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.

© 2000 Optical Society of America

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References

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  1. M. S. Pindzola, D. C Griffin, and C Bottcher, “Validity of time-dependent Hartree-Fock theory for the multiphoton ionization of atoms”, Phys. Rev. Lett. 66, 2305 (1991)
    [Crossref] [PubMed]
  2. D. Bauer, “Two-dimensional, two-electron model atom in a laser pulse”, Phys. Rev. A 56, 3028 (1997)
    [Crossref]
  3. D. Lappas and R. van Leeuwen, “Electron correlation effects in the double ionization of He” J. Phys. B 31, L249 (1998)
    [Crossref]
  4. W.-C Liu, J. H. Eberly, S. L. Haan, and R. Grobe, “Correlation effects in two-electron model atoms in intense laser fields”, Phys. Rev. Lett. 83, 520 (1999)
    [Crossref]
  5. M. Lein, E. K. U. Gross, and V. Engel, “On the mechanism of strong-field double photoionization in the helium atom”, J. Phys. B 33, 433 (2000)
    [Crossref]
  6. D. Dundas, K. T. Taylor, J. S. Parker, and E. S. Smyth, “Double ionization dynamics of laser-driven helium”, J. Phys. B 32, L231 (1999)
    [Crossref]
  7. B. Walker, 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 International Conference on Multiphoton Processes, edited by J Keene et al, AIP press (2000) to appear
  9. Th. Weber, et al, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields”, Phys. Rev. Lett., 84, 443 (2000) R. Moshammer, et al, “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse”, ibid., 447
    [Crossref] [PubMed]
  10. A. Becker and F. H. M. Faisal, “Interplay of electron correlation and intense field dynamics in the double ionization of helium”, Phys. Rev. A 59, R1742 (1999)
    [Crossref]
  11. R. Kopold, W. Becker, H. Rottke, and W. Sandner, “Routes to nonsequential double ionization”, preprint (2000)
  12. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization”, Phys. Rev. Lett. 71, 1994 (1993)
    [Crossref] [PubMed]
  13. B. Sheehy, et al, “Single- and multiple-electron dynamics in the strong-field tunneling limit”, Phys. Rev. A 58, 3942 (1998)
    [Crossref]
  14. I. Galbraith, Y. S. Ching, and E. Abraham, “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. L. DiMauro and P. Agostini, “Ionization dynamics in strong laser fields”, Adv. At. Mol. Opt. Phys. 35, 79 (1995)
    [Crossref]
  17. K. Burnett, J. B. Watson, A. Sanpera, and P. L. Knight, “Multielectron response to intense laser fields”, Phil. Trans. Roy. 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.

2000 (1)

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

1999 (3)

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

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

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

1998 (2)

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

B. Sheehy, et al, “Single- and multiple-electron dynamics in the strong-field tunneling limit”, Phys. Rev. A 58, 3942 (1998)
[Crossref]

1997 (1)

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

1995 (1)

L. DiMauro and P. Agostini, “Ionization dynamics in strong laser fields”, Adv. At. Mol. Opt. Phys. 35, 79 (1995)
[Crossref]

1994 (1)

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

1993 (1)

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

1991 (1)

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

1984 (1)

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

Abraham, E.

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

Agostini, P.

L. DiMauro and P. Agostini, “Ionization dynamics in strong laser fields”, Adv. At. Mol. Opt. Phys. 35, 79 (1995)
[Crossref]

Bauer, D.

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

Becker, A.

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

Becker, W.

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

Bottcher, C

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

Burnett, K.

K. Burnett, J. B. Watson, A. Sanpera, and P. L. Knight, “Multielectron response to intense laser fields”, Phil. Trans. Roy. 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.

Ching, Y. S.

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

Corkum, P. B.

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

DiMauro, L.

L. DiMauro and P. Agostini, “Ionization dynamics in strong laser fields”, Adv. At. Mol. Opt. Phys. 35, 79 (1995)
[Crossref]

Dundas, D.

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

Eberly, J. H.

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

Engel, V.

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

Faisal, F. H. M.

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

Galbraith, I.

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

Griffin, D. C

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

Grobe, R.

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

Gross, E. K. U.

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

Haan, S. L.

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

Knight, P. L.

K. Burnett, J. B. Watson, A. Sanpera, and P. L. Knight, “Multielectron response to intense laser fields”, Phil. Trans. Roy. 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.

Kopold, R.

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

Lappas, D.

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

Lein, M.

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

Liu, W.-C

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

Moshammer, R.

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

Parker, J. S.

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

Pindzola, M. S.

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

Rottke, H.

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

Sandner, W.

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

Sanpera, A.

K. Burnett, J. B. Watson, A. Sanpera, and P. L. Knight, “Multielectron response to intense laser fields”, Phil. Trans. Roy. 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.

Sheehy, B.

B. Sheehy, et al, “Single- and multiple-electron dynamics in the strong-field tunneling limit”, Phys. Rev. A 58, 3942 (1998)
[Crossref]

Smyth, E. S.

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

Taylor, K. T.

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

van Leeuwen, R.

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

Walker, B.

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

Watson, J. B.

K. Burnett, J. B. Watson, A. Sanpera, and P. L. Knight, “Multielectron response to intense laser fields”, Phil. Trans. Roy. 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.

Weber, Th.

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

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

L. DiMauro and P. Agostini, “Ionization dynamics in strong laser fields”, Adv. At. Mol. Opt. Phys. 35, 79 (1995)
[Crossref]

Am. J. Phys. (1)

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

J. Phys. B (3)

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

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

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

Phys. Rev. A (3)

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

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

B. Sheehy, et al, “Single- and multiple-electron dynamics in the strong-field tunneling limit”, Phys. Rev. A 58, 3942 (1998)
[Crossref]

Phys. Rev. Lett. (4)

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

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

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

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

Other (5)

See the proceedings of the 8th International Conference on Multiphoton Processes, edited by J Keene et al, AIP press (2000) to appear

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

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

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

K. Burnett, J. B. Watson, A. Sanpera, and P. L. Knight, “Multielectron response to intense laser fields”, Phil. Trans. Roy. 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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