## Double ionization of HeH+ molecules in intense laser fields

Optics Express, Vol. 16, Issue 21, pp. 17070-17075 (2008)

http://dx.doi.org/10.1364/OE.16.017070

Acrobat PDF (191 KB)

### Abstract

We present quantum mechanical calculations of double ionization of HeH+ molecules by intense laser pulses at various intensities. The resulting two-electron momentum distributions exhibit a clear asymmetry, which depends on the laser intensity. The asymmetric charge configuration of HeH+ is responsible for the asymmetric two-electron momentum distributions. An approach to control the dynamics of double ionization of heteronuclear molecules is proposed.

© 2008 Optical Society of America

^{+}, the simplest two-electron heteronuclear molecule with asymmetric electric charge on nuclei, has not yet been studied. In this paper, we investigate the two-electron momentum distributions from double ionization of HeH

^{+}molecules by linearly polarized laser pulses. This is achieved by solving the time-dependent electronic Schödinger equation of a one-dimensional HeH

^{+}molecule model within the clamped nuclei approximation, where the motion of both electrons is restricted to the

*z*-axis (i.e., the laser polarization axis, see Fig. 3). The molecular axis is aligned parallel to the

*z*-axis. The He and H nuclei are localized at

*z*=-

*R*/2 and

*z*=

*R*/2, respectively. The electron-nuclear interaction and the electron-electron repulsion are represented by a two-center soft-Coulomb potential (in atomic units)

*z*

_{1}and

*z*

_{2}are the electron coordinates,

*R*is the internuclear distance. It has been shown that one-dimensional models qualitatively reproduces all important strong-field effects including double ionization [7

7. M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of Helium: identifying the mechanism,” Phys. Rev. Lett. **85**, 4707–4710 (2000). [CrossRef] [PubMed]

16. M. Lein, T. Kreibich, E. K. U. Gross, and V. Engel, “Strong-field ionization dynamics of a model H_{2} molecule,” Phys. Rev. A **65**, 033403 (2002). [CrossRef]

*E*(

*t*)=

*E*

_{0}

*f*(

*t*)sin(

*ωt*) is the electric field of a laser pulse with amplitude

*E*

_{0}, envelope function

*f*(

*t*) and frequency

*ω*. The ground-state energy of HeH

^{+}is -2.8 a.u., including the ionization potential of HeH

^{+}

*I*

^{(1)}

_{p}=1.05 a.u. and the ionization potential of HeH

^{2}

^{+}

*I*

^{(2)}

*=1.75 a.u. The first excited-state energy of HeH*

_{p}^{2+}is -1.23 a.u.

7. M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of Helium: identifying the mechanism,” Phys. Rev. Lett. **85**, 4707–4710 (2000). [CrossRef] [PubMed]

*z*

_{1}|, |

*z*

_{2}|<

*a*}, (B) {|

*z*

_{1}|<

*a*, |

*z*

_{2}|≥

*a*}, or {|

*z*

_{1}|≥

*a*, |

*z*

_{2}|<

*a*} and (

*C*) {|

*z*

_{1}|, |

*z*

_{2}| ≥

*a*} with a=200 a.u. Regions B and C correspond to single and double ionization respectively. In regions A and B, the wave function is propagated exactly by means of the split-operator spectral method [17

17. M. D. Feit, J. A. Fleck Jr., and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. **47**, 412–433 (1982). [CrossRef]

*V*(

*z*

_{1},

*z*

_{2}) can be neglected. Therefore, the time evolution of the wave function can be performed only in the presence of the laser field by multiplications in momentum space [18

18. S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H^{+}_{2} dissociative ionization in intense laser fields,” Phys. Rev. A **57**, 1176 (1998). [CrossRef]

19. X. M. Tong, K. Hino, and N. Toshima, “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A **74**, 031405(R) (2006). [CrossRef]

*a*ranging from 100 to 200 a.u.

^{+}molecules at an internuclear distance

*R*=4 a.u. The momentum distributions at lower laser intensities are very different from those at higher laser intensities. At lower laser intensities, the two-electron momentum distributions exhibit a ‘butterfly’ shape in the first and third quadrants [see Figs. 1(a)–1(c)]. The ‘butterfly’ shape is resulted from the repulsive force between the two electrons when they are emitted almost at the same time. This means that double ionization in this laser intensity range is nonsequential. In addition, the two-electron momentum distributions exhibit a clear asymmetry with respect to the diagonal

*p*

_{1}=-

*p*

_{2}. The two electrons have the preference for ejection in the positive

*z*-axis direction, especially at an intensity of 4×10

^{14}W/cm

^{2}.

*p*

_{1}=-

*p*

_{2}[see Figs. 1(e) and 1(f)]. However, in contrast to at lower intensities, the two electrons have the preference for ejection in the negative

*z*-axis direction at higher intensities. The Coulomb repulsion between the two electrons completely loses its effect on the two-electron momentum distributions in this laser intensity range and thus the ‘butterfly’ shape disappears. This shows that double ionization is sequential in this laser intensity range. It can also be proved by the product of the single ionization yields of HeH

^{+}and HeH

^{2+}. In single ionization calculations, we also use a soft-Coulomb potential

*b*=2.6 and 0.47 reproduce the ionization potentials of HeH

^{+}and HeH

^{2+}, respectively. The single ionization spectra

*f*

*(p)*for HeH

^{+}and

*g*(

*p*) for HeH

^{2+}are calculated following the method used in Ref. [18

18. S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H^{+}_{2} dissociative ionization in intense laser fields,” Phys. Rev. A **57**, 1176 (1998). [CrossRef]

*F*(

*p*

_{1},

*p*

_{2})=

*f*(

*p*

_{1})

*g*(

*p*

_{2})+

*f*(

*p*

_{2})

*g*(

*p*

_{1}) at an intensity of 1×10

^{15}W/cm

^{2}, which is in good agreement with that in Fig. 1(e).

7. M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of Helium: identifying the mechanism,” Phys. Rev. Lett. **85**, 4707–4710 (2000). [CrossRef] [PubMed]

^{+}molecules have opposite preferences for ejection in space.

^{+}molecules in terms of the particular charge configuration of HeH

^{+}. In SDI, the two electrons are field-ionized independently. In the present simulations, the He nucleus is localized on the negative

*z*-axis and the H nucleus on the positive

*z*-axis, as shown in Fig. 3. The charge of the He nucleus is twice as much as that of the H nucleus, which results in asymmetric potential wells in HeH

^{+}and HeH

^{2+}. Therefore, HeH

^{+}and HeH

^{2+}have the distinct feature that the electron cloud of the ground state is predominantly localized on the left well. Figure 3(a) shows the two-electron probability density in the ground state of HeH

^{+}. We first consider the single ionization of HeH

^{2+}when the instantaneous laser field reaches its maxima. For a negative laser field, the electron cloud of the ground state, predominantly localized on the left well, tunnels through two potential barriers, the inner internuclear and the right potential barriers, to reach the continuum [see the blue line in Fig. 3(b)]. In contrast, for a positive laser field, the electron cloud tunnels from the left well through only one potential barrier (the left potential barrier) to ionize [see the red line in Fig. 3(b)]. Thus, the electron escapes more easily to the left than to the right. The case for the single ionization of HeH

^{+}is also the same. This explains that the two electrons have the preference for ejection in the negative

*z*-axis direction in SDI of HeH

^{+}molecules.

^{2+}essentially defines a permanent dipole

**D**. The center of negative charge of HeH

^{2+}is near the He nucleus and the center of positive charge is

*R*/3 right from the He nucleus. Therefore, the permanent dipole

**D**of HeH

^{2+}is directed from the He nucleus to the H nucleus [see Fig. 4(a)]. The asymmetry of the two-electron momentum distributions from NSDI can be interpreted as due to the influence of the permanent dipole

**D**of HeH

^{2+}on the inelastic recollision process, which leads to NSDI. We demonstrate the influence of the dipole moment on the recollision process using a simple one-dimensional classical model. Suppose the electron is ionized at the origin with zero velocity at time

*t*

_{0}in the presence of only the laser field with an intensity of 4×10

^{14}W/cm

^{2}. When it returns to the origin, it moves in the present of the laser field and the Coulomb field of the dipole moment. The Coulomb field is described by

*E*

*(*

_{c}*z*)=2(

*z*+1)[(

*z*+1)

^{2}+1]

^{-3/2}-2(

*z*-1)[(

*z*-1)

^{2}+1]

^{-3/2}. Figure 4(b) shows the kinetic energy of the returning electron as a function of ionization time

*t*

_{0}. The maximum kinetic energy of the returning electron from the positive

*z*-axis is about 13 eV higher than that from the negative

*z*-axis.

**D**attracts the electron returning from the positive

*z*-axis while repulses it from the negative

*z*-axis. As a consequence, double ionization is enhanced when the electron recollides with the parent ion from the positive

*z*-axis and suppressed from the negative

*z*-axis. Generally, the electron recollides with the parent ion from some direction when the electric field becomes nearly zero. After recollision, the electric field reverses its sign and the two electrons are ejected all the same in this direction. Thus, double ionization in the positive

*z*-axis direction is enhanced while in the negative

*z*-axis direction is suppressed. This explains that the two electrons in NSDI of HeH

^{+}molecules have the preference for ejection in the positive

*z*-axis direction.

*et al*[15

15. D. Zeidler, A. Staudte, A. B. Bardon, D. M. Villeneuve, R. Dö, and P. B. Corkum, “Controlling attosecond double ionization dynamics via molecular alignment,” Phys. Rev. Lett. **95**, 203003 (2005). [CrossRef] [PubMed]

_{2}ensemble, then a time delayed probe pulse was used to ionize the aligned N

_{2}molecules. It was found that the two electrons involved in NSDI more likely exit the molecule in the same direction when it is parallel to the probe pulse than when it is perpendicular. However, only symmetric two-electron momentum distributions were observed because N

_{2}is a symmetric molecule. Here, we propose another approach to control attosecond NSDI dynamics. Our simulations show that the two electrons involved in NSDI more likely exit the HeH

^{+}molecule in the direction of its permanent dipole than in the opposite direction when the molecular axis is parallel to the laser polarization direction. However, it is expected that this preference should disappear when the molecular axis is perpendicular to the laser polarization direction, because the charge configuration of HeH

^{+}is symmetric with respect to the axis perpendicular to the laser polarization direction. Therefore, the dynamics of double ionization can be controlled by changing the angle between the molecular axis and the laser polarization direction.

^{+}molecules have been studied by solving the time-dependent Sch

*ö*dinger equation. For atoms, the momentum distributions are symmetric with respect to both diagonals and the symmetry is independent of the laser intensity [7

**85**, 4707–4710 (2000). [CrossRef] [PubMed]

^{+}molecules, the momentum distributions exhibit a clear asymmetry, which depends on the laser intensity. When HeH

^{+}is aligned parallel to the laser polarization direction, the two electrons tend to be ejected in the direction of its permanent dipole in NSDI, while in the opposite direction in SDI. For SDI, the asymmetry is induced by the asymmetric electron probability density of the ground state. For NSDI, the asymmetry is induced by the influence of the permanent dipole on the recollision process. Since this asymmetric momentum distributions result essentially from the asymmetric charge configuration of HeH

^{+}, it is expected to occur in any heteronuclear molecules. Moreover, this implies that controlling the alignment of the heteronuclear molecule with respect to the laser polarization enables the steering of double ionization in space.

## References and links

1. | 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. |

2. | Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emission in multiphoton double ionization,” Nature |

3. | B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionization of Ar: the role of excitation tunneling,” Phys. Rev. Lett. |

4. | M. Weckenbrock, A. Becker, A. Staudte, S. kammer, M. Smolarski, V. R. Bhardwaj, D. M. Rayner, D. M. Villeneuve, P. B. Corkum, and R. Dörner, “Electron-electron momentum exchange in strong field double ionization,” Phys. Rev. Lett. |

5. | J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. |

6. | A. Becker and F. H. M. Faisal, “Interplay of electron correlation and intense field dynamics in the double ionization of Helium,” Phys. Rev. A |

7. | M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of Helium: identifying the mechanism,” Phys. Rev. Lett. |

8. | R. Kopold, W. Becker, H. Rottke, and W. Sandner, “Routes to nonsequential double ionization,” Phys. Rev. Lett. |

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

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

11. | A. S. Alnaser, T. Osipov, E. P. Benis, A. Wech, B. Shan, C. L. Cocke, X. M. Tong, and C. D. Lin, “Rescattering double ionization of D |

12. | F. Légaré, I. V. Litvinyuk, P. W. Dooley, F. Quéré, A. D. Bandrauk, D. M. Villeneuve, and P. B. Corkum, “Time-resolved double ionization with few cycle laser pulses,” Phys. Rev. Lett. |

13. | S. Saugout and C. Cornaggia, “Temporal separation of H |

14. | C. Beylerian, S. Saugout, and C. Cornaggia, “Non-sequential double ionization of H |

15. | D. Zeidler, A. Staudte, A. B. Bardon, D. M. Villeneuve, R. Dö, and P. B. Corkum, “Controlling attosecond double ionization dynamics via molecular alignment,” Phys. Rev. Lett. |

16. | M. Lein, T. Kreibich, E. K. U. Gross, and V. Engel, “Strong-field ionization dynamics of a model H |

17. | M. D. Feit, J. A. Fleck Jr., and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. |

18. | S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H |

19. | X. M. Tong, K. Hino, and N. Toshima, “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A |

**OCIS Codes**

(020.4180) Atomic and molecular physics : Multiphoton processes

(190.4180) Nonlinear optics : Multiphoton processes

(260.3230) Physical optics : Ionization

(270.6620) Quantum optics : Strong-field processes

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: September 2, 2008

Revised Manuscript: October 9, 2008

Manuscript Accepted: October 9, 2008

Published: October 10, 2008

**Citation**

Qing Liao, Peixiang Lu, Qingbin Zhang, Zhenyu Yang, and Xinbing Wang, "Double ionization of HeH^{+} molecules in intense laser fields," Opt. Express **16**, 17070-17075 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-17070

Sort: Year | Journal | Reset

### References

- 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, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dorner, "Correlated electron emission in multiphoton double ionization," Nature 405, 658-661 (2000). [CrossRef] [PubMed]
- B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schroter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Hohr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, "Separation of recollision mechanisms in nonsequential strong field double ionization of Ar: the role of excitation tunneling," Phys. Rev. Lett. 87, 043003 (2001). [CrossRef] [PubMed]
- M. Weckenbrock, A. Becker, A. Staudte, S. kammer, M. Smolarski, V. R. Bhardwaj, D. M. Rayner, D. M. Villeneuve, P. B. Corkum, and R. Dorner, "Electron-electron momentum exchange in strong field double ionization," Phys. Rev. Lett. 91, 123004 (2003). [CrossRef] [PubMed]
- J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, "High-energy cutoff in the spectrum of strong-field nonsequential double ionization," Phys. Rev. Lett. 96, 133001 (2006). [CrossRef] [PubMed]
- A. Becker and F. H. M. Faisal, "Interplay of electron correlation and intense field dynamics in the double ionization of Helium," Phys. Rev. A 59, R1742-R1745 (1999). [CrossRef]
- M. Lein, E. K. U. Gross, and V. Engel, "Intense-field double ionization of Helium: identifying the mechanism," Phys. Rev. Lett. 85, 4707-4710 (2000). [CrossRef] [PubMed]
- R. Kopold, W. Becker, H. Rottke, and W. Sandner, "Routes to nonsequential double ionization," Phys. Rev. Lett. 85, 3781-3784 (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]
- P. B. Corkum, "Plasma perspective on strong-field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993). [CrossRef] [PubMed]
- A. S. Alnaser, T. Osipov, E. P. Benis, A. Wech, B. Shan, C. L. Cocke, X. M. Tong, and C. D. Lin, "Rescattering double ionization of D2 and H2 by intense laser pulses," Phys. Rev. Lett. 91, 163002 (2003). [CrossRef] [PubMed]
- F. Legare, I. V. Litvinyuk, P. W. Dooley, F. Quere, A. D. Bandrauk, D. M. Villeneuve, and P. B. Corkum, "Timeresolved double ionization with few cycle laser pulses," Phys. Rev. Lett. 91, 093002 (2003). [CrossRef] [PubMed]
- S. Saugout and C. Cornaggia, "Temporal separation of H2 double-ionization channels using intense ultrashort 10-fs laser pulses," Phys. Rev. A 73, 041406(R) (2006). [CrossRef]
- C. Beylerian, S. Saugout and C. Cornaggia, "Non-sequential double ionization of H2 using ultrashort 10 fs laser pulses," J. Phys. B 39, L105-L112 (2006). [CrossRef]
- D. Zeidler, A. Staudte, A. B. Bardon, D. M. Villeneuve, R. Do, and P. B. Corkum, "Controlling attosecond double ionization dynamics via molecular alignment," Phys. Rev. Lett. 95, 203003 (2005). [CrossRef] [PubMed]
- M. Lein, T. Kreibich, E. K. U. Gross, and V. Engel, "Strong-field ionization dynamics of a model H2 molecule," Phys. Rev. A 65, 033403 (2002). [CrossRef]
- M. D. Feit, J. A. Fleck, Jr., and A. Steiger, "Solution of the Schr ¨ odinger equation by a spectral method," J. Comput. Phys. 47, 412-433 (1982). [CrossRef]
- S. Chelkowski, C. Foisy, and A. D. Bandrauk, "Electron-nuclear dynamics of multiphoton H+2 dissociative ionization in intense laser fields," Phys. Rev. A 57, 1176 (1998). [CrossRef]
- X. M. Tong, K. Hino, and N. Toshima, "Phase-dependent atomic ionization in few-cycle intense laser fields," Phys. Rev. A 74, 031405(R) (2006). [CrossRef]

## 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.