Abstract

We compare quantum and classical models of double ionization (DI) for aligned-electron helium in strong laser fields, considering specifically the role of recollision processes in which the returning electron travels in the direction of the laser force. Quantum studies show that for the knee region in our model a small but persistent portion of the total DI occurs through these speed-up collisions. We show that classical modeling displays similar collisions and reveals that with-the-force doubly ionizing collisions typically involve two-particle trajectories in which both electrons can be said to have been bound or very nearly bound at the zero of the laser field just before the collision. Trajectories leading to the with-the-force doubly ionizing collisions can be classified into two categories–direct excitation, in which there is no unambiguous single ionization before the doubly ionizing collision, and recapture, in which an ionized electron returns to the core and is recaptured prior to the speed-up collision. Comparison of the classical and quantum situations for our laser parameters yields evidence that for our parameters the quantum system favors the direct-excitation pathway over the reattachment pathway.

© 2004 Optical Society of America

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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, 2642-2645 (1992).
    [CrossRef]
  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, 1227-1230 (1994).
    [CrossRef] [PubMed]
  3. R. D¨orner, Th. Weber, M. Weckenbrock, A. Staudte, M. Hattass, R. Moshammer, J. Ulrich, and H. Schmidt-B¨ocking, �??Multiple Ionization in Strong Laser Fields,�?? Advances in Atomic, Molecular, and Optical Physics 48, 1-35 (2002).
    [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. 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]
  6. R. Moshammer et al., �??Momentum Distributions of Nen+ Ions Created by an Intense Ultrashort Laser Pulse,�?? Phys. Rev. Lett. 84, 447 (2000).
    [CrossRef] [PubMed]
  7. P. B. Corkum, �??Plasma perspective on strong field multiphoton ionization,�?? Phys. Rev. Lett. 71, 1994-1997 (1993).
    [CrossRef] [PubMed]
  8. K. J. Schafer, B. Yang, L. F. DiMauro and K. C. Kulander, �??Above threshold ionization beyond the high harmonic cutoff,�?? Phys. Rev. Lett. 70, 1599-1602 (1993).
    [CrossRef] [PubMed]
  9. K.C. Kulander, J. Cooper, and K.H. Schafer, �??Laser-assisted inelastic rescattering during above-threshold ionization,�?? Phys. Rev. A 51, 561 (1995).
    [CrossRef] [PubMed]
  10. F. H. M. Faisal and A. Becker, �??Nonsequential double ionization: mechanism and model formula,�?? Laser Phys. 7, 684 (1997).
  11. A. Becker and F.H.M. Faisal, �??Interpretation of momentum distribution of recoil ions from laser induced nonsequential double ionization,�?? Phys. Rev. Lett. 84, 3546 (2000).
    [CrossRef] [PubMed]
  12. C. Figueira de Morisson Faria, H. Schomerus, X. Liu, and W. Becker �??Electron-electron dynamics in laserinduced nonsequential double ionization,�?? Phys. Rev. A 69, 043405 (2004).
    [CrossRef]
  13. H.W. van der Hart and K. Burnett, �??Recollision model for double ionization of atoms in strong lasser fields,�?? Phys. Rev. A 62, 013407 (2000).
    [CrossRef]
  14. E. Eremina et al. �??Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization,�?? J. Phys. B: At. Mol. Opt. Phys. 36, 3269-3280 (2003).
    [CrossRef]
  15. S. L. Haan, P. S. Wheeler, R. Panfili, and J. H. Eberly, �??Origin of correlated electron emission in double ionization of atoms,�?? Phys. Rev. A 66, 061402(R) (2002).
    [CrossRef]
  16. J. Javanainen, J.H. Eberly, and Qichang Su, �??Numerical simulations of multiphoton ionization and abovethreshold electron spectra,�?? Phys. Rev. A 38, 3430-3446 (1988).
    [CrossRef] [PubMed]
  17. R. Grobe and J.H. Eberly, �??Photoelectron spectra for a two-electron system in a strong laser field,�?? Phys. Rev. Lett. 68, 2905-2908 (1992).
    [CrossRef] [PubMed]
  18. D. Bauer, �??Two-dimensional, two-electron model atom in a laser pulse: Exact treatment, single-activie-electron analysis, time-dependent density-functional theory, classical calculations, and nonsequential ionization,�?? Phys. Rev. A 56, 3028-3039 (1997).
    [CrossRef]
  19. J.B. Watson, A. Sanpera, D.G. Lappas, P.L. Knight, and K. Burnett, �??Nonsequentiall Double Ionization of Helium,�?? Phys. Rev. Lett. 78, 1884-1887 (1997).
    [CrossRef]
  20. 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]
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  22. J. S. Parker, B.J.S. Doherty, K.J. Meharg, and K.T. Taylor, �??Time delay between singly and doubly ionizing wavepackets in laser-driven helium,�?? J. Phys. B 36, L393 (2003).
    [CrossRef]
  23. 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, 5009-5017 (1987).
    [CrossRef]
  24. S. L. Haan, K. 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). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-1-29">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-1-29</a>
    [CrossRef] [PubMed]
  25. S. L. Haan, N. Hoekema, R. Panfili, J. H. Eberly, �??Exploration of Double Ionization Using Wavefunction Masking,�?? manuscript in preparation.
  26. R. Panfili, J. H. Eberly and S. Haan, �??Comparing classical and quantum simulations of strong-field double ionization,�?? Opt. Express 8, 431-435 (2001). <a href="http://www.opticsexpress.org/oearchive/source/31132.htm">http://www.opticsexpress.org/oearchive/source/31132.htm</a>
    [CrossRef] [PubMed]
  27. R. Panfili, S. L. Haan, and J. H. Eberly, �??Dynamics of classical slow-down collisions in non-sequential double ionization,�?? Phys. Rev. Lett. 89, 113001 (2002).
    [CrossRef] [PubMed]

Advances in Atomic, Molecular, and Optic (1)

R. D¨orner, Th. Weber, M. Weckenbrock, A. Staudte, M. Hattass, R. Moshammer, J. Ulrich, and H. Schmidt-B¨ocking, �??Multiple Ionization in Strong Laser Fields,�?? Advances in Atomic, Molecular, and Optical Physics 48, 1-35 (2002).
[CrossRef]

J. Chem. Phys. (1)

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, 5009-5017 (1987).
[CrossRef]

J. Phys. B (1)

J. S. Parker, B.J.S. Doherty, K.J. Meharg, and K.T. Taylor, �??Time delay between singly and doubly ionizing wavepackets in laser-driven helium,�?? J. Phys. B 36, L393 (2003).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys. (1)

E. Eremina et al. �??Laser-induced non-sequential double ionization investigated at and below the threshold for electron impact ionization,�?? J. Phys. B: At. Mol. Opt. Phys. 36, 3269-3280 (2003).
[CrossRef]

Laser Phys. (1)

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

Opt. Express (3)

Phys. Rev. A (6)

K.C. Kulander, J. Cooper, and K.H. Schafer, �??Laser-assisted inelastic rescattering during above-threshold ionization,�?? Phys. Rev. A 51, 561 (1995).
[CrossRef] [PubMed]

D. Bauer, �??Two-dimensional, two-electron model atom in a laser pulse: Exact treatment, single-activie-electron analysis, time-dependent density-functional theory, classical calculations, and nonsequential ionization,�?? Phys. Rev. A 56, 3028-3039 (1997).
[CrossRef]

C. Figueira de Morisson Faria, H. Schomerus, X. Liu, and W. Becker �??Electron-electron dynamics in laserinduced nonsequential double ionization,�?? Phys. Rev. A 69, 043405 (2004).
[CrossRef]

H.W. van der Hart and K. Burnett, �??Recollision model for double ionization of atoms in strong lasser fields,�?? Phys. Rev. A 62, 013407 (2000).
[CrossRef]

S. L. Haan, P. S. Wheeler, R. Panfili, and J. H. Eberly, �??Origin of correlated electron emission in double ionization of atoms,�?? Phys. Rev. A 66, 061402(R) (2002).
[CrossRef]

J. Javanainen, J.H. Eberly, and Qichang Su, �??Numerical simulations of multiphoton ionization and abovethreshold electron spectra,�?? Phys. Rev. A 38, 3430-3446 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (10)

R. Grobe and J.H. Eberly, �??Photoelectron spectra for a two-electron system in a strong laser field,�?? Phys. Rev. Lett. 68, 2905-2908 (1992).
[CrossRef] [PubMed]

A. Becker and F.H.M. Faisal, �??Interpretation of momentum distribution of recoil ions from laser induced nonsequential double ionization,�?? Phys. Rev. Lett. 84, 3546 (2000).
[CrossRef] [PubMed]

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, 2642-2645 (1992).
[CrossRef]

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, 1227-1230 (1994).
[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]

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

P. B. Corkum, �??Plasma perspective on strong field multiphoton ionization,�?? Phys. Rev. Lett. 71, 1994-1997 (1993).
[CrossRef] [PubMed]

K. J. Schafer, B. Yang, L. F. DiMauro and K. C. Kulander, �??Above threshold ionization beyond the high harmonic cutoff,�?? Phys. Rev. Lett. 70, 1599-1602 (1993).
[CrossRef] [PubMed]

J.B. Watson, A. Sanpera, D.G. Lappas, P.L. Knight, and K. Burnett, �??Nonsequentiall Double Ionization of Helium,�?? Phys. Rev. Lett. 78, 1884-1887 (1997).
[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]

R. Panfili, S. L. Haan, and J. H. Eberly, �??Dynamics of classical slow-down collisions in non-sequential double ionization,�?? Phys. Rev. Lett. 89, 113001 (2002).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

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).

Other (1)

S. L. Haan, N. Hoekema, R. Panfili, J. H. Eberly, �??Exploration of Double Ionization Using Wavefunction Masking,�?? manuscript in preparation.

Supplementary Material (2)

» Media 1: MOV (253 KB)     
» Media 2: MOV (616 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Logarithmic plots of the modulus squared of the spatial wavefunction vs. positions x 1 and x 2 for the indicated times (in laser cycles). A spatial mask is applied at t = 2.5 c. In the top row the retained population lies 6 to 16 a.u. from the origin and in the half-plane where x 1 + x 2 < 0. The bottom row keeps population that lies further an 16 a.u. from the origin at t=2.5c. The laser frequency is 0.0584 a.u., and the intensity 6.5×1014 W/cm 2. The wedge-shaped jets of DI are typical of any half-cycle during which the laser pulse is at full intensity. Contours are drawn beginning at population density 10-6, with color gradations beginning at 10-7.

Fig. 2.
Fig. 2.

Two-electron classical trajectories that doubly ionize by with-the-force collisions between t = 2.5c and t = 3.0c. The figure on the left shows their positions at the start of the half-cycle (t = 2.5c). The figure on the right shows the jets of DI at t=2.875 c. These can be compared with the quantum results of Fig. 1.

Fig. 3.
Fig. 3.

Absolute yields of all DI (purple, and shown above) for each half cycle and of DI from speed-up collisions (green) below. The laser turns on from t=0 to 2c, is at full strength from t=2c to t=4c, and turns off t=4c to t=6c. The vertical scale is logarithmic, and the quantity actually graphed is yield+0.3 so that zero-yield data points can be included.

Fig. 4.
Fig. 4.

Animations of energy vs. position showing the two electrons and their effective potentials. The still images show the excited bound state at t = 2.0c that leads to a with-the-field collision. Although the two plots are very similar at t = 2.0c, their prior evolutions are very different. One animation illustrates the direct-excitation pathway, and the other shows single ionization and recapture. [Media 1] [Media 2]

Fig. 5.
Fig. 5.

This figure shows a comparison of absolute yields of with-the-force DI occurring during each half cycle via direct excitation (blue), which peaks in the half cycle ending at t = 2.0c, and via prior single ionization and reattachment (red).

Fig. 6.
Fig. 6.

Moduli squared of the spatial wavefunction vs. positions x 1 and x 2 for indicated times. In the top sequence a ring mask similar to that of Fig.1 is applied to the full wave-function at t=3.50 c. For the second row, a series of earlier masks was also applied, so as to keep only the regions where both electrons remain bound. Clearly the full wedge jets at t = 3.875c result primarily from this bound population.

Fig. 7.
Fig. 7.

Modulus squared of the spatial wavefunction vs. positions x 1 and x 2 after application of a ring mask at t=3.5c. Prior to times shown, all population within 6 a.u. of the origin was masked at times 2.5 c and 3.0 c. Jets are not present.

Equations (1)

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

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