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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 9 — May. 6, 2013
  • pp: 11382–11390
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Contribution of recollision ionization to the cross-shaped structure in nonsequential double ionization

Cheng Huang, Yueming Zhou, Qingbin Zhang, and Peixiang Lu  »View Author Affiliations


Optics Express, Vol. 21, Issue 9, pp. 11382-11390 (2013)
http://dx.doi.org/10.1364/OE.21.011382


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Abstract

With the three-dimensional classical ensemble model, we investigate the correlated electron emission in nonsequential double ionization (NSDI) of argon atoms by few-cycle laser pulses. Our calculations well reproduce the experimentally observed cross-shaped structure in the correlated two-electron momentum spectrum [ Nature Commun. 3, 813 (2012)]. By tracing these NSDI trajectories, we find that besides the process of recollision-induced excitation with subsequent ionization just before the next field maximum, the recollision ionization also significantly contributes to the cross-shaped structure.

© 2013 OSA

1. Introduction

As a standard process for studies of dynamical electron correlations, nonsequential double ion-ization (NSDI) has been a hot topic in the strong field physics since the observation of the dramatically enhanced double ionization yields [1

1. A. l’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 μm,” Phys. Rev. A 27,2503–2512 (1983) [CrossRef] .

3

3. 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] .

]. Differently from sequential double ion-ization (SDI) where the two electrons are ejected one by one independently [4

4. A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Döner, and U. Keller, “Timing the release in sequential double ionization,” Nature Phys. 7,428–433 (2011) [CrossRef] .

6

6. Y. Zhou, C. Huang, and P. Lu, “Revealing the multi-electron effects in sequential double ionization using classical simulations,” Opt. Express 20,20201–20209 (2012) [CrossRef] [PubMed] .

], a great number of experimental works and theoretical studies [7

7. R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C. D. Schröer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner, “Momentum distributions of Nen+ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84,447–450 (2000) [CrossRef] [PubMed] .

16

16. C. Huang, Y. Zhou, A. Tong, Q. Liao, W. Hong, and P. Lu, “The effect of molecular alignment on correlated electron dynamics in nonsequential double ionization,” Opt. Express 19,5627–5634 (2011) [CrossRef] [PubMed] .

] provide strong evidences that the quasiclassical recollision model [17

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

,18

18. K. C. Kulander, J. Cooper, and K. J. Schafer, “Laser-assisted inelastic rescattering during above-threshold ionization,” Phys. Rev. A 51,561–568 (1995) [CrossRef] [PubMed] .

] is dominantly responsible for the NSDI process. There, the first released electron is driven back by the oscillating laser field and collides with the parent ion inelastically, leading to the release of the second electron in a direct recollision ionization process (RCI) or indirectly via recollision-induced excitation with subsequent field ionization (RESI) [19

19. 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. 87,043003 (2001) [CrossRef] [PubMed] .

].

The quasiclassical recollision model [17

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

, 18

18. K. C. Kulander, J. Cooper, and K. J. Schafer, “Laser-assisted inelastic rescattering during above-threshold ionization,” Phys. Rev. A 51,561–568 (1995) [CrossRef] [PubMed] .

] provides a general physical picture for NSDI of atoms and molecules in strong laser fields. With the deep study of NSDI, many novel characteristics in the correlated electron momentum spectra were found [20

20. A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett. 99,263002 (2007) [CrossRef] .

24

24. Y. Liu, S. Tschuch, A. Rudenko, M. Dürr, M. Siegel, U. Morgner, R. Moshammer, and J. Ullrich, “Strong-field double ionization of Ar below the recollision threshold,” Phys. Rev. Lett. 101,053001 (2008) [CrossRef] [PubMed] .

]. By means of these novel characteristics many detailed microscopic dynamics processes under the recollision mechanism have been revealed. For example, the high resolution experiments on DI of helium observed a fingerlike (or V-like) structure in the correlated electron momentum distribution for two different laser intensities [20

20. A. Staudte, C. Ruiz, M. Schöffler, S. Schössler, D. Zeidler, Th. Weber, M. Meckel, D. M. Villeneuve, P. B. Corkum, A. Becker, and R. Dörner, “Binary and recoil collisions in strong field double ionization of helium,” Phys. Rev. Lett. 99,263002 (2007) [CrossRef] .

, 21

21. A. Rudenko, V. L. B. de Jesus, Th. Ergler, K. Zrost, B. Feuerstein, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated two-electron momentum spectra for strong-field nonsequential double ionization of He at 800 nm,” Phys. Rev. Lett. 99,263003 (2007) [CrossRef] .

]. For the relatively low intensity, both the nuclear attraction at recollision and electron-electron repulsion in the final state play significant roles in forming the fingerlike shape [25

25. Z. Chen, Y. Liang, and C. D. Lin, “Quantum theory of recollisional (e, 2e) process in strong field nonsequential double ionization of helium,” Phys. Rev. Lett. 104,253201 (2010) [CrossRef] [PubMed] .

, 26

26. D. Ye, X. Liu, and J. Liu, “Classical trajectory diagnosis of a fingerlike pattern in the correlated electron momentum distribution in strong field double ionization of helium,” Phys. Rev. Lett. 101,233003 (2008) [CrossRef] [PubMed] .

]. At the relatively high laser intensity, it is demonstrated that the V-like shape structure originates from asymmetric energy sharing at recollision [27

27. Y. Zhou, Q. Liao, and P. Lu, “Asymmetric electron energy sharing in strong-field double ionization of helium,” Phys. Rev. A 82,053402 (2010) [CrossRef] .

]. At the laser intensity below the recollision threshold, Liu et al. experimentally found the dominant back-to-back emission of the correlated electron pairs from NSDI of atoms [24

24. Y. Liu, S. Tschuch, A. Rudenko, M. Dürr, M. Siegel, U. Morgner, R. Moshammer, and J. Ullrich, “Strong-field double ionization of Ar below the recollision threshold,” Phys. Rev. Lett. 101,053001 (2008) [CrossRef] [PubMed] .

]. The anticorrelation behavior was attributed to the delayed emission of the second electron after recollision [28

28. S. L. Haan, Z. S. Smith, K. N. Shomsky, and P. WPlantinga, “Anticorrelated electrons from weak recollisions in nonsequential double ionization,” J. Phys. B 41,211002 (2008) [CrossRef] .

].

2. The classical ensemble model

Here, we employ the classical ensemble model [35

35. R. Panfili, J. H. Eberly, and S. L. Haan, “Comparing classical and quantum simulations of strong-field double-ionization,” Opt. Express 8,431–435 (2001) [CrossRef] [PubMed] .

, 36

36. S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Variable time lag and backward ejection in full-dimensional analysis of strong-field double ionization,” Phys. Rev. Lett. 97,103008 (2006) [CrossRef] [PubMed] .

], which is widely recognized as a useful approach in studying strong field double ionization [37

37. X. Wang and J. H. Eberly, “Elliptical polarization and probability of double ionization,” Phys. Rev. Lett. 105,083001 (2010) [CrossRef] [PubMed] .

39

39. F. Mauger, C. Chandre, and T. Uzer, “Strong field double ionization: the phase space perspective,” Phys. Rev. Lett. 102,173002 (2009) [CrossRef] [PubMed] .

]. In this model the evolution of the three-particle system is determined by the Newton’s equations of motion (atomic units are used throughout until stated otherwise):
d2ridt2=[Vne(ri)+Vee(r1+r2)]E(t),
(1)
where the subscript i is the label of the two electrons, and E(t) is the electric field of a 750 nm linearly polarized laser pulse with a 4-cycle sin2-shaped envelope (corresponding to a full-width at half-maximum of 3.64 fs). The laser intensity is 3×1014 W/cm2. The potentials Vne(ri)=2/ri2+a2, Vee(r1,r2)=1/(r1r2)2+b2 represent the ion-electron and electron-electron interactions respectively. To avoid autoionization, we set the screening parameter a to be 1.5. b is set to be 0.05. To obtain the initial values, the ensemble is populated starting from a classically allowed position for the Ar ground-state energy of −1.59 a.u. The available kinetic energy is distributed between the two electrons randomly in momentum space. Then the electrons are allowed to evolve a sufficient long time (600 a.u.) in the absence of the laser field to obtain stable position and momentum distribution. Once the initial ensemble is obtained, the laser field is turned on and all trajectories are evolved in the combined Coulomb and laser fields.

3. Results and discussions

Fig. 1 The correlated two-electron momentum distributions for NSDI of Ar by 750 nm, 4-cycle linearly polarized laser pulses at an intensity of 3×1014 W/cm2. (a) all CEPs averaged, (b) ϕ =−0.4π, (c) ϕ =0.1π, (d) ϕ =0.6π. The two electrons are not distinguished.
Fig. 2 The asymmetry of the correlated electron momentum spectrum as a function of the CEP ϕ for the intensity of 3×1014 W/cm2.

In order to explore the origin of the cross-shaped structure in the CEP-averaged correlated two-electron momentum distribution [Fig. 1(a)], we trace classical NSDI trajectories and carefully examine their histories. In this way, we can easily obtain the recollision time and ionization times of two electrons. Here, we define an electron to be ionized if its energy turns positive [38

38. Y. Zhou, C. Huang, and P. Lu, “Coulomb-tail effect of electron-electron interaction on nonsequential double ionization,” Phys. Rev. A 84,023405 (2011) [CrossRef] .

], where the energy of each electron contains the kinetic energy, potential energy of the electron-ion interaction and half electron-electron repulsion. We scan the time interval from the time when one electron first ionizes until final ionization of both electrons, and we define the time of closest approach as the recollision time, which is marked by tr[28

28. S. L. Haan, Z. S. Smith, K. N. Shomsky, and P. WPlantinga, “Anticorrelated electrons from weak recollisions in nonsequential double ionization,” J. Phys. B 41,211002 (2008) [CrossRef] .

,36

36. S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Variable time lag and backward ejection in full-dimensional analysis of strong-field double ionization,” Phys. Rev. Lett. 97,103008 (2006) [CrossRef] [PubMed] .

,38

38. Y. Zhou, C. Huang, and P. Lu, “Coulomb-tail effect of electron-electron interaction on nonsequential double ionization,” Phys. Rev. A 84,023405 (2011) [CrossRef] .

]. tDI represents the double ionization time.

Fig. 3 (a) Final longitudinal momentum distribution of the first electron versus the second electron for ϕ =0.6π. Here, the two electrons are distinguished based on the order of final ionization after recollision (see text for detail). (b) The double ionization time (tDI) versus the recollision time (tr) for ϕ =0.6π. The white dashed curves indicate the maxima of the electric field (1.710T, 2.195T).
Fig. 4 The correlated two-electron momentum distributions for NSDI events in regions G1 (a) and G2 (b) of Fig. 3(b). The two electrons are not distinguished.

Figure 5 shows two sample trajectories selected from groups G1 (the left column) and G2 (the right column) of Fig. 3(b). We examine the time evolutions of the longitudinal momenta, coordinate z in polarization direction, energies of two electrons and the momenta in y direction. For the NSDI trajectory in the left column, the first emitted electron is firstly driven to the positive direction by a negative electric field and then is pulled back to the parent ion when the electric field reverses [Fig. 5(b)]. Just after the maximum of the laser electric field, the returning electron recollides with the second electron (green arrows). From Fig. 5(c) we can find that during recollision the returning electron transfers some energy to the second electron and is still free, but the transfer energy is not enough to promote the second electron to the positive energy. At the instant of recollision, the laser electric field is very large and pronouncedly lowers down the Coulomb barrier of the ion along the z-axis. This results in the second electron well located above the suppressed barrier. Immediately the large electric field force drives the second electron to escape over the suppressed barrier, and meantime the second electron quickly obtains enough energy from the electric field to escape away from the ion. In this process the time interval between the emission of the second electron and the recollision is very short (shorter than 0.1T), and thus it is regarded as RCI mechanism. As is well known, the electron emitted in the laser field will obtain a drift momentum from the subsequent electric field. Here, the first electron is forward rescattered with a negative initial momentum and then it obtains a positive drift momentum from the subsequent electric field. The two options cancel each other, resulting in a near-zero final longitudinal momentum of the first electron [see red curve of Fig. 5(a)]. Due to a near-zero initial momentum after recollision and the acceleration from the subsequent electric field, the second electron has a non-zero final momentum [see blue curve of Fig. 5(a)].

Fig. 5 Two sample trajectories selected from groups G1 (the left column) and G2 (the right column) of Fig. 3(b). The panels from top to bottom show the longitudinal momenta, coordinate z in polarization direction, energies of two electrons and the momenta in y direction versus the time, respectively. The arrows indicate the recollision time (tr) and the vertical lines indicate the final double ionization time (tDI). The black dashed curve marks the laser electric field in arbitrary units.

The discussion above has indicated that for ϕ =0.6π both RCI and RESI mechanisms contribute significantly to NSDI and are responsible for the cross-shaped structure in the correlated electron momentum spectrum. Besides the case of ϕ =0.6π, we also trace and carefully back examine the classical NSDI trajectories from other CEPs. Our analysis finds that for all CEPs both RCI and RESI mechanisms contribute significantly to NSDI, and their contributions are comparable. The only difference is that for some CEPs there is only one recollision event contribute to NSDI, whereas for other CEPs two recollision events are involved.

For a realistic laser focus, the existence of an out-of-phase electric field component in the laser propagation direction produces an effective ellipticity. The work by Paquette et al[40

40. J. P. Paquette and J. L. Chaloupka, “Effect of realistic focal conditions on the strong-field ionization of helium,” Phys. Rev. A 79,043410 (2009) [CrossRef] .

] has demonstrated that the effective ellipticity can result in a significant reduction in doubly charged ion yields for tight focusing condition (such as 1 μm beam waist). We have calculated NSDI for different effective ellipticities. The results show that for the effective ellipticities of 0.05 and 0.10, the correlated electron momenta are uniformly distributed in the four quadrants and the cross-shaped structure disappears. However, for the experiment of Bergues et al[34

34. B. Bergues, M. Kübel, N. G. Johnson, B. Fischer, N. Camus, K. J. Betsch, O. Herrwerth, A. Senftleben, A. M. Sayler, T. Rathje, T. Pfeifer, I. Ben-Itzhak, R. R. Jones, G. G. Paulus, F. Krausz, R. Moshammer, J. Ullrich, and M. F. Kling, “Attosecond tracing of correlated electron-emission in non-sequential double ionization,” Nature Commun. 3,813 (2012) [CrossRef] .

], the beam waist is about 40 μm. In this condition, the effective ellipticity is less than 0.006 within the 1/e2 intensity volume. For such a small ellipticity, its influence on the electron momentum distribution is negligible and the crossed-shaped structure is still clear. Thus under this experimental condition of Bergues et al[34

34. B. Bergues, M. Kübel, N. G. Johnson, B. Fischer, N. Camus, K. J. Betsch, O. Herrwerth, A. Senftleben, A. M. Sayler, T. Rathje, T. Pfeifer, I. Ben-Itzhak, R. R. Jones, G. G. Paulus, F. Krausz, R. Moshammer, J. Ullrich, and M. F. Kling, “Attosecond tracing of correlated electron-emission in non-sequential double ionization,” Nature Commun. 3,813 (2012) [CrossRef] .

], it is valid to neglect the effect of the effective ellipticity of the realistic laser focus. In addition, we have calculated NSDI of argon atoms by 750 nm, 3×1014 W/cm2 laser pulses with the full width of 4, 5 and 6 cycles. The ratios of RCI events to RESI events are 0.90, 0.62 and 0.49, respectively. This indicates that compared with RESI mechanism, the contribution of RCI mechanism to the observed cross-shaped structure decreases with the pulse width increasing.

In the semiclassical model of [34

34. B. Bergues, M. Kübel, N. G. Johnson, B. Fischer, N. Camus, K. J. Betsch, O. Herrwerth, A. Senftleben, A. M. Sayler, T. Rathje, T. Pfeifer, I. Ben-Itzhak, R. R. Jones, G. G. Paulus, F. Krausz, R. Moshammer, J. Ullrich, and M. F. Kling, “Attosecond tracing of correlated electron-emission in non-sequential double ionization,” Nature Commun. 3,813 (2012) [CrossRef] .

] the scattering angle β is a very important free parameter. Its value significantly influences the shape of the correlated electron momentum distribution. In the calculation of [34

34. B. Bergues, M. Kübel, N. G. Johnson, B. Fischer, N. Camus, K. J. Betsch, O. Herrwerth, A. Senftleben, A. M. Sayler, T. Rathje, T. Pfeifer, I. Ben-Itzhak, R. R. Jones, G. G. Paulus, F. Krausz, R. Moshammer, J. Ullrich, and M. F. Kling, “Attosecond tracing of correlated electron-emission in non-sequential double ionization,” Nature Commun. 3,813 (2012) [CrossRef] .

], the cross-shaped structure is well reproduced only when the scattering angle β is set to 20°. In our classical simulation, we also examine the scattering angles of NSDI trajectories. Here, the scattering angle β is defined as the angle between the momentum vectors at the instants 0.03T before and 0.03T after the recollision. Figure 6 shows counts of NSDI trajectories versus the scattering angle β for the CEP of 0.6π. Obviously, for the classical NSDI trajectories the scattering angles β are also around 20°, which is consistent with the fitting value in [34

34. B. Bergues, M. Kübel, N. G. Johnson, B. Fischer, N. Camus, K. J. Betsch, O. Herrwerth, A. Senftleben, A. M. Sayler, T. Rathje, T. Pfeifer, I. Ben-Itzhak, R. R. Jones, G. G. Paulus, F. Krausz, R. Moshammer, J. Ullrich, and M. F. Kling, “Attosecond tracing of correlated electron-emission in non-sequential double ionization,” Nature Commun. 3,813 (2012) [CrossRef] .

].

Fig. 6 Counts of NSDI trajectories versus the scattering angle β for ϕ =0.6π.

4. Conclusion

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 11004070, 11234004, National Science Fund for Distinguished Young Scholars under Grant No. 60925021, and the 973 Program of China under Grant No. 2011CB808103.

References and links

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21.

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Y. Zhou, Q. Liao, Q. Zhang, W. Hong, and P. Lu, “Controlling nonsequential double ionization via two-color few-cycle pulses,” Opt. Express 18,632–638 (2010) [CrossRef] [PubMed] .

33.

C. Ruiz, L. Plaja, L. Roso, and A. Becker, “Ab initio calculation of the double ionization of helium in a few-cycle laser pulse beyond the one-dimensional approximation,” Phys. Rev. Lett. 96,053001 (2006) [CrossRef] [PubMed] .

34.

B. Bergues, M. Kübel, N. G. Johnson, B. Fischer, N. Camus, K. J. Betsch, O. Herrwerth, A. Senftleben, A. M. Sayler, T. Rathje, T. Pfeifer, I. Ben-Itzhak, R. R. Jones, G. G. Paulus, F. Krausz, R. Moshammer, J. Ullrich, and M. F. Kling, “Attosecond tracing of correlated electron-emission in non-sequential double ionization,” Nature Commun. 3,813 (2012) [CrossRef] .

35.

R. Panfili, J. H. Eberly, and S. L. Haan, “Comparing classical and quantum simulations of strong-field double-ionization,” Opt. Express 8,431–435 (2001) [CrossRef] [PubMed] .

36.

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Variable time lag and backward ejection in full-dimensional analysis of strong-field double ionization,” Phys. Rev. Lett. 97,103008 (2006) [CrossRef] [PubMed] .

37.

X. Wang and J. H. Eberly, “Elliptical polarization and probability of double ionization,” Phys. Rev. Lett. 105,083001 (2010) [CrossRef] [PubMed] .

38.

Y. Zhou, C. Huang, and P. Lu, “Coulomb-tail effect of electron-electron interaction on nonsequential double ionization,” Phys. Rev. A 84,023405 (2011) [CrossRef] .

39.

F. Mauger, C. Chandre, and T. Uzer, “Strong field double ionization: the phase space perspective,” Phys. Rev. Lett. 102,173002 (2009) [CrossRef] [PubMed] .

40.

J. P. Paquette and J. L. Chaloupka, “Effect of realistic focal conditions on the strong-field ionization of helium,” Phys. Rev. A 79,043410 (2009) [CrossRef] .

OCIS Codes
(020.4180) Atomic and molecular physics : Multiphoton processes
(260.3230) Physical optics : Ionization
(270.6620) Quantum optics : Strong-field processes

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: March 13, 2013
Revised Manuscript: April 23, 2013
Manuscript Accepted: April 23, 2013
Published: May 2, 2013

Citation
Cheng Huang, Yueming Zhou, Qingbin Zhang, and Peixiang Lu, "Contribution of recollision ionization to the cross-shaped structure in nonsequential double ionization," Opt. Express 21, 11382-11390 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-11382


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