Abstract

We compare quantum mechanical and fully classical treatments of electron dynamics accompanying strong field double ionization. The major features seen in quantum mechanical simulations, including the double-ionization jets, are reproduced when using a classical ensemble of two-particle trajectories.

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References

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  1. 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 (1993).
    [CrossRef] [PubMed]
  2. P. B. Corkum, "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. 71, 1994 (1993).
    [CrossRef] [PubMed]
  3. M. Yu. Ivanov, unpublished.
  4. S. L. Haan, N. Hoekema, S. Poniatowski, W.-C. Liu, and J. H. Eberly, "Directional correlation in direct and sequential double ionization of model atoms," Opt. Express 7, 29-38 (2000). http://www.opticsexpress.org/oearchive/21863.htm
    [CrossRef] [PubMed]
  5. R. Grobe, S. L. Haan, and J. H. Eberly, "A split-domain algorithm for time-dependent multi-electron wave functions," Comp. Phys. Commun. 117, 200-210 (1999).
    [CrossRef]
  6. F. H. M. Faisal and A. Becker, "Nonsequential double ionization: mechanism and model formula," Laser Phys. 7, 684-688 (1997).
  7. D. Dundas, K. T. Taylor, J. S. Parker, and E. S. Smyth, " Double-ionization dynamics of laser-driven helium," J. Phys. B 32, L231-L238 (1999).
    [CrossRef]
  8. 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, 520-523 (1999).
    [CrossRef]

Other

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 (1993).
[CrossRef] [PubMed]

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

M. Yu. Ivanov, unpublished.

S. L. Haan, N. Hoekema, S. Poniatowski, W.-C. Liu, and J. H. Eberly, "Directional correlation in direct and sequential double ionization of model atoms," Opt. Express 7, 29-38 (2000). http://www.opticsexpress.org/oearchive/21863.htm
[CrossRef] [PubMed]

R. Grobe, S. L. Haan, and J. H. Eberly, "A split-domain algorithm for time-dependent multi-electron wave functions," Comp. Phys. Commun. 117, 200-210 (1999).
[CrossRef]

F. H. M. Faisal and A. Becker, "Nonsequential double ionization: mechanism and model formula," Laser Phys. 7, 684-688 (1997).

D. Dundas, K. T. Taylor, J. S. Parker, and E. S. Smyth, " Double-ionization dynamics of laser-driven helium," J. Phys. B 32, L231-L238 (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, 520-523 (1999).
[CrossRef]

Supplementary Material (4)

» Media 1: MOV (721 KB)     
» Media 2: MOV (1491 KB)     
» Media 3: MOV (1634 KB)     
» Media 4: MOV (2577 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

|Ψ(x, y)|2 during a four-cycle trapezoidal (1+2+1) pulse with laser frequency 0.0584 a.u. and intensity 6.5×1014W/cm2. The scale is logarithmic, beginning at 10-7. The still image shows an ionization burst in the fourth quadrant and jets emerging into the third quadrant early in the third cycle. The animation (.7MB) shows the time development for the full pulse.

Fig. 2.
Fig. 2.

(1.4 MB) Position space distribution for a particular numerical experiment usinga classical ensemble and the same laser parameters as in Fig. 1. The red arrow indicates the direction and magnitude of the electric force.

Fig. 3.
Fig. 3.

(1.6 MB) Position space distribution for a particular numerical experiment usingb oth classical and quantum simulations. The laser frequency is ω=0.1837 a.u. and the peak intensity is 6.5×1014W/cm2. The pulse envelope is six cycles long with two cycle linear ramp on and off and a two cycle plateau. The time chosen for the still image is more than one-half cycle later than those of Figs. 1 and 2. As a result, the double-ionization jets appear on the opposite side of the nucleus.

Fig. 4.
Fig. 4.

Initial distribution of 10,000 two-particle trajectories in position space.

Fig. 5.
Fig. 5.

The left hand still image shows an initial distribution of 10,000 two-particle trajectories populated by the method described in the text. The right hand still image shows a collection of 10,000 two-particle trajectories populated using a Gaussian probability distribution. The movie associated with this picture (2.5 MB) shows the free evolution of this collection. The data have been smoothed on a uniform grid of spacing δx=0.1a.u. to generate these contour plots. An atomic unit of time, in terms of fundamental constants is t=2πħ/2|Eg |, where Eg is the ground state energy of the hydrogen atom. It is on the order of 10-17 s.

Equations (3)

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H ( x , y ) = p x 2 2 + p y 2 2 2 x 2 + 1 2 y 2 + 1 + 1 ( x - y ) 2 + 1 + ( x + y ) E ( t ) ,
x ̈ = E ( t ) 2 x ( x 2 + 1 ) 3 2 + ( x y ) ( ( x y ) 2 + 1 ) 3 2
y ̈ = E ( t ) 2 y ( y 2 + 1 ) 3 2 ( x y ) ( ( x y ) 2 + 1 ) 3 2 .

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