Abstract

Numerical integration of the time-dependent Schrödinger equation for two three-dimensional electrons reveals the behavior of helium in the presence of strong 390 nm and 800 nm light. Non-sequential double ionization is seen to take place predominantly at times when the electric-field component of the light reaches its peak value. Double ionization starts only in the second cycle of a flat-top pulse, and reaches a stable value only after many cycles, showing that recollision, sometimes through very long trajectories, must be involved.

© Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. N.B. Delone and V.P. Krainov, "Tunneling and barrier suppression ionization of atoms and ions in a laser radiation field," Phys.-Uspekhi 41, 469 (1998).
    [CrossRef]
  2. S. Augst, D. Strikland, D. Meyerhofer, S.L. Chin, J. Eberly, "Tunneling ionization of noble gases in a high-intensity laser field," Phys. Rev. Lett. 63, 2212 (1989).
    [CrossRef] [PubMed]
  3. P. Lambropoulos, "Mechanisms for multiple ionization of atoms by strong laser pulses," Phys. Rev. Lett. 55, 2141 (1985).
    [CrossRef] [PubMed]
  4. B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer and K.C. Kulander, "Precision measurement of strong field double ionization," Phys. Rev. Lett. 73, 1227 (1994).
    [CrossRef] [PubMed]
  5. A. l'Huillier, A. Lompre, G. Mainfray, and C. Manus, "Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 µm," Phys. Rev. A 27, 2503 (1983).
    [CrossRef]
  6. P. Corkum, "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. 71, 1994 (1993).
    [CrossRef] [PubMed]
  7. 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]
  8. J.S. Parker, L.R. Moore, D. Dundas and K.T. Taylor, "Double ionization of helium at 390 nm," J. Phys. B 33, L691 (2000).
    [CrossRef]
  9. E.S. Smyth, J.S. Parker, K.T. Taylor, "Numerical integration of the time-dependent Schroedinger equation for laser-driven helium," Computer Phys. Comm. 114, 1 (1998).
    [CrossRef]
  10. K.J. Schafer and K.C. Kulander, "Energy analysis of time-dependent wave functions: Application to above-threshold ionization," Phys. Rev. A 42, 5794 (1992).
    [CrossRef]
  11. H.G. Muller, "Solving the time-dependent Schroedinger equation in five dimensions,' in L.F. DiMauro, R.R. Freeman, and K.C. Kulander (eds.) "Multiphoton processes: ICOMP VIII, 8th International Conference," CP525, p. 257 AIP, Melville NY (2000).
  12. H.G. Muller, "An efficient propagation scheme for the time-dependent Schroedinger equation in the velocity gauge," Laser Phys. 9, 138 (1999).
  13. H.G. Muller, "Numerical solution of high-order ATI enhancement in argon," Phys. Rev. A 60, 1341 (1999).
    [CrossRef]
  14. H.G. Muller, "Calculation of double ionization of helium," in B. Piraux et al. (eds.) "Super-Intense Laser-Atom Physics VI proceedings," NATO series B (2001) in print.
  15. J.L. Krause, K.J. Schafer and K.C. Kulander, "Calculation of photoemission from atoms subject to intense laser fields," Phys. Rev. A 45, 4998 (1992).
    [CrossRef] [PubMed]
  16. R. Kopold, W. Becker, and D.B. Milosevic, "Quantum orbits: a space-time picture of intense-laser-induced processes in atoms," Comments At. Mol. Phys. (2000) to be published.
  17. H.G. Muller and F.C. Kooiman, "Bunching and Focusing of Tunneling Wave Packets in Enhancement of High-Order ATI," Phys. Rev. Lett. 81, 1207 (1998).
    [CrossRef]
  18. H.G. Muller, "Identification of states responsible for ATI enhancement in argon by their calculated wave functions," Opt. Express 8, 44 (2001). http://www.opticsexpress.org/oearchive/source/26830.htm
    [CrossRef] [PubMed]
  19. J.B. Watson, A. Sanpera, K. Burnett, D.G. Lappas and P.L. Knight "Double ionization of helium beyond the single electron active electron approximation," in P. Lambropoulos and H. Walther, (eds.) "Multiphoton Processes: ICOMP VII, 7th International Conference," CS154, p. 132 IOP, Bristol, UK (1997).

Other (19)

N.B. Delone and V.P. Krainov, "Tunneling and barrier suppression ionization of atoms and ions in a laser radiation field," Phys.-Uspekhi 41, 469 (1998).
[CrossRef]

S. Augst, D. Strikland, D. Meyerhofer, S.L. Chin, J. Eberly, "Tunneling ionization of noble gases in a high-intensity laser field," Phys. Rev. Lett. 63, 2212 (1989).
[CrossRef] [PubMed]

P. Lambropoulos, "Mechanisms for multiple ionization of atoms by strong laser pulses," Phys. Rev. Lett. 55, 2141 (1985).
[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," Phys. Rev. Lett. 73, 1227 (1994).
[CrossRef] [PubMed]

A. l'Huillier, A. Lompre, G. Mainfray, and C. Manus, "Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 µm," Phys. Rev. A 27, 2503 (1983).
[CrossRef]

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

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]

J.S. Parker, L.R. Moore, D. Dundas and K.T. Taylor, "Double ionization of helium at 390 nm," J. Phys. B 33, L691 (2000).
[CrossRef]

E.S. Smyth, J.S. Parker, K.T. Taylor, "Numerical integration of the time-dependent Schroedinger equation for laser-driven helium," Computer Phys. Comm. 114, 1 (1998).
[CrossRef]

K.J. Schafer and K.C. Kulander, "Energy analysis of time-dependent wave functions: Application to above-threshold ionization," Phys. Rev. A 42, 5794 (1992).
[CrossRef]

H.G. Muller, "Solving the time-dependent Schroedinger equation in five dimensions,' in L.F. DiMauro, R.R. Freeman, and K.C. Kulander (eds.) "Multiphoton processes: ICOMP VIII, 8th International Conference," CP525, p. 257 AIP, Melville NY (2000).

H.G. Muller, "An efficient propagation scheme for the time-dependent Schroedinger equation in the velocity gauge," Laser Phys. 9, 138 (1999).

H.G. Muller, "Numerical solution of high-order ATI enhancement in argon," Phys. Rev. A 60, 1341 (1999).
[CrossRef]

H.G. Muller, "Calculation of double ionization of helium," in B. Piraux et al. (eds.) "Super-Intense Laser-Atom Physics VI proceedings," NATO series B (2001) in print.

J.L. Krause, K.J. Schafer and K.C. Kulander, "Calculation of photoemission from atoms subject to intense laser fields," Phys. Rev. A 45, 4998 (1992).
[CrossRef] [PubMed]

R. Kopold, W. Becker, and D.B. Milosevic, "Quantum orbits: a space-time picture of intense-laser-induced processes in atoms," Comments At. Mol. Phys. (2000) to be published.

H.G. Muller and F.C. Kooiman, "Bunching and Focusing of Tunneling Wave Packets in Enhancement of High-Order ATI," Phys. Rev. Lett. 81, 1207 (1998).
[CrossRef]

H.G. Muller, "Identification of states responsible for ATI enhancement in argon by their calculated wave functions," Opt. Express 8, 44 (2001). http://www.opticsexpress.org/oearchive/source/26830.htm
[CrossRef] [PubMed]

J.B. Watson, A. Sanpera, K. Burnett, D.G. Lappas and P.L. Knight "Double ionization of helium beyond the single electron active electron approximation," in P. Lambropoulos and H. Walther, (eds.) "Multiphoton Processes: ICOMP VII, 7th International Conference," CS154, p. 132 IOP, Bristol, UK (1997).

Supplementary Material (6)

» Media 1: MOV (740 KB)     
» Media 2: MOV (1268 KB)     
» Media 3: MOV (1028 KB)     
» Media 4: MOV (1067 KB)     
» Media 5: MOV (1137 KB)     
» Media 6: MOV (277 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

The red curve gives the double-ionization rate (defined as the outward current of the innermost electron through a sphere with radius 8 Bohr). The electric field is given by the blue line, which has a constant amplitude 0.152 for t>0. Similar curves for field amplitudes from 0.135 to 0.179 a.u. are stacked behind the figure as a movie (285 Kb), for easy comparison. The first burst of double ionization (at t=1.25) grows monotonously with intensity. The magnitude of later bursts varies wildly due to interference with earlier ones. The right plot shows the ratio between double and single ionzation yields over cycle 5 to 10.

Fig. 2.
Fig. 2.

One-cycle movie (1.2 Mb) of the charge distribution of the outer electron at E 0=0.1525 a.u., where the double ionization has a resonant peak.

Fig. 3.
Fig. 3.

The spatial distribution of the inner (left, 1.2 Mb) and outer (right, 1.3 Mb) electron in the first two cycles of the flat part of a flat-top pulse. The arrow represents the electric field vector. The circular cliff in the left movie is at the absorbing grid boundary.

Fig. 4.
Fig. 4.

Comparison of double ionization at 390 nm and 1100 TW/cm2, for the real case (blue) and in an artificial situation where the innermost electron does not feel the laser (red). (The first full E-field peak occurs at t=0.)

Fig. 5.
Fig. 5.

A movie (1.2 Mb) of the innermost electron charge (similar to fig. 2a) when this electron is artificially uncoupled from the laser.

Fig. 6.
Fig. 6.

Double ionization current at 800 nm, 505 TW/cm2, and E field causing it.

Fig. 7.
Fig. 7.

A movie (1.2 Mb) of the innermost electron charge distributions at 800 nm, 1000 TW/cm2. The electron repulsion was only included upto the dipole term.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

i t Ψ = ( 1 2 p 1 2 + 1 2 p 2 2 + V ( r 1 , r 2 ) + A ( t ) · p 1 + E ( t ) · r 2 ) Ψ .
γ l 1 l 2 m = ( Y l 1 m ( ϑ 1 , ϕ 12 ) Y l 2 m ( ϑ 2 , ϕ 12 ) + Y l 1 m ( ϑ 1 , ϕ 12 ) Y l 2 m ( ϑ 2 , ϕ 12 ) ) 2 .

Metrics