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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 18 — Aug. 27, 2012
  • pp: 20201–20209
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Revealing the multi-electron effects in sequential double ionization using classical simulations

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


Optics Express, Vol. 20, Issue 18, pp. 20201-20209 (2012)
http://dx.doi.org/10.1364/OE.20.020201


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Abstract

We theoretically investigated sequential double ionization (SDI) of Ar by the nearly circularly polarized laser pulses with a fully correlated classical ensemble model. The ion momentum distributions of our numerical results at various laser intensities and pulse durations agree well with the experimental results. The experimentally observed multi-electron effects embodied in the joint momentum spectrum of the two electrons is also reproduced by our correlated classical calculations. Interestingly, our calculations show that the angular distribution of the first photoelectron from the trajectories which eventually suffer SDI differs from the distribution of the photoelectrons from above-threshold ionization trajectories. This observation provides additional evidence of multi-electron effects in strong field SDI.

© 2012 OSA

1. Introduction

It has been demonstrated that the angular distribution of the photoelectrons is sensitive to the details of the remaining ion and thus the multi-electron effects have an obvious manifestation on the angular distribution [27

27. A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys. 8, 76–80 (2011). [CrossRef]

, 28

28. N. I. Shvetsov-Shilovski, D. Dimitrovski, and L. B. Madsen, “Ionization in elliptically polarized pulses: Multi-electron polarization effects and asymmetry of photoelectron momentum distributions,” Phys. Rev. A 85, 023428 (2012). [CrossRef]

]. Here, we investigate the angular distributions of the photo-electrons from SDI, aiming to check the multi-electron effects in SDI. We analyze the angular distributions of the photoelectrons of the singly and doubly ionized trajectories separately. Our results reveal that the angular distributions of the first electron of the SDI trajectories are very different from those of the above-threshold ionization (ATI) trajectories. This difference indicates the different ion-electron interactions during the escaping of the outmost electron for the ATI and SDI trajectories. Thus, it provides additional evidence of the breakdown of the independent-step assumption in SDI.

2. The classical ensemble model

The evolution of the two-electron system is determined by the following equations:
dridt=Hpi,dpidt=Hri
(3)
The initial conditions of the equations are obtained as follows. An ensemble is populated starting at a classical allowed position for the ground-state energy of Ar. The available kinetic energy is randomly distributed between the two electron in momentum space [25

25. 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]

]. Then, the electrons are allowed to evolve for a sufficiently long time in the absence of the laser field to obtain a stable distribution in phase space [25

25. 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]

]. When the initial conditions are obtained, the time evolution of the trajectories in the ensemble are governed by Eq. (3). At the end of the laser pulse, we examine the energy of the electrons. The electron is assumed to be ionized if its energy is positive and DI is identified if both electrons achieve positive energy at the end of the pulse. In our calculations, recollision is strongly supressed because of the large ellipticity employed. Thus almost all of the DIs correspond to SDI. We mention that in our classical model the electron correlations are fully taken into account during the ionization process.

3. Results and discussions

First, we show the momentum distributions of the doubly ionized ion in the laser polarization plane. The upper line of Fig. 1 displays the results of the 7-fs pulses and the bottom line corresponds to the results of the 33-fs pulses. We mention that in all of the calculations of this paper, the laser parameters are chosen to be the same as those in the experimental reports [19

19. 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]

, 20

20. A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys. 13, 093008 (2011). [CrossRef]

], i.e, the wavelength and ellipticity are 740 nm (788 nm) and 0.78 (0.77) for the 7-fs (33-fs) pulses, respectively. It is clearly shown that for both pulse durations, the distributions exhibit a three-band structure at the relatively low laser intensity [see Figs. 1(a) and 1(d)] while a four-band structure at the relatively high laser intensity [see Figs. 1(b) and 1(e)]. The origin of the four-band structure is interpreted as due to the different values of the electric field at which the two electrons are released [19

19. 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]

, 33

33. C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403R(2005). [CrossRef]

, 34

34. X. Wang and J. H. Eberly, “Effects of elliptical polarization on strong-field short-pulse double ionization,” Phys. Rev. Lett. 103, 103007 (2009). [CrossRef] [PubMed]

]. The outer bands correspond to the events where the two electrons emit into the parallel directions whereas the inner bands result from the events where the two electrons release into the antiparallel directions. At the relatively low intensity, both electrons release around the center of the pulses. Thus the momentum amplitudes of the two electrons are almost the same, leading to the two inner bands (corresponding to the antiparallel emissions) evolving into a one-band structure located at zero momentum [19

19. 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]

]. In Figs. 1(c) and 1(f), we show the distribution of the ion at 3.0 PW/cm2 with the volume effect taken into account. Figure 1(c) show that for the 7-fs case the distribution exhibits a three-band shape even at the high laser intensity. This is in good agreement with the experimental observation [20

20. A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys. 13, 093008 (2011). [CrossRef]

, 33

33. C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403R(2005). [CrossRef]

]. For the 33-fs case, the four-band structure is still discernable when the focal volume effect is considered [Fig. 1(f)], which is also consistent with the experimental results [19

19. 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]

].

Fig. 1 Ion momentum distributions in the polarization plane for (a)–(c) 7-fs and (d)–(f) 33-fs laser pulses. The laser intensities are (a) and (d) 1.5 PW/cm2, (b) and (e) 3.0 PW/cm2, respectively. In (c) and (f), the peak intensity is 3.0 PW/cm2, and the volume effect assuming a gaussian laser beam has been taken into account.

Fig. 2 The joint momentum distribution of the two electrons from SDI along the minor axis of the polarization. The laser parameters are the same as those in ref. [20], i.e, the wavelength, ellipticity, pulse duration and laser intensity are 740 nm, 0.78, 7 fs and 3.0 PW/cm2, respectively. The volume effect assuming a gaussian laser beam has been considered. The CEP is randomly chosen for each trajectory.

For the laser parameters used in our calculations and the recent experiments [19

19. 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]

, 20

20. A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys. 13, 093008 (2011). [CrossRef]

], recollision is forbidden because of the large ellipticity. Thus the electron correlations in SDI most possibly arise during the process of the first ionization. In this process, the electron correlations may leave footprints on the remaining ion. It has been shown that the interaction between the remaining ion and the escaping electron significantly corrects the trajectory of the escaping electron [35

35. S. V. Popruzhenko, G. G. Paulus, and D. Bauer, “Coulomb-corrected quantum trajectories in strong-field ionization,” Phys. Rev. A 77, 053409 (2008). [CrossRef]

]. The final angular distribution of the electron can reveal the details of the remaining ion [36

36. S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, “Coulomb asymmetry in above-threshold ionization,” Phys. Rev. Lett. 93, 233002 (2004). [CrossRef] [PubMed]

, 37

37. A. Jaroń, J. Z. Kamińskia, and F. Ehlotzky, “Asymmetries in the angular distributions of above threshold ionization in an elliptically polarized laser field,” Opt. Commun. 163, 115–121 (1999). [CrossRef]

]. For instance, it has been shown that the offset angles of the electrons from ATI of Ar and He exhibit different behaviors as a function of the laser intensity [27

27. A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys. 8, 76–80 (2011). [CrossRef]

]. For Ar, the offset angle decreases with the increase of the laser intensity, while it keeps unchanged for He. This difference is ascribed to the multi-electron effects (laser-induced polarization) [27

27. A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys. 8, 76–80 (2011). [CrossRef]

]. For Ar, it is much easier to polarize than He, leading to a strong dependence of offset angle on laser intensity. Thus, by examining the offset angle of the ionized electron, it is possible to extract information of the remaining ion which may hint some multi-electron effects. In the following, we investigate the angular distributions of the electrons from different processes, intending to check the multi-electron effects in SDI.

Figure 3(a) depicts the momentum distribution in the laser polarization plane for the electrons from ATI of Ar [modeled by the two-active-electron atom, see formula (1)]. The ellipticity, wavelength, pulse duration and laser intensity are 0.78, 740 nm, 7 fs and 1.0 PW/cm2, respectively. Because of the ellipticity, electrons are almost ionized along the major axis of the polarization (x axis). Without further interaction with the remaining ion, the most probable electron momentum distribution is along the minor polarization axis (y axis). In Fig. 3(a), a small but visible offset angle with respect to the minor polarization axis exists, indicating the interaction between the remaining ion and the escaping electron [34

34. X. Wang and J. H. Eberly, “Effects of elliptical polarization on strong-field short-pulse double ionization,” Phys. Rev. Lett. 103, 103007 (2009). [CrossRef] [PubMed]

36

36. S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, “Coulomb asymmetry in above-threshold ionization,” Phys. Rev. Lett. 93, 233002 (2004). [CrossRef] [PubMed]

]. In order to read the value of the offset angle, we perform a double gaussian fitting on the angular distribution of the photoelectrons, as shown in Fig. 3(b). In the following, we extract the offset angles with this way.

Fig. 3 (a) The momentum distribution in the polarization plane for the photoelectrons from above-threshold ionization of Ar. (b) The angular distribution of the electrons shown in (a). The red curve corresponds to the double gaussian fitting function. θ indicates the offset angle. The pulse duration, wavelength, ellipticity and the laser intensity are 7 fs, 740 nm,0.78 and 1.0 PW/cm2, respectively. The CEP is randomly chosen for each trajectory.

In order to test the validity of our HPCM in describing the subtlety of the interaction of the remaining ion and the escaping electron, we performed two calculations on ATI of Ar. In the first calculation, we employ the single-active-electron assumption, Thus the multi-electron effects (laser-induced polarization) are excluded. In this calculation, the hamiltonian of Ar is written as:
H=1r1+p122+VH(r1,p1)+r1E(t)
(4)
The interaction of the laser with the atom is determined by Eq. (3). Note that in this calculation the parameters of the Heisenberg-core potential is set as α = 2 and ξ = 0.7225 to fit the first ionization potential of Ar. At the end of the laser pulses, we collect the singly ionized trajectories and analysis the angular distributions of the photoelectrons. Figure 4(a) displays the offset angle of the photoelectrons as a function of laser intensity.

Fig. 4 The intensity-dependent offset angle of the photoelectrons from ATI of Ar. The error bars show the standard deviation of a double gaussian fit of the angular distributions. (a) The atom is modeled with the single-active-electron assumption [formula (4)]. (b) The atom is treated as a two-active-electron system [formula (1)]. The laser parameters are the same as those in the experiment [27], i.e., the pulse duration, wavelength and ellipticity are 7 fs, 740 nm and 0.78, respectively. The CEP is randomly chosen for each trajectory.

In the second calculation, the multi-electron effects are included by considered two active electrons, i.e., the hamiltonian of the Ar is expressed as formula (1) and the evolution of the system in the laser field is determined by Eq. (3). At the end of the pulse we analyzed the angular distributions of the photoelectrons from the singly ionized trajectories. The offset angle as a function of the laser intensity for these electrons is shown in Fig. 4(b). It is clearly seen that for the single-active-electron calculation where the multi-electron effects are excluded, no significant intensity dependence of offset angle is observed over the investigated intensity range [Fig. 4(a)]. However, for the second calculation, where the multi-electron effects are included, a monotonous decrease of the offset angle with increasing laser intensity is obvious. This behavior is in good agreement with recent experimental observations [27

27. A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys. 8, 76–80 (2011). [CrossRef]

]. These results indicate that the multi-electron behavior revealed in the angular distributions of photoelectrons can be well described by our classical model, confirming the validity of our HPCM in analyzing the angular distributions of the photoelectrons below.

Now, we examine the angular distributions of the photoelectrons from SDI calculated by the HPCM. At the end of the pulses, we select out the singly and the doubly ionized trajectories. It is interesting to compare the angular distribution of the photoelectrons from the singly ionized trajectories (ATI photoelectron) with that of the first electron from SDI trajectories because in both cases the electrons start from the same state (the ground state of Ar). In Fig. 5 we display the offset angles of the photoelectrons from the ATI trajectories (green squares) and those of the first photoelectrons from the SDI trajectories (magenta triangles). The top and the bottom plots correspond to the results from the 7-fs and 33-fs pulses, respectively. It is clearly seen that for both pulse durations the offset angles for the ATI photoelectrons are much larger than those of the first photoelectron from SDI trajectories. With the assumption that the two ionization events in SDI are independent, the offset-angle distribution of the first electrons from SDI trajectories will be the same as that of the photoelectrons from ATI trajectories. The results shown in Fig. 5 are in contrast to the prediction of this independent-electron assumption of SDI. Thus it definitely confirms the multi-electron effects in SDI though the details of this faint effect in SDI is currently not clear.

Fig. 5 The offset angle of the photoelectrons as a function of laser intensity. Green squares: the distribution for the photoelectrons from ATI trajectories. Magenta triangles: the distribution for the first electrons from SDI trajectories. The error bars show the standard deviation of a double gaussian fit of the angular distribution. The pulse durations are (a) 7 fs and (b) 33 fs. The ensemble sizes for the 7-fs and 33-fs pulses are 60000 and 30000, respectively. Depending on the laser intensity, tens of thousands of ATI and SDI trajectories are collected. The convergence of our results are confirmed by enlarging the ensemble sizes.

4. Conclusion

In summary, we have investigated the strong-field SDI of Ar by the elliptical laser pulses with the HPCM. The experimentally measured ion momentum distributions at various laser intensities and durations are obtained with our classical calculations. The experimentally observed multi-electron effects revealed by the joint electron momentum spectrum is also catched with our calculations. Furthermore, we have investigated the angular distribution of the photoelectrons from SDI. In order to confirm the validity of the classical model in studying the multi-electron effects revealed by the angular distribution, we first performed calculations on ATI of Ar with two different treatments, one including and the other excluding the multi-electron effects. The offset angles as a function of the laser intensity for these two treatments exhibit very different behaviors, which agrees well with recent experimental results [27

27. A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys. 8, 76–80 (2011). [CrossRef]

], and thus confirms the validity of our classical model. Based on these results, we examined the offset angle of the electrons from SDI. We find that the offset angle for the first electron from SDI is very different from that for photoelectrons from the ATI trajectories (the trajectories that eventually suffer single ionization), in contrast to the prediction of the independent-electron assumption of SDI. Thus, our calculations predict an additional evidence of multi-electron effects in SDI. A full understanding of the subtle multi-electron effects in SDI calls for more sophisticated studies.

Acknowledgment

We thank Dr. A. N. Pfeiffer for his useful suggestions. This work was supported by the National Science Fund (No. 60925021) and the 973 Program of China (No. 2011CB808103).

References and links

1.

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

2.

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]

3.

Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature 405, 658–661 (2000). [CrossRef] [PubMed]

4.

B. Walker, B. Sheehy, L. F. Dimauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionizaiton of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994). [CrossRef] [PubMed]

5.

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 ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett. 87, 043003 (2001). [CrossRef] [PubMed]

6.

M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett. 92, 213002 (2004). [CrossRef] [PubMed]

7.

A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett. 93, 253001 (2004). [CrossRef]

8.

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]

9.

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]

10.

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

11.

Y. Zhou, C. Huang, A. Tong, Q. Liao, and P. Lu, “Correlated electron dynamics in nonsequential double ionization by orthogonal two-color laser pulses,” Opt. Express 19, 2301–2308 (2011). [CrossRef] [PubMed]

12.

Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Lett. 36, 2758–2760 (2011). [CrossRef] [PubMed]

13.

A. Becker, R. Dörner, and R. Moshammer,“Multiple fragmentation of atoms in femtosecond laser pulses,” J. Phys. B 38, S753–S772 (2005). [CrossRef]

14.

Q. Liao, Y. Zhou, C. Huang, and P. Lu, “Multiphoton Rabi oscillations of correlated electrons in strong-field nonsequential double ionization,” New J. Phys. 14, 013001 (2012). [CrossRef]

15.

B. Chang, P. R. Bolton, and D. N. Fittinghoff, “Closed-form solutions for the production of ions in the collisionless ionization of gases by intense lasers,” Phys. Rev. A 47, 4193–4203 (1993). [CrossRef] [PubMed]

16.

K. I. Dimitriou, S. Yoshida, J. Burgdöfer, H. Shimada, H. Oyama, and Y. Yamazaki, “Momentum distribution of multiply charged ions produced by intense (50–70-PW/cm2) lasers,” Phys. Rev. A 75, 013418 (2007). [CrossRef]

17.

N. I. Shvetsov-Shilovski, A. M. Sayler, T. Rathje, and G. G. Paulus, “Momentum distributions of sequential ionization,” Phys. Rev. A 83, 033401 (2011). [CrossRef]

18.

A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett. 107, 113003 (2011). [CrossRef] [PubMed]

19.

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]

20.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys. 13, 093008 (2011). [CrossRef]

21.

S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Recollision dynamics and time delay in strong-field double ionization,” Opt. Express 15, 767–778 (2007). [CrossRef] [PubMed]

22.

Y. Zhou, Q. Liao, and P. Lu, “Mechanism for high-energy electrons in nonsequential double ionization below the recollision-excitation threshold,” Phys. Rev. A 80, 023412 (2009). [CrossRef]

23.

Y. Zhou, Q. Liao, and P. Lu, “Complex sub-laser-cycle electron dynamics in strong-field nonsequential triple ionizaion,” Opt. Express 18, 16025–16034 (2010). [CrossRef] [PubMed]

24.

Phay J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett. 94, 093002 (2005). [CrossRef] [PubMed]

25.

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]

26.

Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett. 109, 053004 (2012). [CrossRef]

27.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys. 8, 76–80 (2011). [CrossRef]

28.

N. I. Shvetsov-Shilovski, D. Dimitrovski, and L. B. Madsen, “Ionization in elliptically polarized pulses: Multi-electron polarization effects and asymmetry of photoelectron momentum distributions,” Phys. Rev. A 85, 023428 (2012). [CrossRef]

29.

C. L. Kirschbaum and L. Wilets, “Classical many-body model for atomic collisions incorporating the Heisenberg and Pauli principles,” Phys. Rev. A 21, 834–841 (1980). [CrossRef]

30.

D. Zajfman and D. Maor, “Heisenberg core in classical-trajectory monte carlo calculations of ionization and charge exchange,” Phys. Rev. Lett. 56, 320–323 (1986). [CrossRef] [PubMed]

31.

J. S. Cohen, “Quasiclassical-trajectory Monte Carlo methods for collisions with two-electron atoms,” Phys. Rev. A 54, 573–586 (1996). [CrossRef] [PubMed]

32.

W. A. Beck and L. Wilets, “Semiclassical description of proton stopping by atomic and molecular targets,” Phys. Rev. A 55, 2821–2829 (1997). [CrossRef]

33.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403R(2005). [CrossRef]

34.

X. Wang and J. H. Eberly, “Effects of elliptical polarization on strong-field short-pulse double ionization,” Phys. Rev. Lett. 103, 103007 (2009). [CrossRef] [PubMed]

35.

S. V. Popruzhenko, G. G. Paulus, and D. Bauer, “Coulomb-corrected quantum trajectories in strong-field ionization,” Phys. Rev. A 77, 053409 (2008). [CrossRef]

36.

S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, “Coulomb asymmetry in above-threshold ionization,” Phys. Rev. Lett. 93, 233002 (2004). [CrossRef] [PubMed]

37.

A. Jaroń, J. Z. Kamińskia, and F. Ehlotzky, “Asymmetries in the angular distributions of above threshold ionization in an elliptically polarized laser field,” Opt. Commun. 163, 115–121 (1999). [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: July 5, 2012
Manuscript Accepted: August 8, 2012
Published: August 20, 2012

Citation
Yueming Zhou, Cheng Huang, and Peixiang Lu, "Revealing the multi-electron effects in sequential double ionization using classical simulations," Opt. Express 20, 20201-20209 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-18-20201


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References

  1. P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett.71, 1994–1997 (1993). [CrossRef] [PubMed]
  2. 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]
  3. Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emmision in multiphoton double ionization,” Nature405, 658–661 (2000). [CrossRef] [PubMed]
  4. B. Walker, B. Sheehy, L. F. Dimauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionizaiton of helium,” Phys. Rev. Lett.73, 1227–1230 (1994). [CrossRef] [PubMed]
  5. 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 ionizaion of Ar: the role of excitation tunneling,” Phys. Rev. Lett.87, 043003 (2001). [CrossRef] [PubMed]
  6. M. Weckenbrock, D. Zeidler, A. Staudte, Th. Weber, M. Schöffler, M. Meckel, S. Kammer, M. Smolarski, O. Jagutzki, V. R. Bhardwaj, D.M. Rayner, D.M. Villeneuve, P. B. Corkum, and R. Dörner, “Fully differential rates for femtosecond multiphoton double ionization of neon,” Phys. Rev. Lett.92, 213002 (2004). [CrossRef] [PubMed]
  7. A. Rudenko, K. Zrost, B. Feuerstein, V. L. B. de Jesus, C. D. Schröter, R. Moshammer, and J. Ullrich, “Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms,” Phys. Rev. Lett.93, 253001 (2004). [CrossRef]
  8. 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]
  9. 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]
  10. S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Variable time lag and backward ejection in full-dimension analysis of strong field double ionization,” Phys. Rev. Lett.97, 103008 (2006). [CrossRef] [PubMed]
  11. Y. Zhou, C. Huang, A. Tong, Q. Liao, and P. Lu, “Correlated electron dynamics in nonsequential double ionization by orthogonal two-color laser pulses,” Opt. Express19, 2301–2308 (2011). [CrossRef] [PubMed]
  12. Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Lett.36, 2758–2760 (2011). [CrossRef] [PubMed]
  13. A. Becker, R. Dörner, and R. Moshammer,“Multiple fragmentation of atoms in femtosecond laser pulses,” J. Phys. B38, S753–S772 (2005). [CrossRef]
  14. Q. Liao, Y. Zhou, C. Huang, and P. Lu, “Multiphoton Rabi oscillations of correlated electrons in strong-field nonsequential double ionization,” New J. Phys.14, 013001 (2012). [CrossRef]
  15. B. Chang, P. R. Bolton, and D. N. Fittinghoff, “Closed-form solutions for the production of ions in the collisionless ionization of gases by intense lasers,” Phys. Rev. A47, 4193–4203 (1993). [CrossRef] [PubMed]
  16. K. I. Dimitriou, S. Yoshida, J. Burgdöfer, H. Shimada, H. Oyama, and Y. Yamazaki, “Momentum distribution of multiply charged ions produced by intense (50–70-PW/cm2) lasers,” Phys. Rev. A75, 013418 (2007). [CrossRef]
  17. N. I. Shvetsov-Shilovski, A. M. Sayler, T. Rathje, and G. G. Paulus, “Momentum distributions of sequential ionization,” Phys. Rev. A83, 033401 (2011). [CrossRef]
  18. A. Fleischer, H. J. Wörner, L. Arissian, L. R. Liu, M. Meckel, A. Rippert, R. Dörner, D. M. Villeneuve, P. B. Corkum, and A. Staudte, “Probing angular correlations in sequential double ionization,” Phys. Rev. Lett.107, 113003 (2011). [CrossRef] [PubMed]
  19. 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]
  20. A. N. Pfeiffer, C. Cirelli, M. Smolarski, X. Wang, J. H. Eberly, R. Döner, and U. Keller, “Breakdown of the independent electron approximation in sequential double ionization,” New. J. Phys.13, 093008 (2011). [CrossRef]
  21. S. L. Haan, L. Breen, A. Karim, and J. H. Eberly, “Recollision dynamics and time delay in strong-field double ionization,” Opt. Express15, 767–778 (2007). [CrossRef] [PubMed]
  22. Y. Zhou, Q. Liao, and P. Lu, “Mechanism for high-energy electrons in nonsequential double ionization below the recollision-excitation threshold,” Phys. Rev. A80, 023412 (2009). [CrossRef]
  23. Y. Zhou, Q. Liao, and P. Lu, “Complex sub-laser-cycle electron dynamics in strong-field nonsequential triple ionizaion,” Opt. Express18, 16025–16034 (2010). [CrossRef] [PubMed]
  24. Phay J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, “Nonsequential double ionization as a completely classical photoelectric effect,” Phys. Rev. Lett.94, 093002 (2005). [CrossRef] [PubMed]
  25. Y. Zhou, Q. Liao, and P. Lu, “Asymmetric electron energy sharing in strong-field double ionization of helium,” Phys. Rev. A82, 053402 (2010). [CrossRef]
  26. Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012). [CrossRef]
  27. A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Phys.8, 76–80 (2011). [CrossRef]
  28. N. I. Shvetsov-Shilovski, D. Dimitrovski, and L. B. Madsen, “Ionization in elliptically polarized pulses: Multi-electron polarization effects and asymmetry of photoelectron momentum distributions,” Phys. Rev. A85, 023428 (2012). [CrossRef]
  29. C. L. Kirschbaum and L. Wilets, “Classical many-body model for atomic collisions incorporating the Heisenberg and Pauli principles,” Phys. Rev. A21, 834–841 (1980). [CrossRef]
  30. D. Zajfman and D. Maor, “Heisenberg core in classical-trajectory monte carlo calculations of ionization and charge exchange,” Phys. Rev. Lett.56, 320–323 (1986). [CrossRef] [PubMed]
  31. J. S. Cohen, “Quasiclassical-trajectory Monte Carlo methods for collisions with two-electron atoms,” Phys. Rev. A54, 573–586 (1996). [CrossRef] [PubMed]
  32. W. A. Beck and L. Wilets, “Semiclassical description of proton stopping by atomic and molecular targets,” Phys. Rev. A55, 2821–2829 (1997). [CrossRef]
  33. C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A72, 041403R(2005). [CrossRef]
  34. X. Wang and J. H. Eberly, “Effects of elliptical polarization on strong-field short-pulse double ionization,” Phys. Rev. Lett.103, 103007 (2009). [CrossRef] [PubMed]
  35. S. V. Popruzhenko, G. G. Paulus, and D. Bauer, “Coulomb-corrected quantum trajectories in strong-field ionization,” Phys. Rev. A77, 053409 (2008). [CrossRef]
  36. S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, “Coulomb asymmetry in above-threshold ionization,” Phys. Rev. Lett.93, 233002 (2004). [CrossRef] [PubMed]
  37. A. Jaroń, J. Z. Kamińskia, and F. Ehlotzky, “Asymmetries in the angular distributions of above threshold ionization in an elliptically polarized laser field,” Opt. Commun.163, 115–121 (1999). [CrossRef]

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