Abstract

We discuss directional dependence in the time development of spatial wavefunctions, which includes jet formation, for two-electron model atoms exposed to intense laser fields. Two competing scenarios for double ionization are evident: (1) both electrons emerge simultaneously from the core region and on the same side of the nucleus, and (2) the electrons detach on opposite sides but not simultaneously. The importance of the electron-electron repulsion contribution to the competing processes is investigated for various laser intensities.

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References

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  1. D. N. Fittinghof, 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]
  2. B. Walker et al., "Precision measurement of strong field double ionization of helium," Phys. Rev. Lett. 73, 1227 (1994).
    [CrossRef] [PubMed]
  3. B. Sheeh et al., "Single and multiple electron dynamics in the strong field tunneling limit," Phys. Rev. A 58, 3942 (1999).
    [CrossRef]
  4. 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 (1986).
  5. S. Larochele, A. Talebpour, and S.L. Chin, "Non sequential multiple ionization of rare gas atoms in a Ti:Sapphire laser field," J. Phys. B 31, 1201 (1998).
    [CrossRef]
  6. A. Becker and F. H. M. Faisal, "Mechanism of laser induced double ionization of helium," J. Phys. B 29, L197 (1996).
    [CrossRef]
  7. F. H. M. Faisal and A. Becker, "Nonsequential double ionization: mechanism and model formula," Laser Phys. 7, 684 (1997).
  8. 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 non sequential ionization," Phys. Rev. A 56, 3028 (1997).
    [CrossRef]
  9. J. B. Watson et al., "Nonsequential Double Ionization of Helium," Phys. Rev. Lett. 78, 1884 (1997).
    [CrossRef]
  10. K. Burnett et al., "Multi electron Response to Intense Laser Fields," Phil Trans. R. Soc. Lond. A 356, 317 (1998).
    [CrossRef]
  11. M. S. Pindzola, F. Robicheaux and P. Gavras, "Double multiphoton ionization of a model atom," Phys. Rev. A 55, 1307 (1997).
    [CrossRef]
  12. D. G. Lappas and R. Leeuwen, "Electron correlation effects in the double ionization of He," J. Phys. B 31, L249 (1998).
    [CrossRef]
  13. W. C. Liu, J.H. Eberl , S.L. Haan and R. Grobe, "Correlation Effects in Two Electron Model Atoms in Intense Laser Fields," Phys. Rev. Lett. 83, 520 (1999).
    [CrossRef]
  14. J. Parker, K. T. Ta lor, C. W. Clark, and S. Blodgett Ford, "Intense field multiphoton ionization of a two electron atom," J. Phys. B 29, L33 (1996).
    [CrossRef]
  15. J. Parker, E. S. Sm th, and K. T. Ta lor, "Intense field multiphoton ionization of helium," J. Phys. B 31, L571 (1998).
    [CrossRef]
  16. P. B. Corkum, "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. 71, 1994 (1993).
    [CrossRef] [PubMed]
  17. 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]
  18. Th. Weber et al., "Sequential and nonsequential contributions to double ionization in strong laser fields," J. Phys. B 33, L127 (2000).
    [CrossRef]
  19. Th. Weber et al., "Correlated electron emission in multiphoton double ionization," Nature 405, 658 (2000).
    [CrossRef] [PubMed]
  20. R. Moshammer et al.,"Momentum Distributions of Ne n+ Ions Created b an Intense Ultrashort Laser Pulse," Phys. Rev. Lett. 84, 447 (2000).
    [CrossRef] [PubMed]
  21. C. Sz manowski, R. Panfili, W. C. Liu, S.L. Haan, and J.H. Eberly, "Role of the correlation charge in the double ionization of two electron model atoms exposed to intense laser fields," Phys. Rev. A 61, 055401 (2000).
    [CrossRef]
  22. M.S. Pindzola, D.C. Griffin and C. Bottcher, "Validit of time dependent Hartree Fock theory for the multiphoton ionization of atoms," Phys. Rev. Lett. 66, 2305 (1991).
    [CrossRef] [PubMed]
  23. R. Grobe and J.H. Eberl , "Photoelectron spectra for a two electron s stem in a strong laser field," Phys. Rev. Lett. 68, 2905 (1992).
    [CrossRef] [PubMed]
  24. Q. Su and J.H. Eberly, "Model atom for multiphoton Physics," Phys. Rev. A 44, 5997 (1991).
    [CrossRef] [PubMed]
  25. J.H. Eberly, R. Grobe, C.K. Law and Q. Su, "Numerical experiments in strong and super strong fields," in Atoms in Intense Laser Fields, edited by M. Gavrila, 301 (Academic Press, Boston), 1992.
  26. R. Grobe and J.H. Eberly, "One dimensional model of a negative ion and its interaction with laser fields," Phys. Rev. A 48, 4664 (1993).
    [CrossRef] [PubMed]
  27. S.L. Haan, R. Grobe and J.H. Eberly, "Numerical stud of autoionizing states in completely correlated two electron systems," Phys. Rev. A 50, 378 (1994).
    [CrossRef] [PubMed]
  28. 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]
  29. M. Dorr, "Double ionization in a one cycle laser pulse," Opt. Express 6, 111 (2000). http://www.opticsexpress.org/oearchive/source/19114.htm
    [CrossRef]
  30. R. Grobe, S.L. Haan and J. H. Eberly, "A split domain algorithm for time dependent multi-electron wave functions," Comput. Phys. Commun. 117, 200 (1999).
    [CrossRef]
  31. R. Heather and H. Metiu, "An efficient procedure for calculating the evolution of the wave function by fast Fourier transform methods for systems with spatially extended wave function and localized potential," J. Chem. Phys. 86, 5009 (1987).
    [CrossRef]
  32. J.H. Eberly, W. C. Liu, and S.L. Haan, "The role of correlation in non sequential double ionization," in press in Multiphoton Processes, ed. by J. Keene, L.F. DiMauro, R.R. Freeman, and K.C. Kulander (AIP Press, New York, 2000).

Other (32)

D. N. Fittinghof, 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]

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

B. Sheeh et al., "Single and multiple electron dynamics in the strong field tunneling limit," Phys. Rev. A 58, 3942 (1999).
[CrossRef]

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 (1986).

S. Larochele, A. Talebpour, and S.L. Chin, "Non sequential multiple ionization of rare gas atoms in a Ti:Sapphire laser field," J. Phys. B 31, 1201 (1998).
[CrossRef]

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

F. H. M. Faisal and A. Becker, "Nonsequential double ionization: mechanism and model formula," Laser Phys. 7, 684 (1997).

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 non sequential ionization," Phys. Rev. A 56, 3028 (1997).
[CrossRef]

J. B. Watson et al., "Nonsequential Double Ionization of Helium," Phys. Rev. Lett. 78, 1884 (1997).
[CrossRef]

K. Burnett et al., "Multi electron Response to Intense Laser Fields," Phil Trans. R. Soc. Lond. A 356, 317 (1998).
[CrossRef]

M. S. Pindzola, F. Robicheaux and P. Gavras, "Double multiphoton ionization of a model atom," Phys. Rev. A 55, 1307 (1997).
[CrossRef]

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

W. C. Liu, J.H. Eberl , S.L. Haan and R. Grobe, "Correlation Effects in Two Electron Model Atoms in Intense Laser Fields," Phys. Rev. Lett. 83, 520 (1999).
[CrossRef]

J. Parker, K. T. Ta lor, C. W. Clark, and S. Blodgett Ford, "Intense field multiphoton ionization of a two electron atom," J. Phys. B 29, L33 (1996).
[CrossRef]

J. Parker, E. S. Sm th, and K. T. Ta lor, "Intense field multiphoton ionization of helium," J. Phys. B 31, L571 (1998).
[CrossRef]

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

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]

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 405, 658 (2000).
[CrossRef] [PubMed]

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

C. Sz manowski, R. Panfili, W. C. Liu, S.L. Haan, and J.H. Eberly, "Role of the correlation charge in the double ionization of two electron model atoms exposed to intense laser fields," Phys. Rev. A 61, 055401 (2000).
[CrossRef]

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

R. Grobe and J.H. Eberl , "Photoelectron spectra for a two electron s stem in a strong laser field," Phys. Rev. Lett. 68, 2905 (1992).
[CrossRef] [PubMed]

Q. Su and J.H. Eberly, "Model atom for multiphoton Physics," Phys. Rev. A 44, 5997 (1991).
[CrossRef] [PubMed]

J.H. Eberly, R. Grobe, C.K. Law and Q. Su, "Numerical experiments in strong and super strong fields," in Atoms in Intense Laser Fields, edited by M. Gavrila, 301 (Academic Press, Boston), 1992.

R. Grobe and J.H. Eberly, "One dimensional model of a negative ion and its interaction with laser fields," Phys. Rev. A 48, 4664 (1993).
[CrossRef] [PubMed]

S.L. Haan, R. Grobe and J.H. Eberly, "Numerical stud of autoionizing states in completely correlated two electron systems," Phys. Rev. A 50, 378 (1994).
[CrossRef] [PubMed]

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

R. Grobe, S.L. Haan and J. H. Eberly, "A split domain algorithm for time dependent multi-electron wave functions," Comput. Phys. Commun. 117, 200 (1999).
[CrossRef]

R. Heather and H. Metiu, "An efficient procedure for calculating the evolution of the wave function by fast Fourier transform methods for systems with spatially extended wave function and localized potential," J. Chem. Phys. 86, 5009 (1987).
[CrossRef]

J.H. Eberly, W. C. Liu, and S.L. Haan, "The role of correlation in non sequential double ionization," in press in Multiphoton Processes, ed. by J. Keene, L.F. DiMauro, R.R. Freeman, and K.C. Kulander (AIP Press, New York, 2000).

Supplementary Material (4)

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Figures (10)

Fig. 1.
Fig. 1.

Animation (0.9 MB) of the time development of |Ψ(x, y)|2 for one-dimensional helium for a four-cycle pulse of intensity 6.5×1014W/cm 2 and frequency 0.1837a.u. The still image is for t=2.875 cycles and shows the jets as well as sequential ionization.

Fig. 2.
Fig. 2.

Animation (1.0 MB) of the time development of |Ψ(x, y)|2 as for Fig. 1, but viewed from along the line y=x, and truncated at 10-5. The still image is for t=2.25 cycles.

Fig. 3.
Fig. 3.

Logarithmic contour plots of |Ψ(x, y)|2 vs. x and y after each of the first three cycles of a 6-cycle (2+2+2 trapezoidal) pulse for C=0.9, 1.0, and 1.1. Other parameters are the same as for Figs. 1 and 2.

Fig. 4.
Fig. 4.

Continuation of Fig. 3, showing |Ψ(x, y)|2 vs. x and y after each of the final three cycles of a 6-cycle (2+2+2 trapezoidal) pulse for C=0.9, 1.0, and 1.1.

Fig. 5.
Fig. 5.

Animation (1.7 MB) of the time development of |Ψ(x, y)|2 as for Fig. 2, but with correlation charge C=1.1 instead of 1.0. The still image shows |Ψ(x, y)|2 at t=2.25 cycles.

Fig. 6.
Fig. 6.

Linear plots of |Ψ(x, y)|2 vs. x and y at t=1.875 cycles for C=1.0 and 1.1, showing only small enhancement of the sequential ionization for increased C. Laser parameters are as for Figs. 15.

Fig. 7.
Fig. 7.

Animation (1.0 MB) of the time development of |Ψ(x, y)|2 for one-dimensional helium for a four-cycle trapezoidal pulse (1+2+1) of intensity 1.0×1015 W/cm 2 and frequency 0.1837a.u.. The still image is for t=2.875 cycles, and shows both jets and sequential ionization.

Fig. 8.
Fig. 8.

Linear plots of |Ψ(x, y)|2 vs. x and y at t=2.25 cycles for C=1.0 and 1.1, and for laser parameters of Fig 7. As for the lower intensity, there is an enhancement of the double-ionization jets.

Fig. 9.
Fig. 9.

Linear plots of |Ψ(x, y)|2 vs. x and y at t=1.875 cycles for C=1.0 and 1.1, and laser parameters as in Figs. 78. Note that the vertical axis is truncated at larger values than in Fig. 8. At this intensity the sequential ionization begins to dominate the double-ionization jets.

Fig. 10.
Fig. 10.

Linear plots of |Ψ(x, y)|2 vs. x and y at t=1.875 cycles (left) and t=2.25 cycles (right) for C=1.0, and laser intensity 3.0×1014 W/cm 2. The laser frequency remains unchanged from earlier plots, and is 0.1837a.u.. The two plots have very different viewpoints.

Equations (2)

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H ( x , y ) = p x 2 2 + p y 2 2 2 x 2 + 1 2 y 2 + 1 + C ( x y ) 2 + 1 + W ( x , y , t )
W ( x , y , t ) = ( x + y ) E 0 f ( t ) sin ω t

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