Bordyug and V. P. Krainov, “Dynamic resonances in ultra-short laser pulses,” Laser Phys. Lett. 4, 418–420 (2007).
[CrossRef]

Kramers, H. A.

H. A. Kramers, Collected Scientific Papers (North-Holland, 1956) p. 272.

Krause, J. L.

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamic stabilization of hydrogen in an intense, high-frequency, pulsed laser field,” Phys. Rev. Lett. 66, 2601–2604 (1991).
[CrossRef]

K. J. Schafer, K. C. Kulander, and J. L. Krause, in Super-Intense Laser-Atom Physics (SILAP III), B. Piraux, ed. (NATO, Plenum Press, 1993), p. 95.

Krausz, F.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

Kühnel, K. U.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Kulander, K. C.

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamic stabilization of hydrogen in an intense, high-frequency, pulsed laser field,” Phys. Rev. Lett. 66, 2601–2604 (1991).
[CrossRef]

K. J. Schafer and K. C. Kulander, “Energy analysis of time-dependent wave functions: application to above-threshold ionization,” Phys. Rev. A 42, 5794–5797 (1990).
[CrossRef]

K. J. Schafer, K. C. Kulander, and J. L. Krause, in Super-Intense Laser-Atom Physics (SILAP III), B. Piraux, ed. (NATO, Plenum Press, 1993), p. 95.

Kurka, M.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Lein, M.

J. Henkel, M. Lein, and V. Engel, “Interference in above-threshold-ionization electron distributions from molecules,” Phys. Rev. A 83, 051401 (2011).
[CrossRef]

Lewenstein, M.

P. Salieres, A. lHuillier, P. Antoine, and M. Lewenstein, “Study of the spatial and temporal coherence of high-order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83–142 (1999).
[CrossRef]

Lezius, M.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

lHuillier, A.

P. Salieres, A. lHuillier, P. Antoine, and M. Lewenstein, “Study of the spatial and temporal coherence of high-order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83–142 (1999).
[CrossRef]

Li, W.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Lin, C. D.

T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
[CrossRef]

Lin, Z.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Lindner, F.

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

Liu, C.

C. Liu and K. Z. Hatsagortsyan, “Origin of unexpected low energy structure in photoelectron spectra induced by mid-infrared strong laser fields,” Phys. Rev. Lett. 105, 113003(2010).
[CrossRef]

Liu, H.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Liu, J.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Liu, X.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Lüdemann, S.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Mainfray, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Marchenko, T.

T. Marchenko, H. G. Muller, K. J. Schafer, and M. J. J. Vrakking, “Wavelength dependence of photoelectron spectra in above-threshold ionization,” J. Phys. B 43, 185001 (2010).
[CrossRef]

McCurdy, C. W.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Miloševic, D. B.

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

Morishita, T.

T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
[CrossRef]

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Slow electrons generated by intense high-frequency laser pulses,” Phys. Rev. Lett. 103, 153003–153006 (2009).
[CrossRef]

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Siegert-state expansion in the Kramers–Henneberger frame: interference substructure of above-threshold ionization peaks in the stabilization regime,” Phys. Rev. A 76, 043418–043425 (2007).
[CrossRef]

Moshammer, R.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Muller, H. G.

T. Marchenko, H. G. Muller, K. J. Schafer, and M. J. J. Vrakking, “Wavelength dependence of photoelectron spectra in above-threshold ionization,” J. Phys. B 43, 185001 (2010).
[CrossRef]

H. G. Muller, “An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge,” Laser Phys. 9, 138–148 (1999).

H. B. van den Heuvell and H. G. Muller, in Multiphoton Processes, S. J. Smith and P. L. Knight, eds. (Cambridge University, 1988), p. 25.

Nagele, S.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Najjari, B.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Nisoli, M.

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

Okunishi, M.

T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
[CrossRef]

Pascolini, M.

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

Paulus, G. G.

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

Pazourek, R.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Petite, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Poletto, L.

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

Popruzhenko, S. V.

T. M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, “Low-energy structures in strong field ionization revealed by quantum orbits,” Phys. Rev. Lett. 105, 253002–253005(2010).
[CrossRef]

Prümper, G.

T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
[CrossRef]

Quan, W.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Rahman, N. K.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Reed, V. C.

V. C. Reed and K. Burnett, “Role of resonances and quantum-mechanical interference in the generation of above-threshold-ionization spectra,” Phys. Rev. A 43, 6217–6226 (1991).
[CrossRef]

Rescigno, T. N.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Roso, Luis

J. R. Vazquez de Aldana and Luis Roso, “Non-relativistic numerical study of atomic ionization by strong laser fields without the dipole approximation in a flat-atom model,” Phys. Rev. A 61, 043403–043409 (2000).
[CrossRef]

Rudenko, A.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Salieres, P.

P. Salieres, A. lHuillier, P. Antoine, and M. Lewenstein, “Study of the spatial and temporal coherence of high-order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83–142 (1999).
[CrossRef]

Sansone, G.

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

Schafer, K. J.

T. Marchenko, H. G. Muller, K. J. Schafer, and M. J. J. Vrakking, “Wavelength dependence of photoelectron spectra in above-threshold ionization,” J. Phys. B 43, 185001 (2010).
[CrossRef]

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamic stabilization of hydrogen in an intense, high-frequency, pulsed laser field,” Phys. Rev. Lett. 66, 2601–2604 (1991).
[CrossRef]

K. J. Schafer and K. C. Kulander, “Energy analysis of time-dependent wave functions: application to above-threshold ionization,” Phys. Rev. A 42, 5794–5797 (1990).
[CrossRef]

K. J. Schafer, K. C. Kulander, and J. L. Krause, in Super-Intense Laser-Atom Physics (SILAP III), B. Piraux, ed. (NATO, Plenum Press, 1993), p. 95.

Schätzel, M. G.

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

Schneider, B. I.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Schöffler, M.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Schössler, S.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Schröter, C. D.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Schulz, M.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Shimada, K.

T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
[CrossRef]

Simbotin, I.

M. Gavrila, I. Simbotin, and M. Stroe, “Low-frequency atomic stabilization and dichotomy in super intense laser fields: full Floquet results,” Phys. Rev. A 78, 033404–033414 (2008).
[CrossRef]

Smolarski, M.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Stagira, S.

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

Stroe, M.

M. Gavrila, I. Simbotin, and M. Stroe, “Low-frequency atomic stabilization and dichotomy in super intense laser fields: full Floquet results,” Phys. Rev. A 78, 033404–033414 (2008).
[CrossRef]

Szoke, A.

J. N. Bardsley, A. Szoke, and M. J. Comella, “Multiphoton ionization from a short-range potential by short-pulse lasers,” J. Phys. B 21, 3899–3916 (1988).
[CrossRef]

Telnov, D. A.

D. A. Telnov and S. I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: role of the Coulomb threshold effect,” Phys. Rev. A 83, 063406–063411 (2011).
[CrossRef]

Tolstikhin, O.

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Slow electrons generated by intense high-frequency laser pulses,” Phys. Rev. Lett. 103, 153003–153006 (2009).
[CrossRef]

O. Tolstikhin, “Siegert-state expansion for non-stationary systems. IV. Three-dimensional case,” Phys. Rev. A 77, 032712–032721 (2008).
[CrossRef]

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Siegert-state expansion in the Kramers–Henneberger frame: interference substructure of above-threshold ionization peaks in the stabilization regime,” Phys. Rev. A 76, 043418–043425 (2007).
[CrossRef]

Toyota, K.

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Slow electrons generated by intense high-frequency laser pulses,” Phys. Rev. Lett. 103, 153003–153006 (2009).
[CrossRef]

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Siegert-state expansion in the Kramers–Henneberger frame: interference substructure of above-threshold ionization peaks in the stabilization regime,” Phys. Rev. A 76, 043418–043425 (2007).
[CrossRef]

Treusch, R.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Ueda, K.

T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
[CrossRef]

Ullrich, J.

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

van den Heuvell, H. B.

H. B. van den Heuvell and H. G. Muller, in Multiphoton Processes, S. J. Smith and P. L. Knight, eds. (Cambridge University, 1988), p. 25.

Varga, R. S.

R. S. Varga, Matrix Iterative Analysis (Prentice-Hall, 1962).

Vazquez de Aldana, J. R.

J. R. Vazquez de Aldana and Luis Roso, “Non-relativistic numerical study of atomic ionization by strong laser fields without the dipole approximation in a flat-atom model,” Phys. Rev. A 61, 043403–043409 (2000).
[CrossRef]

Villoresi, P.

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

Voitkiv, A.

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

Voronov, G. S.

G. S. Voronov, and N. B. Delone, “Ionization of the xenon atom by the electric field of ruby laser emission,” JETP 1, 66–68 (1965).

Vozzi, C.

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

Vrakking, M. J. J.

T. Marchenko, H. G. Muller, K. J. Schafer, and M. J. J. Vrakking, “Wavelength dependence of photoelectron spectra in above-threshold ionization,” J. Phys. B 43, 185001 (2010).
[CrossRef]

T. M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, “Low-energy structures in strong field ionization revealed by quantum orbits,” Phys. Rev. Lett. 105, 253002–253005(2010).
[CrossRef]

Walther, H.

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

Watanabe, S.

T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
[CrossRef]

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Slow electrons generated by intense high-frequency laser pulses,” Phys. Rev. Lett. 103, 153003–153006 (2009).
[CrossRef]

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Siegert-state expansion in the Kramers–Henneberger frame: interference substructure of above-threshold ionization peaks in the stabilization regime,” Phys. Rev. A 76, 043418–043425 (2007).
[CrossRef]

Wu, M.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Xiong, H.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Xu, H.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Xu, Z. Z.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

Yan, T. M.

T. M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, “Low-energy structures in strong field ionization revealed by quantum orbits,” Phys. Rev. Lett. 105, 253002–253005(2010).
[CrossRef]

Yuam, J.

Z. Zhou and J. Yuam, “Fine structures of the harmonic and hyper-Raman spectrum of the hydrogen atom in an intense high-frequency laser pulse,” Phys. Rev. A 77, 063411–063416 (2008).
[CrossRef]

Zhou, Z.

Z. Zhou and J. Yuam, “Fine structures of the harmonic and hyper-Raman spectrum of the hydrogen atom in an intense high-frequency laser pulse,” Phys. Rev. A 77, 063411–063416 (2008).
[CrossRef]

Adv. At. Mol. Opt. Phys. (1)

P. Salieres, A. lHuillier, P. Antoine, and M. Lewenstein, “Study of the spatial and temporal coherence of high-order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83–142 (1999).
[CrossRef]

Ann. Phys. (1)

M. Göppert-Mayer, “Über Elementarakte mit zwei Quantensprüngen,” Ann. Phys. 401, 273–294 (1931).
[CrossRef]

J. Phys. B (3)

T. Morishita, M. Okunishi, K. Shimada, G. Prümper, Z. Chen, S. Watanabe, K. Ueda, and C. D. Lin, “Retrieval of experimental differential electronion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers,” J. Phys. B 42, 105205 (2009).
[CrossRef]

T. Marchenko, H. G. Muller, K. J. Schafer, and M. J. J. Vrakking, “Wavelength dependence of photoelectron spectra in above-threshold ionization,” J. Phys. B 43, 185001 (2010).
[CrossRef]

J. N. Bardsley, A. Szoke, and M. J. Comella, “Multiphoton ionization from a short-range potential by short-pulse lasers,” J. Phys. B 21, 3899–3916 (1988).
[CrossRef]

JETP (1)

G. S. Voronov, and N. B. Delone, “Ionization of the xenon atom by the electric field of ruby laser emission,” JETP 1, 66–68 (1965).

Laser Phys. (1)

H. G. Muller, “An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge,” Laser Phys. 9, 138–148 (1999).

Laser Phys. Lett. (1)

N. V. Bordyug and V. P. Krainov, “Dynamic resonances in ultra-short laser pulses,” Laser Phys. Lett. 4, 418–420 (2007).
[CrossRef]

New J. Phys. (1)

M. Kurka, J. Feist, D. A. Horner, A. Rudenko, Y. H. Jiang, K. U. Kühnel, L. Foucar, T. N. Rescigno, C. W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M. F. Kling, M. Schöffler, A. Belkacem, S. Düsterer, R. Treusch, B. I. Schneider, L. A. Collins, J. Burgdörfer, C. D. Schröter, R. Moshammer, and J. Ullrich, “Differential cross sections for non-sequential double ionization of He by 52 eV photons from the Free Electron Laser in Hamburg, FLASH,” New J. Phys. 12, 073035–073051 (2010).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (10)

D. A. Telnov and S. I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: role of the Coulomb threshold effect,” Phys. Rev. A 83, 063406–063411 (2011).
[CrossRef]

V. C. Reed and K. Burnett, “Role of resonances and quantum-mechanical interference in the generation of above-threshold-ionization spectra,” Phys. Rev. A 43, 6217–6226 (1991).
[CrossRef]

J. Henkel, M. Lein, and V. Engel, “Interference in above-threshold-ionization electron distributions from molecules,” Phys. Rev. A 83, 051401 (2011).
[CrossRef]

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Siegert-state expansion in the Kramers–Henneberger frame: interference substructure of above-threshold ionization peaks in the stabilization regime,” Phys. Rev. A 76, 043418–043425 (2007).
[CrossRef]

O. Tolstikhin, “Siegert-state expansion for non-stationary systems. IV. Three-dimensional case,” Phys. Rev. A 77, 032712–032721 (2008).
[CrossRef]

K. J. Schafer and K. C. Kulander, “Energy analysis of time-dependent wave functions: application to above-threshold ionization,” Phys. Rev. A 42, 5794–5797 (1990).
[CrossRef]

Z. Zhou and J. Yuam, “Fine structures of the harmonic and hyper-Raman spectrum of the hydrogen atom in an intense high-frequency laser pulse,” Phys. Rev. A 77, 063411–063416 (2008).
[CrossRef]

H. Ebadi, C. H. Keitel, and K. Z. Hatsagortsyan, “Time analysis of above-threshold ionization in extreme-ultraviolet laser pulses,” Phys. Rev. A 83, 063418–063425 (2011).
[CrossRef]

J. R. Vazquez de Aldana and Luis Roso, “Non-relativistic numerical study of atomic ionization by strong laser fields without the dipole approximation in a flat-atom model,” Phys. Rev. A 61, 043403–043409 (2000).
[CrossRef]

M. Gavrila, I. Simbotin, and M. Stroe, “Low-frequency atomic stabilization and dichotomy in super intense laser fields: full Floquet results,” Phys. Rev. A 78, 033404–033414 (2008).
[CrossRef]

Phys. Rev. Lett. (12)

W. C. Henneberger, “Perturbation method for atoms in intense light beams,” Phys. Rev. Lett. 21, 838–841 (1968).
[CrossRef]

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamic stabilization of hydrogen in an intense, high-frequency, pulsed laser field,” Phys. Rev. Lett. 66, 2601–2604 (1991).
[CrossRef]

D. Bauer, “Emergence of classical orbits in few-cycle above-threshold ionization of atomic hydrogen,” Phys. Rev. Lett. 94, 113001–113004 (2005).
[CrossRef]

K. Toyota, O. Tolstikhin, T. Morishita, and S. Watanabe, “Slow electrons generated by intense high-frequency laser pulses,” Phys. Rev. Lett. 103, 153003–153006 (2009).
[CrossRef]

A. Rudenko, L. Foucar, M. Kurka, Th. Ergler, K. U. Kühnel, Y. H. Jiang, A. Voitkiv, B. Najjari, A. Kheifets, S. Lüdemann, T. Havermeier, M. Smolarski, S. Schössler, K. Cole, M. Schöffler, R. Dörner, S. Düsterer, W. Li, B. Keitel, R. Treusch, M. Gensch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation,” Phys. Rev. Lett. 101, 073003–073007 (2008).
[CrossRef]

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401–040404 (2005).
[CrossRef]

G. Sansone, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, S. De Silvestri, and M. Nisoli, “Measurement of harmonic phase differences by interference of attosecond light pulses,” Phys. Rev. Lett. 94, 193903 (2005).
[CrossRef]

T. M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, “Low-energy structures in strong field ionization revealed by quantum orbits,” Phys. Rev. Lett. 105, 253002–253005(2010).
[CrossRef]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001–093004 (2009).
[CrossRef]

C. Liu and K. Z. Hatsagortsyan, “Origin of unexpected low energy structure in photoelectron spectra induced by mid-infrared strong laser fields,” Phys. Rev. Lett. 105, 113003(2010).
[CrossRef]

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef]

Rev. Mod. Phys. (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

Other (5)

K. J. Schafer, K. C. Kulander, and J. L. Krause, in Super-Intense Laser-Atom Physics (SILAP III), B. Piraux, ed. (NATO, Plenum Press, 1993), p. 95.

H. B. van den Heuvell and H. G. Muller, in Multiphoton Processes, S. J. Smith and P. L. Knight, eds. (Cambridge University, 1988), p. 25.

http://hasylab.desy.de/facilities/flash/, http://lcls.slac.stanford.edu/, http://www-xfel.spring8.or.jp/.

H. A. Kramers, Collected Scientific Papers (North-Holland, 1956) p. 272.

R. S. Varga, Matrix Iterative Analysis (Prentice-Hall, 1962).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

To choose an appropriate laser intensity, the ionization probability of an atom (blue-gray 3D, black 1D) is shown as a function of the electric field of the laser pulse: (a) ω=3a.u.; (b) ω=0.4a.u. The laser pulse has a sin2 envelope with a zero flat duration and consists of 20 optical cycles.

Fig. 2.
Fig. 2.

(a), (b) The first two peaks of the log-scale ATI spectra of an atom irradiated by a laser pulse with frequency ω=3.0. The spectrum is calculated at θ=0 with γ=5×104. (c), (d) The time profile of the ionization probability at ε=2ωIP [corresponding to the second peak in (a) and (b)] with 2γ=2. (a) and (c) are in the MPI regime (E0=5) and (b) and (d) are in the stabilization regime (E0=25). The laser pulse consisting of 20 optical cycles is indicated with blue-gray line in (c) and (d). The results of the 1D model atom are shown with the green-dashed-gray line.

Fig. 3.
Fig. 3.

(a) Log-scale ATI spectrum of a hydrogen atom in an intense 80-cycle laser pulse including a five-cycle ramp with ω=3 and E0=25. The spectrum is calculated with γ=5×104 at θ=0. (b) The time profile of the ionized electron wave-packet at ε=2ωE1sKH with 2γ=2 is superimposed by the expectation value of the current density (green-gray line) from Fig. 5. The laser pulse is indicated with a red-filled line in (b). The results of the 1D model atom are shown with dashed-blue-gray line.

Fig. 4.
Fig. 4.

Schematic diagram of two-photon Raman coupling, which results in a coherent transition between two states with the same parity.

Fig. 5.
Fig. 5.

(a), (b) Polarization-direction-time profile of the current density of the hydrogen atom irradiated by a laser pulse with ω=3 and E0=25 in the KH frame. (c), (d) The time profile of the electron displacement in the KH frame. A sin2 laser pulse with 20 optical cycles is used in (a) and (c) and a 80-cycle laser pulse with a five-cycle ramp is used in (b) and (d). The results of the 1D model atom are shown with a blue-gray line.

Fig. 6.
Fig. 6.

Time profile of ionization of the hydrogen atom in a laser pulse at ε=2ωIP with 2γ=0.6a.u.. The laser pulse with ω=0.4 consisting 10 optical cycles is shown with a blue-gray line. The electric field of the laser pulse is E0=0.16 in (a) and E0=2.88 in (b). The results of the 1D model atom are indicated with a dashed-green-gray line [27].

Tables (4)

Tables Icon

Table 1. Energy Levels of a Hydrogen Atom

Tables Icon

Table 2. Energy Levels of a Hydrogen Atom in a High-Frequency Laser with ω=3.0 and E0=25

Tables Icon

Table 3. Energy Levels of a 1D Hydrogen Atom

Tables Icon

Table 4. Energy Levels of a 1D Hydrogen Atom in a High-Frequency Laser with ω=3.0 and E0=25

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

itΨ(r,t)={12(P^A(t)c)2+V(r)}Ψ(r,t).
f(t)={sin2(πt/2ton)0<t<ton1ton<t<toffsin2(π(tdt)/2ton)toff<t<td.
W^(ε,n,γ)=γ2n(H^0ε)2n+γ2n.
Pε=Ψf|W^2(ε,n,γ)|Ψf=Ψε(r)|Ψε(r).
ΨKH(r,t)=e1c0tA(t)dtei12c20tA2(t)dtΨLab.(r,t).
rKH(t)=ΨKH(r,t)|r|ΨKH(r,t)
jKH(t)=ImΨKH(r,t)||ΨKH(r,t),
Ψε(r,t;γ)=εγε+γcE(t)dEϕE(r,t)εγε+γdEcE(t)ϕE(r)F(EEj)eiEt+εγε+γdEcE(t)ϕE(r)F(EEk)eiEt,
Ψε(r,t)cEj(t)ϕEj(r)eiEjt+cEk(t)ϕEk(r)eiEkt,
ΨbKH(r,t)j=1,3cj(t)ψjKH(r,t)=c1sKH(t)ψ1sKH(r,t)+c2sKH(t)ψ2sKH(r,t),
jKH(t)cj(t)ck*(t)ψjKH(r)||ψjKH(r)ei(EkEj)t,

Metrics