## Speed-up collisions in strong-field double ionization

Optics Express, Vol. 12, Issue 20, pp. 4758-4767 (2004)

http://dx.doi.org/10.1364/OPEX.12.004758

Acrobat PDF (1156 KB)

### 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

## 1. Introduction

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]

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]

7. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. **71**, 1994–1997 (1993). [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]

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]

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 above-threshold electron spectra,” Phys. Rev. A **38**, 3430–3446 (1988). [CrossRef] [PubMed]

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]

*E*

_{0}

*f*(

*t*)sin

*ωt*is

*x*

_{1}and

*x*

_{2}are the positions of the two particles, and

*p*

_{1}and

*p*

_{2}their momenta.

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]

*a.u.*, with absorbing boundaries. We start the system in the quantum ground state, and apply a 6-cycle trapezoidal (2+2+2) laser pulse. Also, in order to connect most directly with our previous works, we work here with laser intensity 6.5×10

^{14}

*W*/

*cm*

^{2}and frequency

*ω*= 0.0584

*a.u.*, corresponding to 13-photon single ionization and 39-photon double ionization. These parameters place the DI yield in the familiar knee region.

## 2. Quantum masking

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). http://www.opticsexpress.org/oearchive/21863.htm [CrossRef] [PubMed]

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]

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]

**66**, 061402(R) (2002). [CrossRef]

**66**, 061402(R) (2002). [CrossRef]

*x*

_{1}+

*x*

_{2}< 0 half plane, lying from 6 to 16

*a.u.*from the origin. In the lower plot we show remaining population in that half plane with distance more than 16

*a.u.*from the origin. The top row dominates the DI from speed-up collisions. At t=2.75 c, population in the region 5

*a.u.*<

*x*

_{1},

*x*

_{2}< 75

*a.u.*in the upper plot is 1.93×10

^{-3}and the lower is 0.22×10

^{-3}. The jets, most visible at t=2.875 c, propagate close to the axes, indicating one electron traveling faster than the other.

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). http://www.opticsexpress.org/oearchive/source/31132.htm [CrossRef] [PubMed]

## 3. Classical filtering

**66**, 061402(R) (2002). [CrossRef]

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). http://www.opticsexpress.org/oearchive/source/31132.htm [CrossRef] [PubMed]

*E*= -2.238

*a.u.*to a pair of pilot electrons at the origin, randomly allocating the kinetic energy between them, and then allowing them to propagate without the laser field throughout the allowed phase space. Initial conditions are determined by sampling their state at randomly chosen particular times over long time intervals. Our primary ensemble contains one million such two-particle trajectories, of which 28,004 doubly ionize by the end of the six-cycle laser pulse. In the present work a double ionization is defined to have occurred at the end of the pulse if each electron has positive total energy, excluding the electron-electron interaction.

*a.u.*from the nucleus or has energy more than 0.3

*a.u.*. Electrons that are too far from the nucleus or which have too much outward momentum simply do not return in time for an effective speed-up collision.

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]

## 4. Analyzing jet formation

*a.u.*away. In these plots, the electrons are shown as colored dots. The solid curves represent effective potential energies for each electron [27

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]

## 5. Quantum comparison

*a.u.*from the origin is masked out at t=1.0, 1.5, 2.0, 2.5, and 3.0 cycles. Strong jets are still present, despite all these masks. The total population in the region 5

*a.u.*<

*x*1,

*x*2 < 75

*a.u.*at t=3.875 c is 1.10×10

^{-3}, compared with 1.23×10

^{-3}in the top row. Our conclusion is that large excursions are not important for the preponderance of the with-the-force DI.

*a.u.*) at times 2.50 and 3.00 c, and then applying a ring mask at t=3.5 c as in Fig.6. Results are shown in Fig. 7. No jets are visible in quadrant 1. We infer that reattachment does not contribute significantly to the formation of the with-the-force jets shown in the other figures.

**66**, 061402(R) (2002). [CrossRef]

## 6. Summary

## Acknowledgments

## 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, 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. |

3. | R. Dörner, Th. Weber, M. Weckenbrock, A. Staudte, M. Hattass, R. Moshammer, J. Ulrich, and H. Schmidt-Böcking, “Multiple Ionization in Strong Laser Fields,” Advances in Atomic, Molecular, and Optical Physics |

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. | Th. Weber |

6. | R. Moshammer |

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

8. | K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. |

9. | K.C. Kulander, J. Cooper, and K.H. Schafer, “Laser-assisted inelastic rescattering during above-threshold ionization,” Phys. Rev. A |

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

11. | A. Becker and F.H.M. Faisal, “Interpretation of momentum distribution of recoil ions from laser induced nonsequential double ionization,” Phys. Rev. Lett. |

12. | C. Figueira de Morisson Faria, H. Schomerus, X. Liu, and W. Becker “Electron-electron dynamics in laser-induced nonsequential double ionization,” Phys. Rev. A |

13. | H.W. van der Hart and K. Burnett, “Recollision model for double ionization of atoms in strong lasser fields,” Phys. Rev. A |

14. | E. Eremina |

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 |

16. | J. Javanainen, J.H. Eberly, and Qichang Su, “Numerical simulations of multiphoton ionization and above-threshold electron spectra,” Phys. Rev. A |

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

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 |

19. | J.B. Watson, A. Sanpera, D.G. Lappas, P.L. Knight, and K. Burnett, “Nonsequentiall Double Ionization of Helium,” Phys. Rev. Lett. |

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. |

21. | A.M. Popov, O.V. Tikhonova, and E.A. Volkova, “Mechanisms of double-electron ionization of atomic systems in a strong laser field,” Opt. Express |

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 |

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. |

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 |

25. | S. L. Haan, N. Hoekema, R. Panfili, and 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 |

27. | R. Panfili, S. L. Haan, and J. H. Eberly, “Dynamics of classical slow-down collisions in non-sequential double ionization,” 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:**

Research Papers

**History**

Original Manuscript: August 11, 2004

Revised Manuscript: September 16, 2004

Published: October 4, 2004

**Citation**

Stanley Haan, J. Cully, and K. Hoekema, "Speed-up collisions in strong-field double ionization," Opt. Express **12**, 4758-4767 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-20-4758

Sort: Journal | Reset

### 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, 2642-2645 (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]
- 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]
- 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).
- 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]
- 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]
- F. H. M. Faisal and A. Becker, �??Nonsequential double ionization: mechanism and model formula,�?? Laser Phys. 7, 684 (1997).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- A.M. Popov, O.V. Tikhonova, and E.A. Volkova, �??Mechanisms of double-electron ionization of atomic systems in a strong laser field,�?? Opt. Express 8, 441-446 (2001). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- S. L. Haan, N. Hoekema, R. Panfili, J. H. Eberly, �??Exploration of Double Ionization Using Wavefunction Masking,�?? manuscript in preparation.
- 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]
- 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]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.