## Directional correlation in direct and sequential double ionization of model atoms

Optics Express, Vol. 7, Issue 1, pp. 29-38 (2000)

http://dx.doi.org/10.1364/OE.7.000029

Acrobat PDF (1965 KB)

### 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.

© Optical Society of America

## 1 Introduction

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

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

29. M. Dörr, “Double ionization in a one-cycle laser pulse,” Optics Express **6**, 111 (2000). http://www.opticsexpress.org/oearchive/source/19114.htm [CrossRef]

24. Q. Su and J.H. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A **44**, 5997 (1991). [CrossRef] [PubMed]

*x*and

*y*denote position variables for the electrons, and

*C*represents a “correlation charge.” We typically set

*C*=1so that the electron-electron interaction is of equal strength with the electron-proton interaction, but variation of

*C*also can provide information about electron correlation.

*E*

_{0}denotes the field strength,

*ω*the laser frequency, and

*f*(

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

*x*and

*y*variables, and solve the Schrödinger equation on the resulting two-coordinate spatial grid. We evolve the spatial wavefunction Ψ(

*x, y*) in time using split-operator techniques and a split-domain algorithm [26

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]

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 transformmethods for systems with spatially extended wave function and localized potential,” J. Chem. Phys. **86**, 5009 (1987). [CrossRef]

*x, y*)=Ψ(

*y, x*) is preserved for all time.

13. 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 (1999). [CrossRef]

21. C. Szymanowski, 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]

*C*[13

13. 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 (1999). [CrossRef]

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]

20. R. Moshammer*et al*., “Momentum Distributions of Ne^{n+}Ions Created by an Intense Ultrashort Laser Pulse,” Phys. Rev. Lett. **84**, 447 (2000). [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. Dörr, “Double ionization in a one-cycle laser pulse,” Optics Express **6**, 111 (2000). http://www.opticsexpress.org/oearchive/source/19114.htm [CrossRef]

## 2 Time Development of the Spatial Wavefunction

*I*=6.5×10

^{14}W/

*cm*

^{2}with its frequency corresponding to five-photon single ionization. This frequency places the ionization in the knee area [13

13. 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 (1999). [CrossRef]

^{-4}for the clearest viewing of the general characteristics of the development. We have previously presented [32] logarithmic contour plots for this time development, but with much larger time increments. The animation shows 32 images per cycle. The still image in Fig. 1is for t=2.875 cycles.

*y*=

*x*.

*t*=2.25 cycles. The jets emerge during the latter part of each half cycle and in the direction of electric force. Their emergence directly from the origin indicates simultaneous departure from the nuclear region for the two electrons (although this need not be the first departure for both!); their direction of motion implies that the electrons have similar velocities. (Motion directly along the line

*y*=

*x*would correspond to equal velocities.) The

*x*-

*y*symmetry mentioned above is obvious.

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]

20. R. Moshammer*et al*., “Momentum Distributions of Ne^{n+}Ions Created by an Intense Ultrashort Laser Pulse,” Phys. Rev. Lett. **84**, 447 (2000). [CrossRef] [PubMed]

**83**, 520 (1999). [CrossRef]

*C*appearing in the Hamiltonian 1. Our detailed plots allow us to investigate reasons underlying this dependence.

*C*=0.9 or

*C*=1.1to complement our studies with

*C*=1.0. Figures 3 and 4 show logarithmic contour plots of |Ψ(

*x, y*)|

^{2}vs.

*x*and

*y*after each cycle of 6-cycle (2+2+2 trapezoidal) pulse for the three values of

*C*. Other parameters are the same as for Figs. 1 and 2. Because of the longer turn-on time, no significant double ionization occurs until the third laser cycle. These plots show a considerable increase in double ionization with increasing

*C*. The enhancement of the jets with increased

*C*is especially noteworthy.

*C*is increased, Fig. 5 repeats Fig. 2, but with C=1.1. The enhancement of the jets with increased correlation charge

*C*is very dramatic.

*C*, in Fig. 6 we present still images of |Ψ(

*x, y*)|

^{2}at

*t*=1.875 cycles for the two

*C*values from the same viewpoint as in Fig. 1. There is an enhancement of the sequential ionization, but not as dramatic as the jet enhancement. The inference we draw is what might have been expected, namely that the electron-electron repulsion is not as important in the sequential ionization as for rescattering ionization.

*C*-and hence the reason for the enhanced double ionization-is the jets.

^{15}W/

*cm*

^{2}. We keep the same laser frequency. Figure 7 is analogous to Fig. 1, but for this higher laser intensity. Enhancement is clearly visible for the jets as well as for the sequential ionization, but increasing the laser intensity has clearly had greater effect on the sequential ionization than on the jets. This result is consistent with our expectation that sequential ionization should become more dominant as the laser intensity is increased.

*C*at intensities above the knee. This conclusion is supported by Figs. 8 and 9, which compare stop-action views for

*C*=1.0 and 1.1, and shows that increased

*C*provides noticeable enhancement of the jets. Figure 9 shows the sequential ionization at

*t*=1.875 cycles for the two values of

*C*, and shows once again that the sequential ionization is less dependent on

*C*than the jets are. All these results are consistent with the idea that the knee is due to the double-ionization jets. At high intensities such as that of Figs. 7–9, the sequential ionization begins to dominate.

*I*=3×10

^{14}

*W/cm*

^{2}, which is below the knee area. In Figs. 10, we present stop-action shots (for

*C*=1.0) at times

*t*=1.875 cycles (left) and

*t*=2.25 cycles (right). Because of diminished ionization, the plots use vertical scales that are a factor of 10 lower than in our earlier figures. At this intensity, the jets are more visible than the sequential double ionization. These times are the same as for earlier plots.

## 3 Summary

*x, y*)|

^{2}is useful in developing understanding of the single and double-ionization process. One topic we have not discussed is the the role that resonances might play in the ionization process. Changing the value of

*C*will also change energy-levels of the model system, which can alter the dynamics of the double-ionization process. Some of us take up that topic elsewhere [21

21. C. Szymanowski, 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]

## Acknowledgements

## References and links

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. |

2. | B. Walker |

3. | B. Sheehy |

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 |

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 |

6. | A. Becker and F. H. M. Faisal, “Mechanism of laser-induced double ionization of helium,” J. Phys. B |

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

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 |

9. | J. B. Watson |

10. | K. Burnett |

11. | M. S. Pindzola, F. Robicheaux, and P. Gavras, “Double multiphoton ionization of a model atom,” Phys. Rev. A |

12. | D. G. Lappas and R. Leeuwen, “Electron correlation effects in the double ionization of He,” J. Phys. B |

13. | 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. |

14. | J. Parker, K. T. Taylor, C. W. Clark, and S. Blodgett-Ford, “Intense-field multiphoton ionization of a two-electron atom,” J. Phys. B |

15. | J. Parker, E. S. Smyth, and K. T. Taylor, “Intense-field multiphoton ionization of helium,” J. Phys. B |

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

17. | Th. Weber |

18. | Th. Weber |

19. | Th. Weber |

20. | R. Moshammer |

21. | C. Szymanowski, 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 |

22. | M.S. Pindzola, D.C. Griffin, and C. Bottcher, “Validity of time-dependent Hartree-Fock theory for the multiphoton ionization of atoms,” Phys. Rev. Lett. |

23. | R. Grobe and J.H. Eberly, “Photoelectron spectra for a two-electron system in a strong laser field,” Phys. Rev. Lett. |

24. | Q. Su and J.H. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A |

25. | J.H. Eberly, R. Grobe, C.K. Law, and Q. Su, “Numerical experiments in strong and super-strong fields,” in |

26. | R. Grobe and J.H. Eberly, “One-dimensional model of a negative ion and its interaction with laser fields,” Phys. Rev. A |

27. | S.L. Haan, R. Grobe, and J.H. Eberly, “Numerical study of autoionizing states in completely correlated two-electron systems,” Phys. Rev. A |

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 |

29. | M. Dörr, “Double ionization in a one-cycle laser pulse,” Optics Express |

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

31. | R. Heather and H. Metiu, “An efficient procedure for calculating the evolution of the wave function by fast Fourier transformmethods for systems with spatially extended wave function and localized potential,” J. Chem. Phys. |

32. | J.H. Eberly, W.-C. Liu, and S.L. Haan, “The role of correlation in non-sequential double ionization,” in press in |

**OCIS Codes**

(020.4180) Atomic and molecular physics : Multiphoton processes

(260.3230) Physical optics : Ionization

(270.6620) Quantum optics : Strong-field processes

**ToC Category:**

Research Papers

**History**

Original Manuscript: May 18, 2000

Published: July 3, 2000

**Citation**

Stan Haan, N. Hoekema, S. Poniatowski, Wei-Chih Liu, and J. Eberly, "Directional correlation in direct and sequential double ionization of model atoms," Opt. Express **7**, 29-38 (2000)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-1-29

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### References

- 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).

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