Abstract

We use the Wigner transformation to study the electronic center-of-mass motion in phase-space for double ionization in a strong laser field. The rescattering mechanism is clearly visible in the evolution of the fully correlated two-electron system. In a mean-field calculation, on the other hand, the signatures of rescattering are missing. Some properties of the Wigner function in two-particle systems are reported.

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References

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  1. D. N. Fittinghoff, P. R. Bolton, B. Chang, and K. C. Kulander, "Observation of Nonsequential Double Ionization of Helium with Optical Tunneling," Phys. Rev. Lett. 69, 2642 (1992).
    [CrossRef] [PubMed]
  2. 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 (1994).
    [CrossRef] [PubMed]
  3. A. Becker and F. H. M. Faisal, "Mechanism of laser-induced double ionization of helium," J. Phys. B 29, L197 (1996).
    [CrossRef]
  4. D. Bauer, "Two-dimensional, two-electron model atom in a laser pulse: Exact treatment, single-active-electron analysis, time-dependent density-functional theory, classical calculations, and nonsequential ionization," Phys. Rev. A 56, 3028 (1997).
    [CrossRef]
  5. J. B. Watson, A. Sanpera, D. G. Lappas, P. L. Knight, and K. Burnett, "Nonsequential Double Ionization of Helium," Phys. Rev. Lett. 78, 1884 (1997).
    [CrossRef]
  6. D. G. Lappas and R. van Leeuwen, "Electron correlation effects in the double ionization of He," J. Phys. B 31, L249 (1998).
    [CrossRef]
  7. 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]
  8. 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]
  9. 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]
  10. M. Doerr, "Double ionization in a one-cycle laser pulse," Opt. Express 6, 111 (2000), http://www.opticsexpress.org/oearchive/source/19114.htm.
    [CrossRef]
  11. 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).
    [CrossRef] [PubMed]
  12. R. Moshammer et al., "Momentum Distributions of Ne^n+ Ions Created by an Intense Ultrashort Laser Pulse," Phys. Rev. Lett. 84, 447 (2000).
    [CrossRef] [PubMed]
  13. Th. Weber et al., "Sequential and nonsequential contributions to double ionization in strong laser fields," J. Phys. B 33, L127 (2000).
    [CrossRef]
  14. Th. Weber et al., "Correlated electron emission in multiphoton double ionization," Nature (London) 405, 658 (2000).
    [CrossRef]
  15. A. Becker and F. H. M. Faisal, "Interpretation of momentum distribution of recoil ions from laser induced nonsequential double ionization," Phys. Rev. Lett. 84, 3456 (2000).
    [CrossRef]
  16. H. W. van der Hart, "Recollision model for double ionization of atoms in strong laser fields," Phys. Rev. A 62, 013407 (2000).
    [CrossRef]
  17. H. W. van der Hart, "Sequential versus non-sequential double ionization in strong laser fields," J. Phys. B 33, L699 (2000).
    [CrossRef]
  18. R. Kopold, W. Becker, H. Rottke, and W. Sandner, "Routes to Nonsequential Double Ionization," Phys. Rev. Lett. 85, 3781 (2000).
    [CrossRef] [PubMed]
  19. B. Feuerstein, R. Moshammer, and J. Ullrich, "Nonsequential multiple ionization in intense laser pulses: interpretation of ion momentum distributions within the classical `rescattering' model," J. Phys. B 33, L823 (2000).
    [CrossRef]
  20. M. Lein, E. K. U. Gross, and V. Engel, "Intense-Field Double Ionization of Helium: Identifying the Mechanism," Phys. Rev. Lett. 85, 4707 (2000).
    [CrossRef] [PubMed]
  21. J. Chen, J. Liu, L. B. Fu, and W. M. Zheng, "Interpretation of momentum distribution of recoil ions from laser-induced nonsequential double ionization by semiclassical rescattering model," Phys. Rev. A 63, 011404(R) (2001).
  22. P. B. Corkum, "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. 71, 1994 (1993).
    [CrossRef] [PubMed]
  23. M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, "Distribution functions in physics: fundamentals," Phys. Rep. 106, 121 (1984).
    [CrossRef]
  24. R. Grobe and J. H. Eberly, "Single and double ionization and strong-field stabilization of a two-electron system," Phys. Rev. A 47, R1605 (1993).
    [CrossRef] [PubMed]
  25. M. D. Feit, J. A. Fleck, Jr., and A. Steiger, "Solution of the Schroedinger equation by a spectral method," J. Comput. Phys. 47, 412 (1982).
    [CrossRef]

Other (25)

D. N. Fittinghoff, P. R. Bolton, B. Chang, and K. C. Kulander, "Observation of Nonsequential Double Ionization of Helium with Optical Tunneling," Phys. Rev. Lett. 69, 2642 (1992).
[CrossRef] [PubMed]

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 (1994).
[CrossRef] [PubMed]

A. Becker and F. H. M. Faisal, "Mechanism of laser-induced double ionization of helium," J. Phys. B 29, L197 (1996).
[CrossRef]

D. Bauer, "Two-dimensional, two-electron model atom in a laser pulse: Exact treatment, single-active-electron analysis, time-dependent density-functional theory, classical calculations, and nonsequential ionization," Phys. Rev. A 56, 3028 (1997).
[CrossRef]

J. B. Watson, A. Sanpera, D. G. Lappas, P. L. Knight, and K. Burnett, "Nonsequential Double Ionization of Helium," Phys. Rev. Lett. 78, 1884 (1997).
[CrossRef]

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

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]

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]

M. Doerr, "Double ionization in a one-cycle laser pulse," Opt. Express 6, 111 (2000), http://www.opticsexpress.org/oearchive/source/19114.htm.
[CrossRef]

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).
[CrossRef] [PubMed]

R. Moshammer et al., "Momentum Distributions of Ne^n+ Ions Created by an Intense Ultrashort Laser Pulse," Phys. Rev. Lett. 84, 447 (2000).
[CrossRef] [PubMed]

Th. Weber et al., "Sequential and nonsequential contributions to double ionization in strong laser fields," J. Phys. B 33, L127 (2000).
[CrossRef]

Th. Weber et al., "Correlated electron emission in multiphoton double ionization," Nature (London) 405, 658 (2000).
[CrossRef]

A. Becker and F. H. M. Faisal, "Interpretation of momentum distribution of recoil ions from laser induced nonsequential double ionization," Phys. Rev. Lett. 84, 3456 (2000).
[CrossRef]

H. W. van der Hart, "Recollision model for double ionization of atoms in strong laser fields," Phys. Rev. A 62, 013407 (2000).
[CrossRef]

H. W. van der Hart, "Sequential versus non-sequential double ionization in strong laser fields," J. Phys. B 33, L699 (2000).
[CrossRef]

R. Kopold, W. Becker, H. Rottke, and W. Sandner, "Routes to Nonsequential Double Ionization," Phys. Rev. Lett. 85, 3781 (2000).
[CrossRef] [PubMed]

B. Feuerstein, R. Moshammer, and J. Ullrich, "Nonsequential multiple ionization in intense laser pulses: interpretation of ion momentum distributions within the classical `rescattering' model," J. Phys. B 33, L823 (2000).
[CrossRef]

M. Lein, E. K. U. Gross, and V. Engel, "Intense-Field Double Ionization of Helium: Identifying the Mechanism," Phys. Rev. Lett. 85, 4707 (2000).
[CrossRef] [PubMed]

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

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

M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, "Distribution functions in physics: fundamentals," Phys. Rep. 106, 121 (1984).
[CrossRef]

R. Grobe and J. H. Eberly, "Single and double ionization and strong-field stabilization of a two-electron system," Phys. Rev. A 47, R1605 (1993).
[CrossRef] [PubMed]

M. D. Feit, J. A. Fleck, Jr., and A. Steiger, "Solution of the Schroedinger equation by a spectral method," J. Comput. Phys. 47, 412 (1982).
[CrossRef]

Supplementary Material (2)

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Figures (2)

Fig. 1.
Fig. 1.

(2.3 MB) The time evolution of the center-of-mass phase-space distribution.

Fig. 2.
Fig. 2.

(2.5 MB) Same as Fig. 1 in the Hartree-Fock approximation.

Equations (10)

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H = 1 2 2 z 1 2 1 2 2 z 2 2 2 z 1 2 + 1 2 z 2 2 + 1 + 1 ( z 1 z 2 ) 2 + 1 + E ( t ) ( z 1 + z 2 ) .
Ψ HF ( z 1 , z 2 , t ) = φ ( z 1 , t ) φ ( z 2 , t ) .
i t φ ( z , t ) = [ 1 2 2 z 2 + v s ( z , t ) ] φ ( z , t )
v s ( z , t ) = 2 z 2 + 1 + φ ( z , t ) 2 ( z z ) 2 + 1 d z + E ( t ) z .
w ( 1 ) ( x , p ) = φ * ( x y 2 ) φ ( x + y 2 ) e i p y d y .
w ( Z , P , z ) = Ψ * ( Z y 2 z 2 , Z y 2 + z 2 ) Ψ ( Z + y 2 z 2 , Z + y 2 + z 2 ) e i P y d y .
w ( Z , P ) = w ( Z , P , z ) d z .
w HF ( Z , P ) = 1 2 [ w ( 1 ) ( Z , P 2 ) ] 2 ,
Ψ s a ( z 1 , z 2 ) = φ 1 ( z 1 ) φ 2 ( z 2 ) ± φ 1 ( z 2 ) φ 2 ( z 1 ) .
w s a ( Z , P ) = φ 2 * ( Z + y 2 ) φ 1 ( Z y 2 ) e i P y 2 d y 2 ± w φ 1 ( Z , P 2 ) w φ 2 ( Z , P 2 ) ,

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