Abstract

With the classical fermion molecular dynamics model (FMD), we investigated electron emissions from H2+ by circularly polarized laser pulses. The obtained electron momentum distribution clearly shows an angular shift relative to the expected direction for H2+ aligned parallel to the polarization plane, which is in good agreement with the recent experimental result. By tracing the classical trajectory, we provide direct evidence for the electron delayed emission with respect to the instant when the electric field is parallel to the molecular axis, which was regarded as the origin of the angular shift in the electron momentum distribution. Furthermore, we find that the angular shift decreases with increasing the laser wavelength.

© 2012 OSA

1. Introduction

Photoionization of atoms and molecules by the strong laser field [1], as the doorway step of many strong field processes [29], continued attracting much attention over the past thirty years. The simple-man model [10, 11], that the electron firstly leaves the parent ion with zero longitudinal momentum by tunneling at maximum of the electric field and then is determined by the laser field, has obtained great success in understanding the dynamics of the strong field ionization [12, 13]. Because of the increasingly deep study in the strong field ionization, more and more novel phenomena [1418] beyond the scope of the simple-man model are found. The peculiar low-energy structure [14, 15] of ATI electron spectra is generally investigated and the role of the Coulomb potential of the parent ion has been identified [19,20]. The counterintuitive angular shift in the photoelectron momentum distribution for atoms in strong few-cycle circularly polarized laser pulses is also attributed to an intimate interplay between the external field and the binding potential [16].

Furthermore, the situation for the molecule is more complex in comparison with the atom. By solving the time-dependent Schrödinger equation, Takemoto etal. found multiple bursts of ionization of H2+ by a linearly polarized laser pulse within a half-cycle of the laser field [17], which deviates from the widely accepted tunnel ionization picture [21]. The very recent experiment by Odenweller etal. shows the unexpected electron angular distribution with a tilt angle relative to the expected direction (perpendicular to the molecular axis) for H2+ aligned parallel to the polarization plane [18]. The unexpected electron angular shift is related to the attosecond time lag of electron emissions with respect to the instant when the electric field is parallel to the molecular axis in [18]. However, they do not definitely confirm that most of electrons are emitted with a time lag. Here we expect by the classical ensemble model to obtain the direct evidence of the delayed emission of the electron.

In a strong laser field with intensity above 1014 W/cm2, the discrete character of the energy spectrum of a molecule is washed out, since the energy levels can be shifted by the electric field to an amount comparable to the field-free energy level differences. Thus classical models including an infinite number of excited states often behave very well and reveal many detailed dynamics processes in the strong field ionization [2227]. Moreover, previous studies have demonstrated that back analysis of classical trajectories is a powerful tool to explore the origins of the strong field phenomena [22,28,29]. It allows us, at the end of a simulation, to tag individual key trajectories, and then carefully back examine their histories and analyze their dynamics in detail. The laser intensity used in Odenweller’s experiment [18] is 6×1014 W/cm2, which is well in the over-the-barrier ionization regime for H2+. Therefore the classical model is expected to well describe the electron emission of H2+ in this laser intensity. In this paper, we employ the classical fermion molecular dynamics model (FMD) [3032] to investigate electron emissions from H2+ by circularly polarized laser pulses. Our classical calculations well reproduce the observed electron angular shift in Odenweller’s experiment [18]. Moreover, by back analysis of classical trajectories we find that most of electrons are emitted not at the instant when the electric field is parallel to the molecular axis, but hundreds of attoseconds later, providing the direct evidence for the delayed emission of the electron. Furthermore, the strong wavelength dependence of the angular shift is investigated.

2. The fermion molecular dynamics model

The classical fermion molecular dynamics model (FMD) was originally introduced by Kirschbaum and Wilets etal. [30, 31]. In order to prevent autoionization and collapse of the molecule, they add two momentum-dependent pseudopotentials to the usual Hamiltonian. The two pseudopotentials (VH, VP) constrain the motion to satisfy the Heisenberg uncertainty and the Pauli exclusion principles. Then Cohen introduces two additional terms Vm1, Vm2 to improve the treatment of the H2+ and H2 molecules [32]. Vm1 is a one-electron operator, and Vm2 is a two-electron operator. This extension avoids the overbinding of H2+ and H2 and successfully reproduces the Born-Oppenheimer ground state energies of H2+ and H2. Very recently, the FMD model was further developed to study successfully the dynamics of laser-driven D3+ by Lötstedt etal. [33].

In the FMD model, the classical mechanical Hamiltonian of the H2+ ion is written

H=H0+VH+Vm1
where
H0=T+VCoul
is the usual Hamiltonian containing the kinetic energy and Coulomb potentials. VH is effective potential representing the quantum-mechanical effects of the Heisenberg uncertainty. Vm1 is the one-electron operator. The subscripts b and c represent protons. The subscripts 1 and o denote the electron and the midpoint of the molecule. The labels i and j represent any pair of these. The relative distance
rij=rjri,
the relative momentum
pij=mipjmjpimi+mj,
and the reduced mass
μij=mimjmi+mj,
The Hamiltonian for the H2+ ion is (atomic units are used throughout unless stated otherwise)
H=12mppb2+12mppc2+12mep121rb11rc1+1rbc+1μb1rb12f(rb1pb1;ξH)+1μc1rc12f(rc1pc1;ξH)+1μo1rbc2f(ro1po1;ξm1).
where
f(rp;ξ)=ξ24αexp{α[1(rpξ)4]}.

The proton mass mp=1836, and the electron mass me=1. The precise value of the constant α is unimportant. Here α is chosen to be 4.0. The parameters ξH =0.9428, ξm1=0.90 are selected to fit the ground-state energies of H and H2+.

The evolution of the molecular system is determined by the Hamilton’s classical equations of motion:

dridt=Hpi,
dpidt=Hri+qE(t).
where q is the electric charge of the particle and E(t) is the electric field of a circularly polarized laser pulse. At first the two protons are fixed at z=±1.1614 a.u. which is the equilibrium configuration of H2+ in this model, the position and the momentum of the electron are given randomly. Then the energy of the molecular system is minimized by solving the classical equations of motion with a dissipative term [30]. In this way we get some classical H2+ ions with the ground state energy −0.603 a.u. as pilot molecules. Secondly, we imparted a vibrational energy of 2.5 eV to the two protons of these pilot molecules. These pilot molecules are then allowed to evolve freely without the laser field. The positions and momenta of the electrons and protons of these pilot molecules at time nΔt provide the nth initial condition in the initial ensemble. In this way, a initial classical ensemble with enough classical trajectories is generated. Once the initial ensemble is obtained, the laser field is turned on and all trajectories are evolved in the combined Coulomb and laser fields. In our calculation a circularly polarized 800 nm, 6×1014 W/cm2 laser pulse with a 11-cycle sin2-shaped envelope is used. The electric field E(t) rotates in x-y plane.

3. Results and discussions

Figure 1(a) displays the two-dimensional photoelectron momentum distribution from H2+ aligned perpendicular to the polarization plane of circularly polarized laser pulses. The donut-shaped final electron momentum distribution shown in Fig. 1(a) agrees with the simple man model [10]. Figure 1(c) shows the radial momentum distribution of the photoelectron in the polarization plane, and its maximum is located at 1.62 a.u. which is exactly equal to the peak amplitude A0 of the vector potential. The two-dimensional momentum distribution in z-y plane [Fig. 1(b)] is also consistent with the recent observation [Fig. 1(b) in [34]] for atoms.

 

Fig. 1 Photoelectron momentum distributions from H2+ aligned along z axis for a clockwise circularly polarized 800 nm laser pulse at a peak intensity of 6×1014 W/cm2. (a) and (b) show the two-dimensional photoelectron momentum distributions in x-y and z-y planes, respectively. (c) is the photoelectron radial momentum distribution. The electric field E(t) rotates in x-y plane.

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When H2+ is aligned perpendicular to the polarization plane, the electron momentum distribution in the polarization plane is an uniform donut. However, for the case of H2+ aligned parallel to the polarization plane, the ionization rate is expected to be largest when E(t) is aligned along the axis of the molecule [35, 36]. Therefore, two maximum parts are expected to appear in the direction perpendicular to the molecular axis in the final electron momentum distribution. This prediction deviates from the recent experimental observation where two maximum parts are found in the first and third quadrants. Here we obtain the two-dimensional photoelectron momentum distribution in polarization plane for H2+ aligned along x axis by the classical FMD model, as shown in Fig. 2(a). It is obvious that there are two maximum parts in the first and third quadrants not in the expected y direction. This deviation from the expected direction is in qualitative agreement with recent experimental result [see Fig. 1(e) in [18]]. The momentum in the direction perpendicular to the polarization plane is almost zero [Fig. 2(b)]. Figure 2(c) shows the radial momentum distribution with a maximum of 1.5 a.u., which is slightly smaller than the peak amplitude A0 of the vector potential. This is also qualitatively consistent with the experimental observation.

 

Fig. 2 Photoelectron momentum distributions from H2+ aligned along x axis for a clockwise circularly polarized 800 nm laser pulse at a peak intensity of 6×1014 W/cm2. (a) and (b) show the two-dimensional photoelectron momentum distributions in x-y and z-y planes, respectively. (c) is the photoelectron radial momentum distribution. The electric field E(t) rotates in x-y plane.

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In [18] the angular shift is related to the attosecond time lag of electron emissions with respect to the instant when the electric field is parallel to the molecular axis. However, they do not definitely confirm that most of electrons are emitted with a time lag. Here we attempt to find the direct evidence of the delayed emission of the electron by tracing the classical trajectory. Back analysis [22, 37, 38] is used to investigate the electron emission process. The ionization time is defined as the instant when the energy of the electron becomes positive [27, 39], where the energy of the electron contains the kinetic energy, potential energy of the electron-proton interaction and the two momentum-dependent pseudopotentials (VH, Vm1) [38]. According to back analysis, the electrons are predominantly ionized at internuclear distances of 6–9 a.u. in our calculations which is well in the so-called enhanced ionization regime [18, 40, 41]. A sample trajectory from Fig. 2(a) is shown in Fig. 3 from the beginning of the laser field to the end. Panels (a), (b) and (c) correspond to the electron energy, the electron coordinate x and y, and the electron momentum px and py as functions of the time in unit of laser cycle, respectively. Panel (d) displays the electron trajectory in x-y plane. At first the electron is bound [Fig. 3(a)] with negative energy and at the vicinity of the parent ion [Fig. 3(b)]. At the instant of 5.6 T0 the electron gets enough energy to ionize, and then shifts out of the parent ion [Figs. 3(b) and 3(c)]. Obviously, the electron is ionized after the instant when the electric field is parallel to the molecular axis. At the end of the laser field the electron has the positive momenta in both of x and y directions [Fig. 3(c)], i.e., the electron is emitted into the first quadrant [Fig. 3(d)].

 

Fig. 3 A sample trajectory from Fig. 2. Panels (a), (b) and (c) show the electron energy, the electron coordinate x and y, and the electron momentum px and py versus time in unit of laser cycle, respectively. Panel (d) displays the electron trajectory in x-y plane. The arrows mark the ionization time. The black dash-dot curve is the sketch of the electric field along the molecular axis.

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Figure 4 shows the ionization yield as a function of the ionization time in unit of laser cycle for H2+ aligned along z axis [Fig. 4(a)] and aligned along x axis [Fig. 4(b)]. The blue dashed curves mark those instants that the electric field is parallel to the molecular axis. For the perpendicular alignment, the ionization yield firstly increases and then decreases with the time, which is similar to the laser envelope. Compared with Fig. 4(a), it is clear that the ionization yield curve in Fig. 4(b) shows a series of peaks separated by a half-cycle of the laser field. Moreover, these ionization peaks are not located at those instants that the electric field is parallel to the molecular axis, but hundreds of attoseconds later. This provides the direct evidence for the delayed emission of the electron. Without the effect of the Coulomb potential on the free electron considered, the electron final momentum is obtained as pf =piA(ti). A(ti) is the vector potential at the instant of ionization ti, and pi is the initial electron momentum. Because the pi is small relative to A(ti), the final direction is significantly determined by the vector potential A(ti) at the instant of ionization. If the electron is emitted at the instant when the electric field is parallel to the molecular axis, the electron will appear in the direction (y axis) perpendicular to the molecular axis. Because of the time lag of hundreds of attoseconds relative to those instants when the electric field is parallel to the molecular axis, the electron gains a momentum with a tilt angle relative to the direction perpendicular to the molecular axis from the subsequent electric field. Thus the photoelectron momentum distribution shows an angular shift relative to the expected direction for the case of the parallel alignment.

 

Fig. 4 Panels (a) and (b) show the ionization yield versus the ionization time in unit of laser cycle for the cases of Figs. 1 and 2, respectively. The vertical blue dashed curves mark those instants when the electric field is parallel to the molecular axis. The green dash-dot curve is the sketch of the electric field along the molecular axis.

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Our classical calculations have well reproduced the unexpected angular shift in the electron momentum distribution from H2+ aligned parallel to the polarization plane. The attosecond time lag of electron emissions, which is responsible for the angular shift, is confirmed by the back analysis of classical trajectories. This implies that classical simulations can well describe the electron emission of H2+ by circularly polarized laser pulses. By solving the two-dimensional TDSE of H2+, the angular shift feature of the experimental data are reproduced as a part [peaks II of Fig. 1(f)] of the numerical simulation in [18]. However, the additional two prominent parts I and III near the axes [Fig. 1(f)], which do not exist in the experimental result, also appear in the numerical simulation. In our classical simulations the two additional parts are not found. In order to analyze the origin of the delayed electron emission with our model, we carefully examine the evolution of the classical ensemble in the circularly polarized laser pulses. We find the numbers of the electrons near the two protons are almost same at the instant when the electric field is parallel to the molecular axis. However, just after the electric field is parallel to the molecular axis many electrons are transferred to one of the protons and thus the electrons near one proton are much more than those near the other proton. This scenario is very similar to that reported by Takemoto et al. for linear polarization [17]. We consider that the transient electron localization at one of the protons results in the dominant electron emissions just after the instant when the electric field is parallel to the molecular axis.

In addition, our calculations obtain a final radial momentum of 1.5 a.u., which is slightly smaller than the vector potential (1.62 a.u.). In [18] the low final momentum is attributed to the non-zero initial momentum of the electron at the instant of ionization. Here by tracing the classical trajectory it is obtained that the electron is emitted with an initial momentum of 0.5 a.u., and there is a 106 degree angle between the initial momentum pi and the inverse of the vector potential at the instant of ionization −A(ti). If the Coulomb attraction between the parent ion and the escaping electron is neglected, the electron final momentum is 1.56 a.u., which is a little smaller than the vector potential but bigger than the final momentum obtained by our numerical calculations. This indicates that the non-zero initial momentum is one reason for the low final momentum but not the only reason. We suggest that Coulomb attraction between the parent ion and the escaping electron could also result in the decrease of the electron momentum.

We further explore the effect of the laser wavelength on the angular shift of aligned H2+ by circularly polarized laser pulses. Figures 5(a) and 5(c) show the two-dimensional photoelectron momentum distributions from H2+ aligned along x axis for circularly polarized laser pulses at I=6×1014 W/cm2, λ=1200 nm and 1600 nm, respectively. The electron momentum distributions for 1200 nm and 1600 nm both show clear angular shifts. Furthermore, by comparing Figs. 2(a), 5(a) and 5(c), it is obvious that the tilt angle decreases with the laser wavelength increasing. By analyzing the ionization yield curves for different laser wavelengths [Figs. 4(b), 5(b) and 5(d)], one can easily find that the longer the laser wavelength is, the smaller the time lag in the electron emission is. This wavelength dependence of the time lag is responsible for the decrease of the angular shift with the laser wavelength increasing. Since the final emission direction of the electron depends on the laser phase of ionization, the ionization time lag is presented in unit of laser cycle in this paper. In our calculations we find that the time lags in atomic units for different wavelengths are almost same. For the same time lag in atomic units the long wavelength corresponds to a smaller value of time lag in unit of laser cycle in comparison with the short wavelength. Thus the time lag in unit of laser cycle decreases with the laser wavelength increasing. In order to more clearly display the strong wavelength dependence of the angular shift, we present the tilt angle as a function of the laser wavelength in Fig. 6.

 

Fig. 5 The two-dimensional photoelectron momentum distributions from H2+ aligned along x axis for a clockwise circularly polarized laser pulse at I=6×1014 W/cm2, λ=1200 nm (a) and 1600 nm (c). (b) and (d) show the ionization yield versus the ionization time in unit of laser cycle for the cases of (a) and (c) respectively. The vertical red dashed curves mark those instants when the electric field is parallel to the molecular axis. The electric field E(t) rotates in x-y plane.

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Fig. 6 Dependence of the tilt angle on the laser wavelength.

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4. Conclusion

In conclusion, we have investigated the electron momentum distributions from H2+ by circularly polarized laser pulses with the classical fermion molecular dynamics model. For H2+ aligned perpendicular to the polarization plane, the electron momentum distribution exhibits donut-shaped structure which is similar to the case of atoms. For H2+ aligned parallel to the polarization plane the ionization events are clustered in the first and third quadrants in the electron momentum distribution, i.e., the ejection direction of the electron has a tilt angle relative to the y axis direction (the expected direction), which is in good agreement with the recent experimental result. By back analysis of classical trajectories we definitely confirm that this angular shift in the electron momentum distribution originates from the delayed emission of the electron [18], i.e., most of electrons are emitted not at the instant when the electric field is parallel to the molecular axis, but hundreds of attoseconds later. Further study indicates that the angular shift from H2+ by circularly polarized laser pulses decreases with increasing the laser wavelength.

Acknowledgment

This work was supported by the National Natural Science Foundation of China under Grant No. 11004070, 10904045, National Science Fund for Distinguished Young Scholars under Grant No. 60925021, and the 973 Program of China under Grant No. 2011CB808103.

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References

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  1. P. Agostini, F. Fabre, G. Mainfray, and G. Petite, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
    [CrossRef]
  2. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
    [CrossRef] [PubMed]
  3. M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
    [CrossRef] [PubMed]
  4. H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417, 917–922 (2002).
    [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. S. Micheau, Z. Chen, A. T. Le, J. Rauschenberger, M. F. Kling, and C. D. Lin, “Accurate retrieval of target structures and laser parameters of few-cycle pulses from photoelectron momentum spectra,” Phys. Rev. Lett. 102, 073001 (2009).
    [CrossRef] [PubMed]
  8. J. Wu, M. Meckel, S. Voss, H. Sann, M. Kunitski, L. Ph. H. Schmidt, A. Czasch, H. Kim, T. Jahnke, and R. Dörner, “Coulomb asymmetry in strong field multielectron ionization of diatomic molecules,” Phys. Rev. Lett. 108, 043002 (2012).
    [CrossRef] [PubMed]
  9. 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]
  10. P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
    [CrossRef] [PubMed]
  11. K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulanderc, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
    [CrossRef] [PubMed]
  12. G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
    [CrossRef]
  13. M. Lein, J. P. Marangos, and P. L. Knight, “Electron diffraction in above-threshold ionization of molecules,” Phys. Rev. A 66, 051404(R) (2002).
    [CrossRef]
  14. C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
    [CrossRef]
  15. W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
    [CrossRef] [PubMed]
  16. C. P. J. Martiny, M. Abu-samha, and L. B. Madsen, “Counterintuitive angular shifts in the photoelectron momentum distribution for atoms in strong few-cycle circularly polarized laser pulses,” J. Phys. B 42, 161001 (2009).
    [CrossRef]
  17. N. Takemoto and A. Becker, “Multiple ionization bursts in laser-driven hydrogen molecular ion,” Phys. Rev. Lett. 105, 203004 (2010).
    [CrossRef]
  18. M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
    [CrossRef] [PubMed]
  19. C. Liu and K. Z. Hatsagortsyan, “Origin of unexpected low energy structure in photoelectron spectra induced by midinfrared strong laser fields,” Phys. Rev. Lett. 105, 113003 (2010).
    [CrossRef] [PubMed]
  20. D. A. Telnov and S. I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: role of the coulomb threshold effect,” Phys. Rev. A 83, 063406 (2011).
    [CrossRef]
  21. N. B. Delone and V. P. Krainov, “Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation,” J. Opt. Soc. Am. B 8, 1207–1211 (1991).
    [CrossRef]
  22. 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]
  23. 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]
  24. Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Letters 36, 2758–2760 (2011).
    [CrossRef]
  25. F. Mauger, C. Chandre, and T. Uzer, “Recollisions and correlated double ionization with circularly polarized light,” Phys. Rev. Lett. 105, 083002 (2010).
    [CrossRef] [PubMed]
  26. P. B. Lerner, K. J. LaGattuta, and J. S. Cohen, “Ionization of helium by a short pulse of radiation: a fermi molecular-dynamics calculation,” Phys. Rev. A 49, R12–R15 (1994).
    [CrossRef] [PubMed]
  27. 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]
  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]
  29. 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]
  30. L. Wilets, E. M. Henley, M. Kraft, and A. D. MacKellar, “Classical many-body model for heavy-ion collisions incorporating the pauli principle,” Nucl. Phys. A 282, 341–350 (1977).
    [CrossRef]
  31. 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]
  32. J. S. Cohen, “Molecular effects on antiproton capture by H2 and the states of pp¯ formed,” Phys. Rev. A 56, 3583–3596 (1997).
    [CrossRef]
  33. E. Lötstedt, T. Kato, and K. Yamanouchi, “Classical dynamics of laser-driven D3+,” Phys. Rev. Lett. 106, 203001 (2011).
    [CrossRef] [PubMed]
  34. L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
    [CrossRef]
  35. X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66, 033402 (2002).
    [CrossRef]
  36. G. L. Kamta and A. D. Bandrauk, “Imaging electron molecular orbitals via ionization by intense femtosecond pulses,” Phys. Rev. A 74, 033415 (2006).
    [CrossRef]
  37. 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]
  38. D. A. Wasson and S. E. Koonin, “Molecular-dynamics simulations of atomic ionization by strong laser fields,” Phys. Rev. A 39, 5676–5685 (1989).
    [CrossRef] [PubMed]
  39. Y. Zhou, C. Huang, A. Tong, Q. Liao, and P. Lu, “Correlated electron dynamics in nonsequential double ioniza-tion by orthogonal two-color laser pulses,” Opt. Express 19, 2301–2308 (2011).
    [CrossRef] [PubMed]
  40. T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52, R2511–R2514 (1995).
    [CrossRef] [PubMed]
  41. T. Seideman, M. Yu. Ivanov, and P. B. Corkum, “Role of electron localization in intense-field molecular ionization,” Phys. Rev. Lett. 75, 2819–2822 (1995).
    [CrossRef] [PubMed]

2012 (2)

J. Wu, M. Meckel, S. Voss, H. Sann, M. Kunitski, L. Ph. H. Schmidt, A. Czasch, H. Kim, T. Jahnke, and R. Dörner, “Coulomb asymmetry in strong field multielectron ionization of diatomic molecules,” Phys. Rev. Lett. 108, 043002 (2012).
[CrossRef] [PubMed]

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]

2011 (6)

M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
[CrossRef] [PubMed]

D. A. Telnov and S. I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: role of the coulomb threshold effect,” Phys. Rev. A 83, 063406 (2011).
[CrossRef]

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

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]

E. Lötstedt, T. Kato, and K. Yamanouchi, “Classical dynamics of laser-driven D3+,” Phys. Rev. Lett. 106, 203001 (2011).
[CrossRef] [PubMed]

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

2010 (6)

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]

L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
[CrossRef]

F. Mauger, C. Chandre, and T. Uzer, “Recollisions and correlated double ionization with circularly polarized light,” Phys. Rev. Lett. 105, 083002 (2010).
[CrossRef] [PubMed]

N. Takemoto and A. Becker, “Multiple ionization bursts in laser-driven hydrogen molecular ion,” Phys. Rev. Lett. 105, 203004 (2010).
[CrossRef]

C. Liu and K. Z. Hatsagortsyan, “Origin of unexpected low energy structure in photoelectron spectra induced by midinfrared strong laser fields,” Phys. Rev. Lett. 105, 113003 (2010).
[CrossRef] [PubMed]

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]

2009 (6)

S. Micheau, Z. Chen, A. T. Le, J. Rauschenberger, M. F. Kling, and C. D. Lin, “Accurate retrieval of target structures and laser parameters of few-cycle pulses from photoelectron momentum spectra,” Phys. Rev. Lett. 102, 073001 (2009).
[CrossRef] [PubMed]

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[CrossRef]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[CrossRef] [PubMed]

C. P. J. Martiny, M. Abu-samha, and L. B. Madsen, “Counterintuitive angular shifts in the photoelectron momentum distribution for atoms in strong few-cycle circularly polarized laser pulses,” J. Phys. B 42, 161001 (2009).
[CrossRef]

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]

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]

2008 (3)

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]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[CrossRef] [PubMed]

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[CrossRef] [PubMed]

2006 (2)

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]

G. L. Kamta and A. D. Bandrauk, “Imaging electron molecular orbitals via ionization by intense femtosecond pulses,” Phys. Rev. A 74, 033415 (2006).
[CrossRef]

2002 (3)

X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66, 033402 (2002).
[CrossRef]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417, 917–922 (2002).
[CrossRef] [PubMed]

M. Lein, J. P. Marangos, and P. L. Knight, “Electron diffraction in above-threshold ionization of molecules,” Phys. Rev. A 66, 051404(R) (2002).
[CrossRef]

2000 (1)

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]

1997 (1)

J. S. Cohen, “Molecular effects on antiproton capture by H2 and the states of pp¯ formed,” Phys. Rev. A 56, 3583–3596 (1997).
[CrossRef]

1995 (2)

T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52, R2511–R2514 (1995).
[CrossRef] [PubMed]

T. Seideman, M. Yu. Ivanov, and P. B. Corkum, “Role of electron localization in intense-field molecular ionization,” Phys. Rev. Lett. 75, 2819–2822 (1995).
[CrossRef] [PubMed]

1994 (2)

P. B. Lerner, K. J. LaGattuta, and J. S. Cohen, “Ionization of helium by a short pulse of radiation: a fermi molecular-dynamics calculation,” Phys. Rev. A 49, R12–R15 (1994).
[CrossRef] [PubMed]

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[CrossRef]

1993 (1)

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulanderc, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
[CrossRef] [PubMed]

1991 (1)

1989 (2)

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[CrossRef] [PubMed]

D. A. Wasson and S. E. Koonin, “Molecular-dynamics simulations of atomic ionization by strong laser fields,” Phys. Rev. A 39, 5676–5685 (1989).
[CrossRef] [PubMed]

1980 (1)

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]

1979 (1)

P. Agostini, F. Fabre, G. Mainfray, and G. Petite, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

1977 (1)

L. Wilets, E. M. Henley, M. Kraft, and A. D. MacKellar, “Classical many-body model for heavy-ion collisions incorporating the pauli principle,” Nucl. Phys. A 282, 341–350 (1977).
[CrossRef]

Abu-samha, M.

C. P. J. Martiny, M. Abu-samha, and L. B. Madsen, “Counterintuitive angular shifts in the photoelectron momentum distribution for atoms in strong few-cycle circularly polarized laser pulses,” J. Phys. B 42, 161001 (2009).
[CrossRef]

Agostini, P.

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[CrossRef]

P. Agostini, F. Fabre, G. Mainfray, and G. Petite, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[CrossRef] [PubMed]

Arissian, L.

L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
[CrossRef]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[CrossRef] [PubMed]

Bandrauk, A. D.

G. L. Kamta and A. D. Bandrauk, “Imaging electron molecular orbitals via ionization by intense femtosecond pulses,” Phys. Rev. A 74, 033415 (2006).
[CrossRef]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417, 917–922 (2002).
[CrossRef] [PubMed]

T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52, R2511–R2514 (1995).
[CrossRef] [PubMed]

Bandulet, H. C.

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[CrossRef] [PubMed]

Becker, A.

M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
[CrossRef] [PubMed]

N. Takemoto and A. Becker, “Multiple ionization bursts in laser-driven hydrogen molecular ion,” Phys. Rev. Lett. 105, 203004 (2010).
[CrossRef]

Becker, W.

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[CrossRef]

Blaga, C. I.

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[CrossRef]

Breen, L.

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]

Brunel, F.

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[CrossRef] [PubMed]

Burnett, N. H.

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[CrossRef] [PubMed]

Catoire, F.

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[CrossRef]

Chandre, C.

F. Mauger, C. Chandre, and T. Uzer, “Recollisions and correlated double ionization with circularly polarized light,” Phys. Rev. Lett. 105, 083002 (2010).
[CrossRef] [PubMed]

Chen, J.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[CrossRef] [PubMed]

Chen, S.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[CrossRef] [PubMed]

Chen, Z.

S. Micheau, Z. Chen, A. T. Le, J. Rauschenberger, M. F. Kling, and C. D. Lin, “Accurate retrieval of target structures and laser parameters of few-cycle pulses from photoelectron momentum spectra,” Phys. Rev. Lett. 102, 073001 (2009).
[CrossRef] [PubMed]

Cheng, Y.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[CrossRef] [PubMed]

Chu, S. I.

D. A. Telnov and S. I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: role of the coulomb threshold effect,” Phys. Rev. A 83, 063406 (2011).
[CrossRef]

Cohen, J. S.

J. S. Cohen, “Molecular effects on antiproton capture by H2 and the states of pp¯ formed,” Phys. Rev. A 56, 3583–3596 (1997).
[CrossRef]

P. B. Lerner, K. J. LaGattuta, and J. S. Cohen, “Ionization of helium by a short pulse of radiation: a fermi molecular-dynamics calculation,” Phys. Rev. A 49, R12–R15 (1994).
[CrossRef] [PubMed]

Cole, K.

M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
[CrossRef] [PubMed]

Colosimo, P.

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[CrossRef]

Comtois, D.

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[CrossRef] [PubMed]

Corkum, P. B.

L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
[CrossRef]

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[CrossRef] [PubMed]

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Huang, C.

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Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Letters 36, 2758–2760 (2011).
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Krausz, F.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
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K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulanderc, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
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J. Wu, M. Meckel, S. Voss, H. Sann, M. Kunitski, L. Ph. H. Schmidt, A. Czasch, H. Kim, T. Jahnke, and R. Dörner, “Coulomb asymmetry in strong field multielectron ionization of diatomic molecules,” Phys. Rev. Lett. 108, 043002 (2012).
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H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417, 917–922 (2002).
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Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Letters 36, 2758–2760 (2011).
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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).
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Y. Zhou, C. Huang, A. Tong, Q. Liao, and P. Lu, “Correlated electron dynamics in nonsequential double ioniza-tion by orthogonal two-color laser pulses,” Opt. Express 19, 2301–2308 (2011).
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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).
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Y. Zhou, Q. Liao, and P. Lu, “Asymmetric electron energy sharing in strong-field double ionization of helium,” Phys. Rev. A 82, 053402 (2010).
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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).
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S. Micheau, Z. Chen, A. T. Le, J. Rauschenberger, M. F. Kling, and C. D. Lin, “Accurate retrieval of target structures and laser parameters of few-cycle pulses from photoelectron momentum spectra,” Phys. Rev. Lett. 102, 073001 (2009).
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C. Liu and K. Z. Hatsagortsyan, “Origin of unexpected low energy structure in photoelectron spectra induced by midinfrared strong laser fields,” Phys. Rev. Lett. 105, 113003 (2010).
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W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
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W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
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W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
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E. Lötstedt, T. Kato, and K. Yamanouchi, “Classical dynamics of laser-driven D3+,” Phys. Rev. Lett. 106, 203001 (2011).
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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).
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Y. Zhou, C. Huang, Q. Liao, W. Hong, and P. Lu, “Control the revisit time of the electron wave packet,” Opt. Letters 36, 2758–2760 (2011).
[CrossRef]

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]

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

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]

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]

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]

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L. Wilets, E. M. Henley, M. Kraft, and A. D. MacKellar, “Classical many-body model for heavy-ion collisions incorporating the pauli principle,” Nucl. Phys. A 282, 341–350 (1977).
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M. Lein, J. P. Marangos, and P. L. Knight, “Electron diffraction in above-threshold ionization of molecules,” Phys. Rev. A 66, 051404(R) (2002).
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C. P. J. Martiny, M. Abu-samha, and L. B. Madsen, “Counterintuitive angular shifts in the photoelectron momentum distribution for atoms in strong few-cycle circularly polarized laser pulses,” J. Phys. B 42, 161001 (2009).
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J. Wu, M. Meckel, S. Voss, H. Sann, M. Kunitski, L. Ph. H. Schmidt, A. Czasch, H. Kim, T. Jahnke, and R. Dörner, “Coulomb asymmetry in strong field multielectron ionization of diatomic molecules,” Phys. Rev. Lett. 108, 043002 (2012).
[CrossRef] [PubMed]

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
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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).
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S. Micheau, Z. Chen, A. T. Le, J. Rauschenberger, M. F. Kling, and C. D. Lin, “Accurate retrieval of target structures and laser parameters of few-cycle pulses from photoelectron momentum spectra,” Phys. Rev. Lett. 102, 073001 (2009).
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C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
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M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
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M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
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Paulus, G. G.

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[CrossRef]

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[CrossRef]

Pavicic, D.

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[CrossRef] [PubMed]

Pépin, H.

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[CrossRef] [PubMed]

Petite, G.

P. Agostini, F. Fabre, G. Mainfray, and G. Petite, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

Quan, W.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[CrossRef] [PubMed]

Rauschenberger, J.

S. Micheau, Z. Chen, A. T. Le, J. Rauschenberger, M. F. Kling, and C. D. Lin, “Accurate retrieval of target structures and laser parameters of few-cycle pulses from photoelectron momentum spectra,” Phys. Rev. Lett. 102, 073001 (2009).
[CrossRef] [PubMed]

Sann, H.

J. Wu, M. Meckel, S. Voss, H. Sann, M. Kunitski, L. Ph. H. Schmidt, A. Czasch, H. Kim, T. Jahnke, and R. Dörner, “Coulomb asymmetry in strong field multielectron ionization of diatomic molecules,” Phys. Rev. Lett. 108, 043002 (2012).
[CrossRef] [PubMed]

Schafer, K. J.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulanderc, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
[CrossRef] [PubMed]

Schmidt, L. Ph. H.

J. Wu, M. Meckel, S. Voss, H. Sann, M. Kunitski, L. Ph. H. Schmidt, A. Czasch, H. Kim, T. Jahnke, and R. Dörner, “Coulomb asymmetry in strong field multielectron ionization of diatomic molecules,” Phys. Rev. Lett. 108, 043002 (2012).
[CrossRef] [PubMed]

M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
[CrossRef] [PubMed]

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[CrossRef] [PubMed]

Seideman, T.

T. Seideman, M. Yu. Ivanov, and P. B. Corkum, “Role of electron localization in intense-field molecular ionization,” Phys. Rev. Lett. 75, 2819–2822 (1995).
[CrossRef] [PubMed]

Shomsky, K. N.

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]

Smeenk, C.

L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
[CrossRef]

Smith, Z. S.

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]

Sokolov, A. V.

L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
[CrossRef]

Spielberger, L.

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]

Staudte, A.

L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
[CrossRef]

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[CrossRef] [PubMed]

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]

Takemoto, N.

M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
[CrossRef] [PubMed]

N. Takemoto and A. Becker, “Multiple ionization bursts in laser-driven hydrogen molecular ion,” Phys. Rev. Lett. 105, 203004 (2010).
[CrossRef]

Telnov, D. A.

D. A. Telnov and S. I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: role of the coulomb threshold effect,” Phys. Rev. A 83, 063406 (2011).
[CrossRef]

Titze, J.

M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
[CrossRef] [PubMed]

Tong, A.

Tong, X. M.

X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66, 033402 (2002).
[CrossRef]

Trallero, C.

L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
[CrossRef]

Turner, F.

L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
[CrossRef]

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[CrossRef] [PubMed]

Urbasch, G.

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]

Uzer, T.

F. Mauger, C. Chandre, and T. Uzer, “Recollisions and correlated double ionization with circularly polarized light,” Phys. Rev. Lett. 105, 083002 (2010).
[CrossRef] [PubMed]

Villeneuve, D. M.

L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
[CrossRef]

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[CrossRef] [PubMed]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417, 917–922 (2002).
[CrossRef] [PubMed]

Vollmer, M.

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]

Voss, S.

J. Wu, M. Meckel, S. Voss, H. Sann, M. Kunitski, L. Ph. H. Schmidt, A. Czasch, H. Kim, T. Jahnke, and R. Dörner, “Coulomb asymmetry in strong field multielectron ionization of diatomic molecules,” Phys. Rev. Lett. 108, 043002 (2012).
[CrossRef] [PubMed]

Vredenborg, A.

M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
[CrossRef] [PubMed]

Walther, H.

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[CrossRef]

Wang, X.

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]

Wasson, D. A.

D. A. Wasson and S. E. Koonin, “Molecular-dynamics simulations of atomic ionization by strong laser fields,” Phys. Rev. A 39, 5676–5685 (1989).
[CrossRef] [PubMed]

Weber, Th.

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]

Weckenbrock, M.

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]

Wilets, L.

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]

L. Wilets, E. M. Henley, M. Kraft, and A. D. MacKellar, “Classical many-body model for heavy-ion collisions incorporating the pauli principle,” Nucl. Phys. A 282, 341–350 (1977).
[CrossRef]

WPlantinga, P.

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]

Wu, J.

J. Wu, M. Meckel, S. Voss, H. Sann, M. Kunitski, L. Ph. H. Schmidt, A. Czasch, H. Kim, T. Jahnke, and R. Dörner, “Coulomb asymmetry in strong field multielectron ionization of diatomic molecules,” Phys. Rev. Lett. 108, 043002 (2012).
[CrossRef] [PubMed]

Wu, M.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[CrossRef] [PubMed]

Xiong, H.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[CrossRef] [PubMed]

Xu, H.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[CrossRef] [PubMed]

Xu, Z.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[CrossRef] [PubMed]

Yakovlev, V. S.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[CrossRef] [PubMed]

Yamanouchi, K.

E. Lötstedt, T. Kato, and K. Yamanouchi, “Classical dynamics of laser-driven D3+,” Phys. Rev. Lett. 106, 203001 (2011).
[CrossRef] [PubMed]

Yang, B.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulanderc, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
[CrossRef] [PubMed]

Zeidler, D.

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[CrossRef] [PubMed]

Zhao, Z. X.

X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66, 033402 (2002).
[CrossRef]

Zhou, Y.

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]

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

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

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]

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]

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).
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Zuo, T.

T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52, R2511–R2514 (1995).
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J. Opt. Soc. Am. B (1)

J. Phys. B (3)

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]

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703–L708 (1994).
[CrossRef]

C. P. J. Martiny, M. Abu-samha, and L. B. Madsen, “Counterintuitive angular shifts in the photoelectron momentum distribution for atoms in strong few-cycle circularly polarized laser pulses,” J. Phys. B 42, 161001 (2009).
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Nat. Phys. (1)

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[CrossRef]

Nature (2)

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Yu. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417, 917–922 (2002).
[CrossRef] [PubMed]

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]

New J. Phys. (1)

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]

Nucl. Phys. A (1)

L. Wilets, E. M. Henley, M. Kraft, and A. D. MacKellar, “Classical many-body model for heavy-ion collisions incorporating the pauli principle,” Nucl. Phys. A 282, 341–350 (1977).
[CrossRef]

Opt. Express (3)

Opt. Letters (1)

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

Phys. Rev. A (11)

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]

D. A. Telnov and S. I. Chu, “Low-energy structure of above-threshold-ionization electron spectra: role of the coulomb threshold effect,” Phys. Rev. A 83, 063406 (2011).
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P. B. Lerner, K. J. LaGattuta, and J. S. Cohen, “Ionization of helium by a short pulse of radiation: a fermi molecular-dynamics calculation,” Phys. Rev. A 49, R12–R15 (1994).
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D. A. Wasson and S. E. Koonin, “Molecular-dynamics simulations of atomic ionization by strong laser fields,” Phys. Rev. A 39, 5676–5685 (1989).
[CrossRef] [PubMed]

X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66, 033402 (2002).
[CrossRef]

G. L. Kamta and A. D. Bandrauk, “Imaging electron molecular orbitals via ionization by intense femtosecond pulses,” Phys. Rev. A 74, 033415 (2006).
[CrossRef]

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]

J. S. Cohen, “Molecular effects on antiproton capture by H2 and the states of pp¯ formed,” Phys. Rev. A 56, 3583–3596 (1997).
[CrossRef]

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]

M. Lein, J. P. Marangos, and P. L. Knight, “Electron diffraction in above-threshold ionization of molecules,” Phys. Rev. A 66, 051404(R) (2002).
[CrossRef]

T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52, R2511–R2514 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (15)

T. Seideman, M. Yu. Ivanov, and P. B. Corkum, “Role of electron localization in intense-field molecular ionization,” Phys. Rev. Lett. 75, 2819–2822 (1995).
[CrossRef] [PubMed]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. He, S. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Xu, “Classical aspects in above-threshold ionization with a mid-infrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[CrossRef] [PubMed]

N. Takemoto and A. Becker, “Multiple ionization bursts in laser-driven hydrogen molecular ion,” Phys. Rev. Lett. 105, 203004 (2010).
[CrossRef]

M. Odenweller, N. Takemoto, A. Vredenborg, K. Cole, K. Pahl, J. Titze, L. Ph. H. Schmidt, T. Jahnke, R. Dörner, and A. Becker, “Strong field electron emission from fixed in space H2+ ions,” Phys. Rev. Lett. 107, 143004 (2011).
[CrossRef] [PubMed]

C. Liu and K. Z. Hatsagortsyan, “Origin of unexpected low energy structure in photoelectron spectra induced by midinfrared strong laser fields,” Phys. Rev. Lett. 105, 113003 (2010).
[CrossRef] [PubMed]

S. Micheau, Z. Chen, A. T. Le, J. Rauschenberger, M. F. Kling, and C. D. Lin, “Accurate retrieval of target structures and laser parameters of few-cycle pulses from photoelectron momentum spectra,” Phys. Rev. Lett. 102, 073001 (2009).
[CrossRef] [PubMed]

J. Wu, M. Meckel, S. Voss, H. Sann, M. Kunitski, L. Ph. H. Schmidt, A. Czasch, H. Kim, T. Jahnke, and R. Dörner, “Coulomb asymmetry in strong field multielectron ionization of diatomic molecules,” Phys. Rev. Lett. 108, 043002 (2012).
[CrossRef] [PubMed]

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[CrossRef] [PubMed]

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulanderc, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
[CrossRef] [PubMed]

P. Agostini, F. Fabre, G. Mainfray, and G. Petite, “Free-free transitions following six-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[CrossRef]

E. Lötstedt, T. Kato, and K. Yamanouchi, “Classical dynamics of laser-driven D3+,” Phys. Rev. Lett. 106, 203001 (2011).
[CrossRef] [PubMed]

L. Arissian, C. Smeenk, F. Turner, C. Trallero, A. V. Sokolov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, “Direct test of laser tunneling with electron momentum imaging,” Phys. Rev. Lett. 105, 133002 (2010).
[CrossRef]

F. Mauger, C. Chandre, and T. Uzer, “Recollisions and correlated double ionization with circularly polarized light,” Phys. Rev. Lett. 105, 083002 (2010).
[CrossRef] [PubMed]

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]

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]

Science (2)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[CrossRef] [PubMed]

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Photoelectron momentum distributions from H 2 + aligned along z axis for a clockwise circularly polarized 800 nm laser pulse at a peak intensity of 6×1014 W/cm2. (a) and (b) show the two-dimensional photoelectron momentum distributions in x-y and z-y planes, respectively. (c) is the photoelectron radial momentum distribution. The electric field E(t) rotates in x-y plane.

Fig. 2
Fig. 2

Photoelectron momentum distributions from H 2 + aligned along x axis for a clockwise circularly polarized 800 nm laser pulse at a peak intensity of 6×1014 W/cm2. (a) and (b) show the two-dimensional photoelectron momentum distributions in x-y and z-y planes, respectively. (c) is the photoelectron radial momentum distribution. The electric field E(t) rotates in x-y plane.

Fig. 3
Fig. 3

A sample trajectory from Fig. 2. Panels (a), (b) and (c) show the electron energy, the electron coordinate x and y, and the electron momentum px and py versus time in unit of laser cycle, respectively. Panel (d) displays the electron trajectory in x-y plane. The arrows mark the ionization time. The black dash-dot curve is the sketch of the electric field along the molecular axis.

Fig. 4
Fig. 4

Panels (a) and (b) show the ionization yield versus the ionization time in unit of laser cycle for the cases of Figs. 1 and 2, respectively. The vertical blue dashed curves mark those instants when the electric field is parallel to the molecular axis. The green dash-dot curve is the sketch of the electric field along the molecular axis.

Fig. 5
Fig. 5

The two-dimensional photoelectron momentum distributions from H 2 + aligned along x axis for a clockwise circularly polarized laser pulse at I=6×1014 W/cm2, λ=1200 nm (a) and 1600 nm (c). (b) and (d) show the ionization yield versus the ionization time in unit of laser cycle for the cases of (a) and (c) respectively. The vertical red dashed curves mark those instants when the electric field is parallel to the molecular axis. The electric field E(t) rotates in x-y plane.

Fig. 6
Fig. 6

Dependence of the tilt angle on the laser wavelength.

Equations (9)

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H = H 0 + V H + V m 1
H 0 = T + V Coul
r i j = r j r i ,
p i j = m i p j m j p i m i + m j ,
μ i j = m i m j m i + m j ,
H = 1 2 m p p b 2 + 1 2 m p p c 2 + 1 2 m e p 1 2 1 r b 1 1 r c 1 + 1 r b c + 1 μ b 1 r b 1 2 f ( r b 1 p b 1 ; ξ H ) + 1 μ c 1 r c 1 2 f ( r c 1 p c 1 ; ξ H ) + 1 μ o 1 r b c 2 f ( r o 1 p o 1 ; ξ m 1 ) .
f ( r p ; ξ ) = ξ 2 4 α exp { α [ 1 ( r p ξ ) 4 ] } .
d r i d t = H p i ,
d p i d t = H r i + q E ( t ) .

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