## Comparing classical and quantum dynamics of strong-field double ionization

Optics Express, Vol. 8, Issue 7, pp. 431-435 (2001)

http://dx.doi.org/10.1364/OE.8.000431

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### 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.

© Optical Society of America

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]

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]

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]

*x*and

*y*denote position variables for the electrons, and

*E*(

*t*)=

*E*

_{0}

*f*(

*t*) sin

*ωt*is the electric field of the laser.

*E*

_{0}is the peak field strength,

*ω*is the laser (angular) frequency, and

*f*(

*t*) is a pulse-shape function which we take to be trapezoidal.

^{14}W/cm

^{2}, which gives appreciable single and double ionization [8

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]

*x*,

*y*)|

^{2}is plotted on a logarithmic scale during a four-cycle trapezoidal pulse (one cycle linear ramp on, two cycle plateau and one cycle linear ramp off). Population along the axes in Fig. 1 indicates one electron is near the origin and the other is far away and is a signature of single-electron excitation or ionization. Population moving out into the various quadrants indicates double ionization.

*ω*=0.1837 a.u. corresponding to five-photon single ionization and 13-photon double ionization. The similarity between quantum and classical dynamics is clear. The spatial extent of population moving along each axis is nearly identical, as is the timing of the appearance of double ionization bursts and jets.

*F*⃑(

*x*,

*y*)=-

*E*(

*t*)-∇

*V*(

*x*,

*y*)). In atomic units, these equations are:

*x*and

*y*), but other than that one complication these equations can be solved using any of a number of well-known techniques.

*n*element of the initial ensemble is generated by finding the position and momentum of the original trajectory at time

^{th}*n*Δ

*t*. The time step Δ

*t*is chosen large enough to ensure that the entire region of space that is energetically allowed is filled. Fig. 4 shows an initial state of this ensemble using 10,000 trajectories.

## Acknowledgements

## References and links

1. | K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above Threshold Ionization Beyond the High Harmonic Cutoff,” Phys. Rev. Lett. |

2. | P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. |

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 |

5. | R. Grobe, S. L. Haan, and J. H. Eberly, “A split-domain algorithm for time-dependent multi-electron wave functions,” Comp. Phys. Commun. |

6. | F. H. M. Faisal and A. Becker, “Nonsequential double ionization: mechanism and model formula,” Laser Phys. |

7. | D. Dundas, K. T. Taylor, J. S. Parker, and E. S. Smyth, “Double-ionization dynamics of laser-driven helium,” J. Phys. B |

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. |

**OCIS Codes**

(020.4180) Atomic and molecular physics : Multiphoton processes

(260.3230) Physical optics : Ionization

(270.6620) Quantum optics : Strong-field processes

**ToC Category:**

Focus Issue: Laser-induced multiple ionization

**History**

Original Manuscript: February 9, 2001

Published: March 26, 2001

**Citation**

Raphael Panfili, J. Eberly, and Stan Haan, "Comparing classical and quantum simulations of strong-field double-ionization," Opt. Express **8**, 431-435 (2001)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-7-431

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### References

- 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]

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