Abstract

We theoretically investigated sequential double ionization (SDI) of Ar by the nearly circularly polarized laser pulses with a fully correlated classical ensemble model. The ion momentum distributions of our numerical results at various laser intensities and pulse durations agree well with the experimental results. The experimentally observed multi-electron effects embodied in the joint momentum spectrum of the two electrons is also reproduced by our correlated classical calculations. Interestingly, our calculations show that the angular distribution of the first photoelectron from the trajectories which eventually suffer SDI differs from the distribution of the photoelectrons from above-threshold ionization trajectories. This observation provides additional evidence of multi-electron effects in strong field SDI.

© 2012 OSA

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  1. P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett.71, 1994–1997 (1993).
    [CrossRef] [PubMed]
  2. K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett.70, 1599–1602 (1993).
    [CrossRef] [PubMed]
  3. Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000).
    [CrossRef] [PubMed]
  4. B. Walker, B. Sheehy, L. F. Dimauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionizaiton of helium,” Phys. Rev. Lett.73, 1227–1230 (1994).
    [CrossRef] [PubMed]
  5. B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
    [CrossRef] [PubMed]
  6. M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
    [CrossRef] [PubMed]
  7. A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett.93, 253001 (2004).
    [CrossRef]
  8. M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of helium: identifying the mechanism,” Phys. Rev. Lett.85, 4707–4710 (2000).
    [CrossRef] [PubMed]
  9. A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
    [CrossRef]
  10. S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Variable time lag and backward ejection in full-dimension analysis of strong field double ionization,” Phys. Rev. Lett.97, 103008 (2006).
    [CrossRef] [PubMed]
  11. Y. Zhou, C. Huang, A. Tong, Q. Liao, and P. Lu, “Correlated electron dynamics in nonsequential double ionization by orthogonal two-color laser pulses,” Opt. Express19, 2301–2308 (2011).
    [CrossRef] [PubMed]
  12. Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Lett.36, 2758–2760 (2011).
    [CrossRef] [PubMed]
  13. A. Becker, R. Dörner, and R. Moshammer,“Multiple fragmentation of atoms in femtosecond laser pulses,” J. Phys. B38, S753–S772 (2005).
    [CrossRef]
  14. Q. Liao, Y. Zhou, C. Huang, and P. Lu, “Multiphoton Rabi oscillations of correlated electrons in strong-field nonsequential double ionization,” New J. Phys.14, 013001 (2012).
    [CrossRef]
  15. B. Chang, P. R. Bolton, and D. N. Fittinghoff, “Closed-form solutions for the production of ions in the collisionless ionization of gases by intense lasers,” Phys. Rev. A47, 4193–4203 (1993).
    [CrossRef] [PubMed]
  16. K. I. Dimitriou, S. Yoshida, J. Burgdöfer, H. Shimada, H. Oyama, and Y. Yamazaki, “Momentum distribution of multiply charged ions produced by intense (50–70-PW/cm2) lasers,” Phys. Rev. A75, 013418 (2007).
    [CrossRef]
  17. N. I. Shvetsov-Shilovski, A. M. Sayler, T. Rathje, and G. G. Paulus, “Momentum distributions of sequential ionization,” Phys. Rev. A83, 033401 (2011).
    [CrossRef]
  18. A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
    [CrossRef] [PubMed]
  19. A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Döner, and U. Keller, “Timing the release in sequential double ionization,” Nature Phys.7, 428–433 (2011).
    [CrossRef]
  20. A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011).
    [CrossRef]
  21. S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Recollision dynamics and time delay in strong-field double ionization,” Opt. Express15, 767–778 (2007).
    [CrossRef] [PubMed]
  22. Y. Zhou, Q. Liao, and P. Lu, “Mechanism for high-energy electrons in nonsequential double ionization below the recollision-excitation threshold,” Phys. Rev. A80, 023412 (2009).
    [CrossRef]
  23. Y. Zhou, Q. Liao, and P. Lu, “Complex sub-laser-cycle electron dynamics in strong-field nonsequential triple ionizaion,” Opt. Express18, 16025–16034 (2010).
    [CrossRef] [PubMed]
  24. Phay J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett.94, 093002 (2005).
    [CrossRef] [PubMed]
  25. Y. Zhou, Q. Liao, and P. Lu, “Asymmetric electron energy sharing in strong-field double ionization of helium,” Phys. Rev. A82, 053402 (2010).
    [CrossRef]
  26. Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012).
    [CrossRef]
  27. A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys.8, 76–80 (2011).
    [CrossRef]
  28. N. I. Shvetsov-Shilovski, D. Dimitrovski, and L. B. Madsen, “Ionization in elliptically polarized pulses: Multi-electron polarization effects and asymmetry of photoelectron momentum distributions,” Phys. Rev. A85, 023428 (2012).
    [CrossRef]
  29. C. L. Kirschbaum and L. Wilets, “Classical many-body model for atomic collisions incorporating the Heisenberg and Pauli principles,” Phys. Rev. A21, 834–841 (1980).
    [CrossRef]
  30. D. Zajfman and D. Maor, “Heisenberg core in classical-trajectory monte carlo calculations of ionization and charge exchange,” Phys. Rev. Lett.56, 320–323 (1986).
    [CrossRef] [PubMed]
  31. J. S. Cohen, “Quasiclassical-trajectory Monte Carlo methods for collisions with two-electron atoms,” Phys. Rev. A54, 573–586 (1996).
    [CrossRef] [PubMed]
  32. W. A. Beck and L. Wilets, “Semiclassical description of proton stopping by atomic and molecular targets,” Phys. Rev. A55, 2821–2829 (1997).
    [CrossRef]
  33. C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A72, 041403R(2005).
    [CrossRef]
  34. X. Wang and J. H. Eberly, “Effects of elliptical polarization on strong-field short-pulse double ionization,” Phys. Rev. Lett.103, 103007 (2009).
    [CrossRef] [PubMed]
  35. S. V. Popruzhenko, G. G. Paulus, and D. Bauer, “Coulomb-corrected quantum trajectories in strong-field ionization,” Phys. Rev. A77, 053409 (2008).
    [CrossRef]
  36. S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, “Coulomb asymmetry in above-threshold ionization,” Phys. Rev. Lett.93, 233002 (2004).
    [CrossRef] [PubMed]
  37. A. Jaroń, J. Z. Kamińskia, and F. Ehlotzky, “Asymmetries in the angular distributions of above threshold ionization in an elliptically polarized laser field,” Opt. Commun.163, 115–121 (1999).
    [CrossRef]

2012

Q. Liao, Y. Zhou, C. Huang, and P. Lu, “Multiphoton Rabi oscillations of correlated electrons in strong-field nonsequential double ionization,” New J. Phys.14, 013001 (2012).
[CrossRef]

Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012).
[CrossRef]

N. I. Shvetsov-Shilovski, D. Dimitrovski, and L. B. Madsen, “Ionization in elliptically polarized pulses: Multi-electron polarization effects and asymmetry of photoelectron momentum distributions,” Phys. Rev. A85, 023428 (2012).
[CrossRef]

2011

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys.8, 76–80 (2011).
[CrossRef]

Y. Zhou, C. Huang, A. Tong, Q. Liao, and P. Lu, “Correlated electron dynamics in nonsequential double ionization by orthogonal two-color laser pulses,” Opt. Express19, 2301–2308 (2011).
[CrossRef] [PubMed]

Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Lett.36, 2758–2760 (2011).
[CrossRef] [PubMed]

N. I. Shvetsov-Shilovski, A. M. Sayler, T. Rathje, and G. G. Paulus, “Momentum distributions of sequential ionization,” Phys. Rev. A83, 033401 (2011).
[CrossRef]

A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
[CrossRef] [PubMed]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Döner, and U. Keller, “Timing the release in sequential double ionization,” Nature Phys.7, 428–433 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011).
[CrossRef]

2010

Y. Zhou, Q. Liao, and P. Lu, “Asymmetric electron energy sharing in strong-field double ionization of helium,” Phys. Rev. A82, 053402 (2010).
[CrossRef]

Y. Zhou, Q. Liao, and P. Lu, “Complex sub-laser-cycle electron dynamics in strong-field nonsequential triple ionizaion,” Opt. Express18, 16025–16034 (2010).
[CrossRef] [PubMed]

2009

Y. Zhou, Q. Liao, and P. Lu, “Mechanism for high-energy electrons in nonsequential double ionization below the recollision-excitation threshold,” Phys. Rev. A80, 023412 (2009).
[CrossRef]

X. Wang and J. H. Eberly, “Effects of elliptical polarization on strong-field short-pulse double ionization,” Phys. Rev. Lett.103, 103007 (2009).
[CrossRef] [PubMed]

2008

S. V. Popruzhenko, G. G. Paulus, and D. Bauer, “Coulomb-corrected quantum trajectories in strong-field ionization,” Phys. Rev. A77, 053409 (2008).
[CrossRef]

2007

K. I. Dimitriou, S. Yoshida, J. Burgdöfer, H. Shimada, H. Oyama, and Y. Yamazaki, “Momentum distribution of multiply charged ions produced by intense (50–70-PW/cm2) lasers,” Phys. Rev. A75, 013418 (2007).
[CrossRef]

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Recollision dynamics and time delay in strong-field double ionization,” Opt. Express15, 767–778 (2007).
[CrossRef] [PubMed]

A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
[CrossRef]

2006

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Variable time lag and backward ejection in full-dimension analysis of strong field double ionization,” Phys. Rev. Lett.97, 103008 (2006).
[CrossRef] [PubMed]

2005

A. Becker, R. Dörner, and R. Moshammer,“Multiple fragmentation of atoms in femtosecond laser pulses,” J. Phys. B38, S753–S772 (2005).
[CrossRef]

Phay J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett.94, 093002 (2005).
[CrossRef] [PubMed]

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A72, 041403R(2005).
[CrossRef]

2004

S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, “Coulomb asymmetry in above-threshold ionization,” Phys. Rev. Lett.93, 233002 (2004).
[CrossRef] [PubMed]

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett.93, 253001 (2004).
[CrossRef]

2001

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

2000

M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of helium: identifying the mechanism,” Phys. Rev. Lett.85, 4707–4710 (2000).
[CrossRef] [PubMed]

Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000).
[CrossRef] [PubMed]

1999

A. Jaroń, J. Z. Kamińskia, and F. Ehlotzky, “Asymmetries in the angular distributions of above threshold ionization in an elliptically polarized laser field,” Opt. Commun.163, 115–121 (1999).
[CrossRef]

1997

W. A. Beck and L. Wilets, “Semiclassical description of proton stopping by atomic and molecular targets,” Phys. Rev. A55, 2821–2829 (1997).
[CrossRef]

1996

J. S. Cohen, “Quasiclassical-trajectory Monte Carlo methods for collisions with two-electron atoms,” Phys. Rev. A54, 573–586 (1996).
[CrossRef] [PubMed]

1994

B. Walker, B. Sheehy, L. F. Dimauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionizaiton of helium,” Phys. Rev. Lett.73, 1227–1230 (1994).
[CrossRef] [PubMed]

1993

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

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett.70, 1599–1602 (1993).
[CrossRef] [PubMed]

B. Chang, P. R. Bolton, and D. N. Fittinghoff, “Closed-form solutions for the production of ions in the collisionless ionization of gases by intense lasers,” Phys. Rev. A47, 4193–4203 (1993).
[CrossRef] [PubMed]

1986

D. Zajfman and D. Maor, “Heisenberg core in classical-trajectory monte carlo calculations of ionization and charge exchange,” Phys. Rev. Lett.56, 320–323 (1986).
[CrossRef] [PubMed]

1980

C. L. Kirschbaum and L. Wilets, “Classical many-body model for atomic collisions incorporating the Heisenberg and Pauli principles,” Phys. Rev. A21, 834–841 (1980).
[CrossRef]

Abu-samha, M.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys.8, 76–80 (2011).
[CrossRef]

Agostini, P.

B. Walker, B. Sheehy, L. F. Dimauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionizaiton of helium,” Phys. Rev. Lett.73, 1227–1230 (1994).
[CrossRef] [PubMed]

Alnaser, A. S.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A72, 041403R(2005).
[CrossRef]

Arissian, L.

A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
[CrossRef] [PubMed]

Bauer, D.

S. V. Popruzhenko, G. G. Paulus, and D. Bauer, “Coulomb-corrected quantum trajectories in strong-field ionization,” Phys. Rev. A77, 053409 (2008).
[CrossRef]

Beck, W. A.

W. A. Beck and L. Wilets, “Semiclassical description of proton stopping by atomic and molecular targets,” Phys. Rev. A55, 2821–2829 (1997).
[CrossRef]

Becker, A.

A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
[CrossRef]

A. Becker, R. Dörner, and R. Moshammer,“Multiple fragmentation of atoms in femtosecond laser pulses,” J. Phys. B38, S753–S772 (2005).
[CrossRef]

Bhardwaj, V. R.

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

Bolton, P. R.

B. Chang, P. R. Bolton, and D. N. Fittinghoff, “Closed-form solutions for the production of ions in the collisionless ionization of gases by intense lasers,” Phys. Rev. A47, 4193–4203 (1993).
[CrossRef] [PubMed]

Breen, L.

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Recollision dynamics and time delay in strong-field double ionization,” Opt. Express15, 767–778 (2007).
[CrossRef] [PubMed]

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Variable time lag and backward ejection in full-dimension analysis of strong field double ionization,” Phys. Rev. Lett.97, 103008 (2006).
[CrossRef] [PubMed]

Burgdöfer, J.

K. I. Dimitriou, S. Yoshida, J. Burgdöfer, H. Shimada, H. Oyama, and Y. Yamazaki, “Momentum distribution of multiply charged ions produced by intense (50–70-PW/cm2) lasers,” Phys. Rev. A75, 013418 (2007).
[CrossRef]

Chang, B.

B. Chang, P. R. Bolton, and D. N. Fittinghoff, “Closed-form solutions for the production of ions in the collisionless ionization of gases by intense lasers,” Phys. Rev. A47, 4193–4203 (1993).
[CrossRef] [PubMed]

Chang, Z.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A72, 041403R(2005).
[CrossRef]

Cirelli, C.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys.8, 76–80 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Döner, and U. Keller, “Timing the release in sequential double ionization,” Nature Phys.7, 428–433 (2011).
[CrossRef]

Cocke, C. L.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A72, 041403R(2005).
[CrossRef]

Cohen, J. S.

J. S. Cohen, “Quasiclassical-trajectory Monte Carlo methods for collisions with two-electron atoms,” Phys. Rev. A54, 573–586 (1996).
[CrossRef] [PubMed]

Corkum, P. B.

A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
[CrossRef] [PubMed]

A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
[CrossRef]

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

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

Crespo Lopez-Urrutia, J. R.

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

de Jesus, V. L. B.

A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett.93, 253001 (2004).
[CrossRef]

Deipenwisch, J.

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

Dimauro, L. F.

B. Walker, B. Sheehy, L. F. Dimauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionizaiton of helium,” Phys. Rev. Lett.73, 1227–1230 (1994).
[CrossRef] [PubMed]

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett.70, 1599–1602 (1993).
[CrossRef] [PubMed]

Dimitriou, K. I.

K. I. Dimitriou, S. Yoshida, J. Burgdöfer, H. Shimada, H. Oyama, and Y. Yamazaki, “Momentum distribution of multiply charged ions produced by intense (50–70-PW/cm2) lasers,” Phys. Rev. A75, 013418 (2007).
[CrossRef]

Dimitrovski, D.

N. I. Shvetsov-Shilovski, D. Dimitrovski, and L. B. Madsen, “Ionization in elliptically polarized pulses: Multi-electron polarization effects and asymmetry of photoelectron momentum distributions,” Phys. Rev. A85, 023428 (2012).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys.8, 76–80 (2011).
[CrossRef]

Döner, R.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Döner, and U. Keller, “Timing the release in sequential double ionization,” Nature Phys.7, 428–433 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011).
[CrossRef]

Dorn, A.

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

Dörner, R.

A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
[CrossRef] [PubMed]

A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
[CrossRef]

A. Becker, R. Dörner, and R. Moshammer,“Multiple fragmentation of atoms in femtosecond laser pulses,” J. Phys. B38, S753–S772 (2005).
[CrossRef]

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000).
[CrossRef] [PubMed]

Eberly, J. H.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011).
[CrossRef]

X. Wang and J. H. Eberly, “Effects of elliptical polarization on strong-field short-pulse double ionization,” Phys. Rev. Lett.103, 103007 (2009).
[CrossRef] [PubMed]

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Recollision dynamics and time delay in strong-field double ionization,” Opt. Express15, 767–778 (2007).
[CrossRef] [PubMed]

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Variable time lag and backward ejection in full-dimension analysis of strong field double ionization,” Phys. Rev. Lett.97, 103008 (2006).
[CrossRef] [PubMed]

Phay J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett.94, 093002 (2005).
[CrossRef] [PubMed]

Ehlotzky, F.

A. Jaroń, J. Z. Kamińskia, and F. Ehlotzky, “Asymmetries in the angular distributions of above threshold ionization in an elliptically polarized laser field,” Opt. Commun.163, 115–121 (1999).
[CrossRef]

Engel, V.

M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of helium: identifying the mechanism,” Phys. Rev. Lett.85, 4707–4710 (2000).
[CrossRef] [PubMed]

Feuerstein, B.

A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett.93, 253001 (2004).
[CrossRef]

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

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B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
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B. Chang, P. R. Bolton, and D. N. Fittinghoff, “Closed-form solutions for the production of ions in the collisionless ionization of gases by intense lasers,” Phys. Rev. A47, 4193–4203 (1993).
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A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
[CrossRef] [PubMed]

Ghimire, S.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A72, 041403R(2005).
[CrossRef]

Giessen, H.

Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000).
[CrossRef] [PubMed]

Goreslavski, S. P.

S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, “Coulomb asymmetry in above-threshold ionization,” Phys. Rev. Lett.93, 233002 (2004).
[CrossRef] [PubMed]

Gross, E. K. U.

M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of helium: identifying the mechanism,” Phys. Rev. Lett.85, 4707–4710 (2000).
[CrossRef] [PubMed]

Haan, S. L.

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Recollision dynamics and time delay in strong-field double ionization,” Opt. Express15, 767–778 (2007).
[CrossRef] [PubMed]

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Variable time lag and backward ejection in full-dimension analysis of strong field double ionization,” Phys. Rev. Lett.97, 103008 (2006).
[CrossRef] [PubMed]

Phay J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett.94, 093002 (2005).
[CrossRef] [PubMed]

Ho, Phay J.

Phay J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett.94, 093002 (2005).
[CrossRef] [PubMed]

Höhr, C.

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

Hong, W.

Huang, C.

Q. Liao, Y. Zhou, C. Huang, and P. Lu, “Multiphoton Rabi oscillations of correlated electrons in strong-field nonsequential double ionization,” New J. Phys.14, 013001 (2012).
[CrossRef]

Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012).
[CrossRef]

Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Lett.36, 2758–2760 (2011).
[CrossRef] [PubMed]

Y. Zhou, C. Huang, A. Tong, Q. Liao, and P. Lu, “Correlated electron dynamics in nonsequential double ionization by orthogonal two-color laser pulses,” Opt. Express19, 2301–2308 (2011).
[CrossRef] [PubMed]

Jagutzki, O.

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000).
[CrossRef] [PubMed]

Jaron, A.

A. Jaroń, J. Z. Kamińskia, and F. Ehlotzky, “Asymmetries in the angular distributions of above threshold ionization in an elliptically polarized laser field,” Opt. Commun.163, 115–121 (1999).
[CrossRef]

Kaminskia, J. Z.

A. Jaroń, J. Z. Kamińskia, and F. Ehlotzky, “Asymmetries in the angular distributions of above threshold ionization in an elliptically polarized laser field,” Opt. Commun.163, 115–121 (1999).
[CrossRef]

Kammer, S.

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

Karim, A.

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Recollision dynamics and time delay in strong-field double ionization,” Opt. Express15, 767–778 (2007).
[CrossRef] [PubMed]

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Variable time lag and backward ejection in full-dimension analysis of strong field double ionization,” Phys. Rev. Lett.97, 103008 (2006).
[CrossRef] [PubMed]

Keller, U.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Döner, and U. Keller, “Timing the release in sequential double ionization,” Nature Phys.7, 428–433 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys.8, 76–80 (2011).
[CrossRef]

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C. L. Kirschbaum and L. Wilets, “Classical many-body model for atomic collisions incorporating the Heisenberg and Pauli principles,” Phys. Rev. A21, 834–841 (1980).
[CrossRef]

Korn, G.

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

Kulander, K. C.

B. Walker, B. Sheehy, L. F. Dimauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionizaiton of helium,” Phys. Rev. Lett.73, 1227–1230 (1994).
[CrossRef] [PubMed]

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett.70, 1599–1602 (1993).
[CrossRef] [PubMed]

Lein, M.

M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of helium: identifying the mechanism,” Phys. Rev. Lett.85, 4707–4710 (2000).
[CrossRef] [PubMed]

Liao, Q.

Q. Liao, Y. Zhou, C. Huang, and P. Lu, “Multiphoton Rabi oscillations of correlated electrons in strong-field nonsequential double ionization,” New J. Phys.14, 013001 (2012).
[CrossRef]

Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012).
[CrossRef]

Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Lett.36, 2758–2760 (2011).
[CrossRef] [PubMed]

Y. Zhou, C. Huang, A. Tong, Q. Liao, and P. Lu, “Correlated electron dynamics in nonsequential double ionization by orthogonal two-color laser pulses,” Opt. Express19, 2301–2308 (2011).
[CrossRef] [PubMed]

Y. Zhou, Q. Liao, and P. Lu, “Complex sub-laser-cycle electron dynamics in strong-field nonsequential triple ionizaion,” Opt. Express18, 16025–16034 (2010).
[CrossRef] [PubMed]

Y. Zhou, Q. Liao, and P. Lu, “Asymmetric electron energy sharing in strong-field double ionization of helium,” Phys. Rev. A82, 053402 (2010).
[CrossRef]

Y. Zhou, Q. Liao, and P. Lu, “Mechanism for high-energy electrons in nonsequential double ionization below the recollision-excitation threshold,” Phys. Rev. A80, 023412 (2009).
[CrossRef]

Litvinyuk, I. V.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A72, 041403R(2005).
[CrossRef]

Liu, L. R.

A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
[CrossRef] [PubMed]

Lu, P.

Q. Liao, Y. Zhou, C. Huang, and P. Lu, “Multiphoton Rabi oscillations of correlated electrons in strong-field nonsequential double ionization,” New J. Phys.14, 013001 (2012).
[CrossRef]

Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012).
[CrossRef]

Y. Zhou, C. Huang, A. Tong, Q. Liao, and P. Lu, “Correlated electron dynamics in nonsequential double ionization by orthogonal two-color laser pulses,” Opt. Express19, 2301–2308 (2011).
[CrossRef] [PubMed]

Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Lett.36, 2758–2760 (2011).
[CrossRef] [PubMed]

Y. Zhou, Q. Liao, and P. Lu, “Complex sub-laser-cycle electron dynamics in strong-field nonsequential triple ionizaion,” Opt. Express18, 16025–16034 (2010).
[CrossRef] [PubMed]

Y. Zhou, Q. Liao, and P. Lu, “Asymmetric electron energy sharing in strong-field double ionization of helium,” Phys. Rev. A82, 053402 (2010).
[CrossRef]

Y. Zhou, Q. Liao, and P. Lu, “Mechanism for high-energy electrons in nonsequential double ionization below the recollision-excitation threshold,” Phys. Rev. A80, 023412 (2009).
[CrossRef]

Madsen, L. B.

N. I. Shvetsov-Shilovski, D. Dimitrovski, and L. B. Madsen, “Ionization in elliptically polarized pulses: Multi-electron polarization effects and asymmetry of photoelectron momentum distributions,” Phys. Rev. A85, 023428 (2012).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys.8, 76–80 (2011).
[CrossRef]

Maharjan, C. M.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A72, 041403R(2005).
[CrossRef]

Maor, D.

D. Zajfman and D. Maor, “Heisenberg core in classical-trajectory monte carlo calculations of ionization and charge exchange,” Phys. Rev. Lett.56, 320–323 (1986).
[CrossRef] [PubMed]

Meckel, M.

A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
[CrossRef] [PubMed]

A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
[CrossRef]

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

Mergel, V.

Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000).
[CrossRef] [PubMed]

Moshammer, R.

A. Becker, R. Dörner, and R. Moshammer,“Multiple fragmentation of atoms in femtosecond laser pulses,” J. Phys. B38, S753–S772 (2005).
[CrossRef]

A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett.93, 253001 (2004).
[CrossRef]

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

Neumayer, P.

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

Oyama, H.

K. I. Dimitriou, S. Yoshida, J. Burgdöfer, H. Shimada, H. Oyama, and Y. Yamazaki, “Momentum distribution of multiply charged ions produced by intense (50–70-PW/cm2) lasers,” Phys. Rev. A75, 013418 (2007).
[CrossRef]

Panfili, R.

Phay J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett.94, 093002 (2005).
[CrossRef] [PubMed]

Paulus, G. G.

N. I. Shvetsov-Shilovski, A. M. Sayler, T. Rathje, and G. G. Paulus, “Momentum distributions of sequential ionization,” Phys. Rev. A83, 033401 (2011).
[CrossRef]

S. V. Popruzhenko, G. G. Paulus, and D. Bauer, “Coulomb-corrected quantum trajectories in strong-field ionization,” Phys. Rev. A77, 053409 (2008).
[CrossRef]

S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, “Coulomb asymmetry in above-threshold ionization,” Phys. Rev. Lett.93, 233002 (2004).
[CrossRef] [PubMed]

Pfeiffer, A. N.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys.8, 76–80 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Döner, and U. Keller, “Timing the release in sequential double ionization,” Nature Phys.7, 428–433 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011).
[CrossRef]

Popruzhenko, S. V.

S. V. Popruzhenko, G. G. Paulus, and D. Bauer, “Coulomb-corrected quantum trajectories in strong-field ionization,” Phys. Rev. A77, 053409 (2008).
[CrossRef]

S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, “Coulomb asymmetry in above-threshold ionization,” Phys. Rev. Lett.93, 233002 (2004).
[CrossRef] [PubMed]

Ranitovic, P.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A72, 041403R(2005).
[CrossRef]

Rathje, T.

N. I. Shvetsov-Shilovski, A. M. Sayler, T. Rathje, and G. G. Paulus, “Momentum distributions of sequential ionization,” Phys. Rev. A83, 033401 (2011).
[CrossRef]

Rayner, D.M.

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

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A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
[CrossRef] [PubMed]

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B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

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A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett.93, 253001 (2004).
[CrossRef]

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A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
[CrossRef]

Sandner, W.

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
[CrossRef] [PubMed]

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N. I. Shvetsov-Shilovski, A. M. Sayler, T. Rathje, and G. G. Paulus, “Momentum distributions of sequential ionization,” Phys. Rev. A83, 033401 (2011).
[CrossRef]

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B. Walker, B. Sheehy, L. F. Dimauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionizaiton of helium,” Phys. Rev. Lett.73, 1227–1230 (1994).
[CrossRef] [PubMed]

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett.70, 1599–1602 (1993).
[CrossRef] [PubMed]

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A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
[CrossRef]

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

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A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
[CrossRef]

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A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett.93, 253001 (2004).
[CrossRef]

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
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B. Walker, B. Sheehy, L. F. Dimauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionizaiton of helium,” Phys. Rev. Lett.73, 1227–1230 (1994).
[CrossRef] [PubMed]

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K. I. Dimitriou, S. Yoshida, J. Burgdöfer, H. Shimada, H. Oyama, and Y. Yamazaki, “Momentum distribution of multiply charged ions produced by intense (50–70-PW/cm2) lasers,” Phys. Rev. A75, 013418 (2007).
[CrossRef]

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N. I. Shvetsov-Shilovski, D. Dimitrovski, and L. B. Madsen, “Ionization in elliptically polarized pulses: Multi-electron polarization effects and asymmetry of photoelectron momentum distributions,” Phys. Rev. A85, 023428 (2012).
[CrossRef]

N. I. Shvetsov-Shilovski, A. M. Sayler, T. Rathje, and G. G. Paulus, “Momentum distributions of sequential ionization,” Phys. Rev. A83, 033401 (2011).
[CrossRef]

S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, “Coulomb asymmetry in above-threshold ionization,” Phys. Rev. Lett.93, 233002 (2004).
[CrossRef] [PubMed]

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A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys.8, 76–80 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Döner, and U. Keller, “Timing the release in sequential double ionization,” Nature Phys.7, 428–433 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011).
[CrossRef]

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

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Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000).
[CrossRef] [PubMed]

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A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
[CrossRef] [PubMed]

A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
[CrossRef]

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
[CrossRef] [PubMed]

Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000).
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Tong, X. M.

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A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett.93, 253001 (2004).
[CrossRef]

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001).
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A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
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M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
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B. Walker, B. Sheehy, L. F. Dimauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionizaiton of helium,” Phys. Rev. Lett.73, 1227–1230 (1994).
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A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011).
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A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett.99, 263002 (2007).
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M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
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Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000).
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Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000).
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A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011).
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K. I. Dimitriou, S. Yoshida, J. Burgdöfer, H. Shimada, H. Oyama, and Y. Yamazaki, “Momentum distribution of multiply charged ions produced by intense (50–70-PW/cm2) lasers,” Phys. Rev. A75, 013418 (2007).
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K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett.70, 1599–1602 (1993).
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M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004).
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A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett.93, 253001 (2004).
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A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Döner, and U. Keller, “Timing the release in sequential double ionization,” Nature Phys.7, 428–433 (2011).
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A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011).
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Figures (5)

Fig. 1
Fig. 1

Ion momentum distributions in the polarization plane for (a)–(c) 7-fs and (d)–(f) 33-fs laser pulses. The laser intensities are (a) and (d) 1.5 PW/cm2, (b) and (e) 3.0 PW/cm2, respectively. In (c) and (f), the peak intensity is 3.0 PW/cm2, and the volume effect assuming a gaussian laser beam has been taken into account.

Fig. 2
Fig. 2

The joint momentum distribution of the two electrons from SDI along the minor axis of the polarization. The laser parameters are the same as those in ref. [20], i.e, the wavelength, ellipticity, pulse duration and laser intensity are 740 nm, 0.78, 7 fs and 3.0 PW/cm2, respectively. The volume effect assuming a gaussian laser beam has been considered. The CEP is randomly chosen for each trajectory.

Fig. 3
Fig. 3

(a) The momentum distribution in the polarization plane for the photoelectrons from above-threshold ionization of Ar. (b) The angular distribution of the electrons shown in (a). The red curve corresponds to the double gaussian fitting function. θ indicates the offset angle. The pulse duration, wavelength, ellipticity and the laser intensity are 7 fs, 740 nm,0.78 and 1.0 PW/cm2, respectively. The CEP is randomly chosen for each trajectory.

Fig. 4
Fig. 4

The intensity-dependent offset angle of the photoelectrons from ATI of Ar. The error bars show the standard deviation of a double gaussian fit of the angular distributions. (a) The atom is modeled with the single-active-electron assumption [formula (4)]. (b) The atom is treated as a two-active-electron system [formula (1)]. The laser parameters are the same as those in the experiment [27], i.e., the pulse duration, wavelength and ellipticity are 7 fs, 740 nm and 0.78, respectively. The CEP is randomly chosen for each trajectory.

Fig. 5
Fig. 5

The offset angle of the photoelectrons as a function of laser intensity. Green squares: the distribution for the photoelectrons from ATI trajectories. Magenta triangles: the distribution for the first electrons from SDI trajectories. The error bars show the standard deviation of a double gaussian fit of the angular distribution. The pulse durations are (a) 7 fs and (b) 33 fs. The ensemble sizes for the 7-fs and 33-fs pulses are 60000 and 30000, respectively. Depending on the laser intensity, tens of thousands of ATI and SDI trajectories are collected. The convergence of our results are confirmed by enlarging the ensemble sizes.

Equations (4)

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H = 1 | r 1 r 2 | + i = 1 , 2 [ 2 r i + p i 2 2 + V H ( r i , p i ) ] + [ r 1 + r 2 ] E ( t )
V H ( r i , p i ) = ξ 2 4 α r i 2 exp { α [ 1 ( r i p i ξ ) 4 ] }
d r i d t = H p i , d p i d t = H r i
H = 1 r 1 + p 1 2 2 + V H ( r 1 , p 1 ) + r 1 E ( t )

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