Abstract

The influence of carrier-envelope phase (CEP) of a few-cycle laser pulse on non-sequential double ionization (NSDI) of an atom is investigated by applying the three-dimensional semi-classical re-scattering method. The asymmetric momentum distribution of the double-charged ion parallel to the laser polarization, which depends on the CEP, is explained by comparing the contributions from several half-cycles in the laser pulse. The ionization rate and the returning kinetic energy of the first electron dramatically affect the contributions from each half-cycles, and play different roles in different laser intensity regimes.

© 2008 Optical Society of America

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2006

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

2003

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

2000

J. G. Leopold and I. C. Percival, "Ionisation of highly excited atoms by electric fields 3. microwave ionisation and excitation," J. Phys. B. 33, L823-L830 (2000).

1999

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hänsch, "Measuring the frequency of light with mode-locked lasers," Opt. Commun. 172, 59-68 (1999).
[CrossRef]

1997

B Hu, J. Liu, and S. G. Chen, "Plateau in above-threshold-ionization spectra and chaotic behavior in rescattering processes," Phys. Lett. A 236, 533-542 (1997).
[CrossRef]

1996

J. Liu, S. G. Chen, and D. H. Bao, "ATI spectra and angular distributions of the ionized electrons in strong fields: classical approaches," Commun. Theor. Phys 25, 129-134 (1996).

1994

B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, "Precision measurement of strong field double ionization 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]

1986

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. Jetp. 64, 1191-1194 (1986).

1982

J. S. Cohen, "Comment on the classical-trajectory Monte Carlo method for ion-atom collisions," Phys. Rev. A 26, 3008-3010 (1982).
[CrossRef]

M. Y. Amusia and M. Y. Kuchiev, "Multiple pole in the electron-hydrogen-atom scattering amplitude," Phys. Rev. Lett. 48, 1726-1729 (1982).
[CrossRef]

1979

B. Feuerstein, R. Moshammer, and J. Ullrich, "Nonsequential multiple ionization in intense laser pulses: interpretation of ion momentum distribution within the classical ‘rescattering’ model," J. Phys. B. 12, 709-721 (1979).

1966

R. Abrines and I. C. Percival, "Classical theory of charge transfer and ionization of hydrogen atoms by protons," Proc. Phys. Soc. London 88, 861-872 (1966).
[CrossRef]

Abrines, R.

R. Abrines and I. C. Percival, "Classical theory of charge transfer and ionization of hydrogen atoms by protons," Proc. Phys. Soc. London 88, 861-872 (1966).
[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 ionization of helium," Phys. Rev. Lett. 73, 1227-1230 (1994).
[CrossRef] [PubMed]

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. Jetp. 64, 1191-1194 (1986).

Amusia, M. Y.

M. Y. Amusia and M. Y. Kuchiev, "Multiple pole in the electron-hydrogen-atom scattering amplitude," Phys. Rev. Lett. 48, 1726-1729 (1982).
[CrossRef]

Bao, D. H.

J. Liu, S. G. Chen, and D. H. Bao, "ATI spectra and angular distributions of the ionized electrons in strong fields: classical approaches," Commun. Theor. Phys 25, 129-134 (1996).

Chen, S. G.

B Hu, J. Liu, and S. G. Chen, "Plateau in above-threshold-ionization spectra and chaotic behavior in rescattering processes," Phys. Lett. A 236, 533-542 (1997).
[CrossRef]

J. Liu, S. G. Chen, and D. H. Bao, "ATI spectra and angular distributions of the ionized electrons in strong fields: classical approaches," Commun. Theor. Phys 25, 129-134 (1996).

Cohen, J. S.

J. S. Cohen, "Comment on the classical-trajectory Monte Carlo method for ion-atom collisions," Phys. Rev. A 26, 3008-3010 (1982).
[CrossRef]

Corkum, P. B.

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

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. Jetp. 64, 1191-1194 (1986).

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 ionization 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]

Dreischuh, A.

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

Eremina, E.

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

Ermina, E.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

Feuerstein, B.

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

B. Feuerstein, R. Moshammer, and J. Ullrich, "Nonsequential multiple ionization in intense laser pulses: interpretation of ion momentum distribution within the classical ‘rescattering’ model," J. Phys. B. 12, 709-721 (1979).

Goulielmakis, E.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

Grasbon, F.

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

Hänsch, T. W.

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hänsch, "Measuring the frequency of light with mode-locked lasers," Opt. Commun. 172, 59-68 (1999).
[CrossRef]

Holzwarth, R.

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hänsch, "Measuring the frequency of light with mode-locked lasers," Opt. Commun. 172, 59-68 (1999).
[CrossRef]

Hu, B

B Hu, J. Liu, and S. G. Chen, "Plateau in above-threshold-ionization spectra and chaotic behavior in rescattering processes," Phys. Lett. A 236, 533-542 (1997).
[CrossRef]

Keeffe, K. O.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

Krainov, V. P.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. Jetp. 64, 1191-1194 (1986).

Krausz, F.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

Kuchiev, M. Y.

M. Y. Amusia and M. Y. Kuchiev, "Multiple pole in the electron-hydrogen-atom scattering amplitude," Phys. Rev. Lett. 48, 1726-1729 (1982).
[CrossRef]

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 ionization 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]

Leopold, J. G.

J. G. Leopold and I. C. Percival, "Ionisation of highly excited atoms by electric fields 3. microwave ionisation and excitation," J. Phys. B. 33, L823-L830 (2000).

Lezius, M.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

Lindner, F.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

Liu, J.

B Hu, J. Liu, and S. G. Chen, "Plateau in above-threshold-ionization spectra and chaotic behavior in rescattering processes," Phys. Lett. A 236, 533-542 (1997).
[CrossRef]

J. Liu, S. G. Chen, and D. H. Bao, "ATI spectra and angular distributions of the ionized electrons in strong fields: classical approaches," Commun. Theor. Phys 25, 129-134 (1996).

Liu, X.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

Moshammer, R.

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

B. Feuerstein, R. Moshammer, and J. Ullrich, "Nonsequential multiple ionization in intense laser pulses: interpretation of ion momentum distribution within the classical ‘rescattering’ model," J. Phys. B. 12, 709-721 (1979).

Paulus, G. G.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

Percival, I. C.

J. G. Leopold and I. C. Percival, "Ionisation of highly excited atoms by electric fields 3. microwave ionisation and excitation," J. Phys. B. 33, L823-L830 (2000).

R. Abrines and I. C. Percival, "Classical theory of charge transfer and ionization of hydrogen atoms by protons," Proc. Phys. Soc. London 88, 861-872 (1966).
[CrossRef]

Reichert, J.

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hänsch, "Measuring the frequency of light with mode-locked lasers," Opt. Commun. 172, 59-68 (1999).
[CrossRef]

Rottke, H.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

Sandner, M.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

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E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[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 ionization of helium," Phys. Rev. Lett. 73, 1227-1230 (1994).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Schätzel, M. G.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

Sheehy, B.

B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, "Precision measurement of strong field double ionization of helium," Phys. Rev. Lett. 73, 1227-1230 (1994).
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J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hänsch, "Measuring the frequency of light with mode-locked lasers," Opt. Commun. 172, 59-68 (1999).
[CrossRef]

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E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
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Walker, B.

B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, "Precision measurement of strong field double ionization of helium," Phys. Rev. Lett. 73, 1227-1230 (1994).
[CrossRef] [PubMed]

Walther, H.

H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

Yang, B.

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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H. Rottke, X. Liu, E. Ermina, M. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Non-sequential double ionization in a few-cycle laser pulse: the influence of the carrier-envelope phase," J. Mod. Opt. 53, 149-162 (2006).
[CrossRef]

J. Phys. B.

E. Eremina, X. Liu, H. Rottke, W. Sandner, A. Dreischuh, F. Lindner, F. Grasbon, G. G. Paulus, H. Walther, R. Moshammer, B. Feuerstein, and J. Ullrich, "Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization," J. Phys. B. 36, 3269-3280 (2003).
[CrossRef]

J. G. Leopold and I. C. Percival, "Ionisation of highly excited atoms by electric fields 3. microwave ionisation and excitation," J. Phys. B. 33, L823-L830 (2000).

B. Feuerstein, R. Moshammer, and J. Ullrich, "Nonsequential multiple ionization in intense laser pulses: interpretation of ion momentum distribution within the classical ‘rescattering’ model," J. Phys. B. 12, 709-721 (1979).

Opt. Commun.

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hänsch, "Measuring the frequency of light with mode-locked lasers," Opt. Commun. 172, 59-68 (1999).
[CrossRef]

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[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 ionization of helium," Phys. Rev. Lett. 73, 1227-1230 (1994).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef] [PubMed]

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Other

J. Chen, J. Liu, L. B. Fu, and W. M. Zheng, "Interpretation of momentum distribution of recoil ions from laserinduced nonsequential double ionization by semiclassical rescattering model," Phys. Rev. A 63, 011404-1-011404-4 (2000).

L. B. Fu, J. Liu, J. Chen, and S-G Chen, "Classical collisional trajectories as the source of strong-field double ionization of helium in the knee regime," Phys. Rev. A 63, 043416-1-043416-7 (2001).
[CrossRef]

H. Li, B. Wang, J. Chen, H. Jiang, X. Li, J. Liu, Q. Gong, Z-C Yan, and P. Fu, "Effects of a static electric field on nonsequential double ionization," Phys. Rev. A 76, 033405-1-033405-5 (2007).
[CrossRef]

A. S. Alnaser, D. Comtois, A. T. Hasan, D. M. Villeneuve, J. C. Kieffer, and I. V. Litvinyuk, "Strong-field nonsequential double ionization: wavelength dependence of ion momentum distributions for neon and argon," J. Phys. B. 41, 031001-1-031001-5 (2008).

P. J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, "Nonsequential double ionization as a completely classical photoelectric effect," Phys. Rev. Lett. 94, 093002-1-093002-4 (2005).
[CrossRef]

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, "Variable time lag and backward ejection in full-dimensional analysis of strong -field double ionization," Phys. Rev. Lett. 97, 103008-1-103008-4 (2006).
[CrossRef]

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwishch, 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 ionization of Ar: the role of excitation tunneling," Phys. Rev. Lett. 87, 043003-1-043003-4 (2001).
[CrossRef]

A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Beker, and R. Dörner, "Binary and recoil collisions in strong field double ionization of helium," Phys. Rev. Lett.  99, 263002-1-263002-4 (2007).
[CrossRef]

A. Rudenko, V. L. B. de Jesus, Th. Ergler, K. Zrost, B. Feuerstein, C. D. Schröter, R. Moshammer, and J. Ullrich, "Correlated two-electron momentum spectra for strong-field nonsequential double ionization of He at 800nm," Phys. Rev. Lett. 99, 263003-1-263003-4 (2007).
[CrossRef]

X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, "Nonsequential double ionization at the single-optical-cycle limit," Phys. Rev. Lett. 93, 263001-1-263001-4 (2004).
[CrossRef]

J. Chen, L. B. Fu, J. Liu, and W. M. Zheng, "Interpretation of momentum distribution of recoil ions from laserinduced nonsequential double ionization by semiclassical rescattering model," Phys. Rev. A 63, 011404(R)-1-011404(R)-4 (2001).
[CrossRef]

J. Liu, D. F. Ye, J. Chen, and X. Liu, "Complex dynamics of correlated electrons in molecular double ionization by an ultrashort intense laser pulse," Phys. Rev. Lett. 99, 013003-1-013003-4 (2007).
[CrossRef]

D. F. Ye, J. Chen, and J. Liu, "Classical trajectory perspective on double-ionization dynamics of diatomic molecules irradiated by ultrashort intense laser pulses," Phys. Rev. A 77, 013403-1-013403-10 (2008).

C. F. M. Faria, X. Liu, A. Sanpera, and M. Lewenstein, "Classical and quantum-mechanical treatments of nonsequential double ionization with few-cycle laser pulses," Phys. Rev. A 70,043406-1-043406-12 (2004).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

The electric field of few-cycle pulse with φ 0=0 (solid line) and 0.5π (dot line). Three half-cycles are denoted by H1, H2 and H3. They move towards left as φ0 increases.

Fig. 2.
Fig. 2.

The momentum distribution of He2+ parallel to the polarization of few-cycle pulse with φ0=0 (a), 0.5π (b), 0.6π (c), and 0.9π (d). The contributions of half-cycles H1 (empty triangle), H2 (solid circle), and H3 (empty circle) are presented respectively. The laser intensity is I = 7×1014W/cm2.

Fig. 3.
Fig. 3.

(a) The tunneling rate of the first ionized electron ejected at the peak of H1 (empty triangle), H2 (solid circle), and H3 (empty circle). (b) The maximum returning kinetic energy obtained by the first ionized electron ejected in H1 (empty triangle), H2 (solid circle), and H3 (empty circle). The laser intensity is 7×1014W/cm2.

Fig. 4.
Fig. 4.

The momentum distribution of He2+ parallel to the polarization of laser pulse with φ 0=0 (a) and 0.5π (b). The contributions of H1 (empty triangle), H2 (solid circle), and H3 (empty circle) are presented. The maximum tunneling rate and the returning kinetic energy of the first ionized electron are given in (c) and (d), respectively. The laser intensity is 2.5×1014W/cm2.

Fig. 5.
Fig. 5.

(Color online) (a) and (b) are two typical trajectories selected from the left and right peak in Fig. 2(a), respectively, for the case of 7.0×1014W/cm2 and φ0=0, while (c) and (d)) are selected from the left and right peak in Fig. 4(a), respectively, for the case of 2.5×1014W/cm2 and φ0=0. The energy evolution of the first electron (blue circle line) and the bound electron (red solid line) is presented. The electric field (dash line) is also presented and the arrows indicate the collision moments.

Equations (2)

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d r j 2 dt 2 = E ( t ) ( V ne j + V ee )
w ˉ ( t 0 , v per ) = ( 2 I p ) 1 2 E ( t 0 ) π exp ( v per 2 ( 2 I p ) 1 2 E ( t 0 ) ) ,

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