Abstract

The time-dependent Schrodinger equation is solved for a 1D×1D two-electron model helium atom subject to a low-frequency short, intense laser pulse. A half-cycle pulse leads to strong single but no double ionization. A full-cycle pulse leads to double ionization which begins precisely at the classical return time for the first ejected electron. When the excursion range for the first electron is truncated, the double ionization at later times, corresponding to longer excursions, disappears. When the field near the nucleus is turned off during the return of the first electron, double ionization persists.

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References

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  1. Pindzola, M. S., Griffin, D. C., and Bottcher, C., "Validity of time-dependent Hartree-Fock theory for the multiphoton ionization of atoms," Phys. Rev. Lett. 66, 2305 (1991)
    [CrossRef] [PubMed]
  2. Bauer, D., "Two-dimensional, two-electron model atom in a laser pulse," Phys. Rev. A 56, 3028 (1997)
    [CrossRef]
  3. Lappas, D., and van Leeuwen, R., "Electron correlation effects in the double ionization of He," J. Phys. B 31, L249 (1998)
    [CrossRef]
  4. Liu, W.-C., Eberl , J. H., Haan, S. L., and Grobe, R., "Correlation effects in two-electron model atoms in intense laser fields," Phys. Rev. Lett. 83, 520 (1999)
    [CrossRef]
  5. Lein, M., Gross, E. K. U., and Engel, V., "On the mechanism of strong-field double photoionization in the helium atom," J. Phys. B 33, 433 (2000)
    [CrossRef]
  6. Dundas, D., Taylor, K. T., Parker, J. S., and Smyth, E. S., "Double ionization dynamics of laser-driven helium," J. Phys. B 32, L231 (1999)
    [CrossRef]
  7. Walker, B., et al, "Precision measurement of strong field double ionization of helium," Phys. Rev. Lett. 73, 1227 (1994)
    [CrossRef] [PubMed]
  8. See the proceedings of the 8th nternational Conference on Multiphoton Processes, edited by J. Keene et al, A P press (2000) to appear
  9. Weber, Th., et al, "Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields," Phys. Rev. Lett., 84, 443 (2000). Moshammer, R., et al, "Momentum distribution of Ne n+ ions created by an intense ultrashort laser pulse," ibid., 447
    [CrossRef] [PubMed]
  10. Becker, A., and Faisal, F. H. M., "Interplay of electron correlation and intense field dynamics in the double ionization of helium," Phys. Rev. A 59, R1742 (1999)
    [CrossRef]
  11. Kopold, R., Becker, W., Rottke, H., and Sandner, W., "Routes to nonsequential double ionization," preprint (2000)
  12. Corkum, P. B., "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. 71, 1994 (1993)
    [CrossRef] [PubMed]
  13. Sheeh , B., et al, "Single- and multiple-electron dynamics in the strong-field tunneling limit", Phys. Rev. A 58, 3942 (1998)
    [CrossRef]
  14. Galbraith, I., Ching, Y. S., and Abraham, E., "Two-dimensional time-dependent quantum-mechanical scattering event," Am. J. Phys. 52, 60 (1984)
    [CrossRef]
  15. Cf the programs at http://mitarbeiter.mbi-berlin.de/doerr/mathematica/simplemans.txt
  16. DiMauro, L., and Agostini, P., " onization dynamics in strong laser fields", Adv. At. Mol. Opt. Phys. 35, 79 (1995)
    [CrossRef]
  17. Burnett, K., Watson, J. B., Sanpera, A., and Knight, P. L., "Multielectron response to intense laser fields," Phil. Trans. Ro . Soc. Lond. A356, 317 (1998). This group has also performed a "field-assisted rescattering" study recently [8], using their "crapola" model, and turning off the laser-electron interaction for the second, "inner" electron.

Other

Pindzola, M. S., Griffin, D. C., and Bottcher, C., "Validity of time-dependent Hartree-Fock theory for the multiphoton ionization of atoms," Phys. Rev. Lett. 66, 2305 (1991)
[CrossRef] [PubMed]

Bauer, D., "Two-dimensional, two-electron model atom in a laser pulse," Phys. Rev. A 56, 3028 (1997)
[CrossRef]

Lappas, D., and van Leeuwen, R., "Electron correlation effects in the double ionization of He," J. Phys. B 31, L249 (1998)
[CrossRef]

Liu, W.-C., Eberl , J. H., Haan, S. L., and Grobe, R., "Correlation effects in two-electron model atoms in intense laser fields," Phys. Rev. Lett. 83, 520 (1999)
[CrossRef]

Lein, M., Gross, E. K. U., and Engel, V., "On the mechanism of strong-field double photoionization in the helium atom," J. Phys. B 33, 433 (2000)
[CrossRef]

Dundas, D., Taylor, K. T., Parker, J. S., and Smyth, E. S., "Double ionization dynamics of laser-driven helium," J. Phys. B 32, L231 (1999)
[CrossRef]

Walker, B., et al, "Precision measurement of strong field double ionization of helium," Phys. Rev. Lett. 73, 1227 (1994)
[CrossRef] [PubMed]

See the proceedings of the 8th nternational Conference on Multiphoton Processes, edited by J. Keene et al, A P press (2000) to appear

Weber, Th., et al, "Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields," Phys. Rev. Lett., 84, 443 (2000). Moshammer, R., et al, "Momentum distribution of Ne n+ ions created by an intense ultrashort laser pulse," ibid., 447
[CrossRef] [PubMed]

Becker, A., and Faisal, F. H. M., "Interplay of electron correlation and intense field dynamics in the double ionization of helium," Phys. Rev. A 59, R1742 (1999)
[CrossRef]

Kopold, R., Becker, W., Rottke, H., and Sandner, W., "Routes to nonsequential double ionization," preprint (2000)

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

Sheeh , B., et al, "Single- and multiple-electron dynamics in the strong-field tunneling limit", Phys. Rev. A 58, 3942 (1998)
[CrossRef]

Galbraith, I., Ching, Y. S., and Abraham, E., "Two-dimensional time-dependent quantum-mechanical scattering event," Am. J. Phys. 52, 60 (1984)
[CrossRef]

Cf the programs at http://mitarbeiter.mbi-berlin.de/doerr/mathematica/simplemans.txt

DiMauro, L., and Agostini, P., " onization dynamics in strong laser fields", Adv. At. Mol. Opt. Phys. 35, 79 (1995)
[CrossRef]

Burnett, K., Watson, J. B., Sanpera, A., and Knight, P. L., "Multielectron response to intense laser fields," Phil. Trans. Ro . Soc. Lond. A356, 317 (1998). This group has also performed a "field-assisted rescattering" study recently [8], using their "crapola" model, and turning off the laser-electron interaction for the second, "inner" electron.

Supplementary Material (9)

» Media 1: GIF (438 KB)     
» Media 2: GIF (228 KB)     
» Media 3: GIF (1063 KB)     
» Media 4: GIF (458 KB)     
» Media 5: GIF (1195 KB)     
» Media 6: GIF (508 KB)     
» Media 7: GIF (521 KB)     
» Media 8: GIF (259 KB)     
» Media 9: GIF (394 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Fields E(t) (solid) and E 0 sin(ωt) (dashed). Position (red solid) and velocity (black short-dashed) for a classical free particle in the field, starting at time ti =80 (red circle) and returning to x=0 at t 1=145 with an energy of 3.4, after an excursion with a maximum spatial amplitude of 34 [15, 16].

Fig. 2.
Fig. 2.

(430kB, lower-resolution version 230kB) Probability contours during the first half of a single-cycle laser pulse showing the distorted and singly ionized wavepacket at peak electric field, t=76. The log contour scale is given on the left-hand side.

Fig. 3.
Fig. 3.

(1.2MB, smaller version 0.5MB) Probability contours during the second half of a single-cycle laser pulse. The first sign of a double ionization jet (in the direction of the arrows) appears at t=130.

Fig. 4.
Fig. 4.

(1.2MB, smaller version 0.5MB) Probability contours during the second half of a single-cycle laser pulse where the field acts only in the lower and right parts.

Fig. 5.
Fig. 5.

(530kB, smaller version 260kB) Probability contours during the second half of a single-cycle laser pulse, for a weak field of E 0=0.075, at t=148.

Fig. 6.
Fig. 6.

(400kB) Probability contours during the second half of a single-cycle laser pulse of field strength E 0=0.12. The box size is purposefully chosen too small, namely 26, including an absorber of effective absorbing width 6. Left: the first sign of a double ionization jet, at t=126; right: the double ionization yield is further ejected and no further double ionization occurs, after t=148.

Equations (3)

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H ( t ) = 1 2 ( L 1 + L 2 ) + V ( x 1 ) + V ( x 2 ) + V 12 ( x 1 x 2 ) + E ( t ) · ( x 1 + x 2 ) .
V ( x ) = Z x 2 + a 2 .
E ( t ) = b ( t t 0 ) exp [ d ( t t 0 ) 2 ] .

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