Abstract

The carrier-envelope phase (CEP)-dependent above-barrier ionization (ABI) has been investigated in order to probe the bound-state electron dynamics. It is found that when the system is initially prepared in the excited state, the ionization yield asymmetry between left and right sides can occur both in low-energy and high-energy parts of the photoelectron spectra. Moreover, in electron momentum map, a new interference effect along the direction perpendicular to the laser polarization is found. We show that this interference is related to the competition among different excited states. The interference effect is dependent on CEPs of few-cycle probe pulses, which can be used to trace the superposition information and control the electron wave packet of low excited states.

© 2012 OSA

1. Introduction

Triggering and steering electron motion in atoms and molecules is one of the most important aims in ultrafast physics and attosecond science [19]. The ultrafast pump-probe technology allows tracking of microscopic electronic dynamic process, such as real-time observation of electron tunnelling in atoms [10], retrieval of atomic inner-shell electron motion [11], probing sub-cycle molecular dynamics [12], ultrafast molecular nuclear dynamics [13], and so on. In pump-probe set up, the first pump pulse initiates the following ultrafast dynamics. The delayed probe pulse plays the role of a fast camera which takes snapshots of electrons moving in atoms and molecules [14]. Electron motion typically occurs on a sub-femtosecond to few-femtosecond timescale. On the other side, tunnelling and ionization are determined by each wave crest of electric field of a laser pulse. Great effort has been given to tailoring light electric field and improving the energy of a single wave crest [1518]. The well-defined electric field evolution of carrier-envelope phase (CEP)-stable few-cycle laser pulses also provides an ideal tool for probing electron dynamics [1925]. Firstly, different CEPs of few-cycle pulse correspond to different shapes of electric field and different delay on attosecond timescale; Secondly, different electromagnetic forces of wave crests lead to different transient ionization, which gives a chance to unfold dynamics of electron of different bound states.

Light-induced electron tunnelling in strong fields has attracted much attention in recent years. Previous investigation [26] predicted that the tunnelling occurs when the binding potential is suppressed by the electric field at the peak of the pulse, which is followed by a number of major processes in strong field physics, such as high-order harmonic generation (HHG) [2729], above-threshold ionization (ATI) [3032], and so on. Recently, a technique for focusing an intense coherent soft-x-ray beam with a surprising peak intensity of 1014 W/cm2 has been demonstrated [33], which opens a way to x-ray-pump-probe of strong field dynamics of bound and continuum electrons, such as the electron probability in transversal direction and reconstructing the temporal evolution of the electron wavepacket [34].

In this work, a completely different physical mechanism in contrast to the tunnelling ionization will be showed: an initial electronic wave packet is populated to excited states by xuv resonant π pulse; when the binding potential is repressed by the following strong few-cycle pulse, the eigen energy of the excited state electron is higher than the potential in one direction along which electron escapes directly. Therefore, above-barrier ionization (ABI) occurs in this case. More importantly, a new interference effect in the direction perpendicular to the laser polarization in electron momentum map is found. This interference effect, which cannot occur in ATI or single tunnelling channel, is based on ABI mechanism and on the competition among different bound states. We will show that the interference effect is dependent on CEPs of few-cycle probe pulses, which can trace the coherence of electron wave packet of low excited states.

2. Theory

We have carried out the numerical calculation with solving the two-dimensional (2D) and 1D time-dependent Schrödinger equation (TDSE). The 1D and 2D results are well agreed with each other and give a clear physical insight into this ABI electronic dynamics.

itΨ(r,t)=(p22+pxA(t)+V(r))Ψ(r,t)
Here, V(r) is the soft-Coulomb potential of atom. We employ argon (Ar) atom in computation. The wave function at a given time ti is split as [3537]
Ψ(ti)=Ψ(ti)[1Fs(Rc)]+Ψ(ti)Fs(Rc)=ΨI(ti)+ΨII(ti)
where Fs(Rc)=1/(1+e(rRc)/Δ) is a split function that separates the whole space wave function Ψ(ti) into the inner (0Rc) wave function ΨI(ti) and outer (RcRmax) wave function ΨII(ti). Here represents the width of crossover region. The exact time evolution of Ψ(ti) is evaluated using the Crank-Nicolson method [37]. We calculate
C(p,ti)=ΨII(ti)ei[pA(ti)]r2πd2r,
then ΨII is propagated to the final time as
ΨII(,ti)=C¯(p,ti)eipr2πd2p,
with C¯(p,ti)=exp(iti12[pA(t')]2dt')C(p,ti). The outer region wave function is propagated by the above Eq. (4) so that there is no boundary problem anymore. The final momentum distribution is obtained as
dP(p)dE=2E|iC¯(p,ti)|2.
Here, E is the electron energy associated with p.

The few-cycle laser pulse has a sine squared envelope with a laser frequency ωl = 0.042 a.u. In the following results, it can be seen that ionization rate is very small and electron wave packet is still in its ground state in the ATI scheme if only the few-cycle pulse with this intensity interacted with the atom. The total pulse duration Tp is four optical cycles. The electric field of the laser is

E(t,ϕ)=E0sin2(ωlt/8)cos[ωl(tTp/2)+ϕ],
where ϕ is the CEP. A pump pulse is used to prepare the system in the first excited state. According to the famous area theorem [38, 39], if a resonant pulse has an envelope area A=π, the system can be excited fully from ground state to excited state. The envelope area is determined by A=(μ10/)E˜(t')dt' with μ10=Ψ0(r)|r|Ψ1(r), where Ψ0(r) and Ψ1(r) are the field-free ground state and first excited state wave functions, respectively. In our work, we choose the pulse area equals to π, and the frequency is 0.42 a.u.. Such pulse can be obtained by filtering the desired frequency from the high-harmonic generation [31,4042], and then focused into the atom we considered to achieve the population inversion. We choose Rmax=400a.u., Rc=100a.u., and Δ=20a.u..

In simulation, Ar atom is adopted and the calculated ground state energy is −0.5794 a.u. which is very close to the first ionization potential of Ar atom [43]. The ABI spectra of the ionized electrons in the left and right sides are calculated as

dPL(p)dE=2E|iC¯(p,ti)|2
and
dPR(p)dE=2E|iC¯+(p,ti)|2.
Here, C¯ and C¯+ are wave functions corresponding to the electron moving in the negative and positive direction along the axis, respectively.

3. Results and discussions

The scheme in our work can be shown from time-dependent populations of bound states (see Fig. 1 ). The intensity of the xuv pulse (see Fig. 1(b), denoted by the arrow) is much weaker than that of the following few-cycle pulse. From Fig. 1(a), we see that after the resonant pump pulse, almost all the population of the Ar atom is pumped to the first excited state. When the following few-cycle pulse interacts with the prepared system, the first peak of the few-cycle pulse can also excite the first excited state to higher excited states, so the system is in a coherent superposition state of several excited states. At the same time, the population in the first excited state (C1, red line, Cn (n = 0,1,2…) is bound state n) drops rapidly.

 

Fig. 1 (a) The time-dependent population of different bound states. (b) Electric field E(t) as a function of time in optical cycles for the CEP (ϕ=0) of the few-cycle pulse.

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To uncover the detailed dynamics on sub-cycle timescale, we further show the enlarged time-dependent populations of different bound states within the duration of few-cycle probe pulse with different CEPs (see Figs. 2(a) for ϕ=0 and (b) for ϕ=0.5π). The arrow indicates the population when the first peak of laser electric field comes. It can be seen that the first peak of few-cycle pulse is slightly delayed for ϕ=0.5πthan that for ϕ=0. The time difference between two peaks of ϕ=0 and ϕ=0.5π (see the two arrows in Figs. 2(a) and 2(b)) is about 0.15 cycles corresponding to a few hundred attoseconds. The first peak of laser electric field is slightly more intense for ϕ=0.5πthan that for ϕ=0, as a result, the population densities of higher excited states are much larger for ϕ=0.5π. Only the first three excited states (C1, C2, and C3) have population forϕ=0, and the population in C1 is much larger than that in C2 and C3. On the contrary, forϕ=0.5π, more higher excited states, from C1 to C5, have population.

 

Fig. 2 The time-dependent population of different bound states for CEPs (a) ϕ=0and (b) ϕ=0.5π.

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We further calculated the energy of time-dependent potential barrier when the first peak of laser electric field comes, and found that for ϕ=0, the time-dependent potential barrier is lower than the second excited state C2, but higher than the first excited state C1. This means that ABI can occur only for the second and the third excited. Since most of population is on the first excited, ATI still plays a predominant role. With increasing the CEP the first peak gradually increased and the ration of the ABI increased accordingly. Forϕ=0.5π, even the eigen energy of the first excited state C1 is higher than that of potential barrier due to higher laser intensity of the first peak, which means ABI is the only ionization channel. The changes of these different ionization processes can be directly reflected in the corresponding photoelectron spectra which are shown in Fig. 3 . It can be seen that for ϕ=0, in the low-energy part, the photoelectron spectra from right and left sides are nearly the same order, while the asymmetry of the ionization yields between left and right sides occurs only for high-energy part. This situation is quite similar to that ATI spectrum in the previous 3D simulations [30] and the experimental results [19] in which the initial population is in the ground state. With increasing the CEP, the asymmetry moves to low energy part. Whenϕ=0.5π, the ionization yield asymmetry between left and right sides occurs for the entire spectrum range, which means ABI plays a central role. These phenomena are consistent with the previous analysis based on Fig. 2. One thing we should point out that the reason we use such laser intensity to set the above-barrier ionization at the head of the laser is to eliminate the influence of the adjacent half-cycles of few-cycle and show a clear physical picture. To implement this scheme in experiment, one can use the subcycle field transients synthesized recently [18]. The central field crest of the generated transients can be about 1.7 times more intense than the adjacent half cycles. By adjusting the pulse intensity so that the effect of the adjacent half cycles is weak, the influence of different ionization process can be performed.

 

Fig. 3 Ionization yields to the left and right sides as a function of the CEP of few-cycle pulse. Plots (a)-(d) are for CEPs ϕ=0,0.3π,0.5πand0.8π, respectively. The peak intensity of the few-cycle pulse is I=2.0×1014W/cm2.

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Next, we intend to explore imaging and controlling the bound-state electron wave packet. For such a purpose, we carry out the 2D TDSE calculation in our simulation. We calculate the real part of electron wave functions (Figs. 4(a) and 4(c)) and momentum distribution (Figs. 4(b) and 4(d)) when the system is initially prepared in the first excited state for different CEPs: Figs. 4(a) and 4(b) for ϕ=0, and Figs. 4(c) and 4(d) for ϕ=0.5π, respectively. It can be seen that, after the interaction, the electron wave packet is populated in a coherent superposition state of several bound states. The most interesting thing is the momentum distribution along y direction in which there is an obvious interference structure. Moreover, forϕ=0.5π, the interference structure is more complex than that for ϕ=0. From Fig. 2, we can see that when the few-cycle pulse interacts with the initially prepared atom, the pulse can further excite the first excited state to some other higher excited states. Therefore, interference effect can occur among these wave packets which are set free from different repopulated bound states. This is consistent with those shown in Figs. 4(a) and 4(c), that the repopulation makes the system in a coherent superposition state of several excited states. In x-direction (the direction of laser polarization), once the electrons are set free, the laser field dominates the motion of the continuum electron wave packet. As a result, the electron momentum distribution in this direction carries the information of the CEP of the corresponding few-cycle pulse. In y direction, since the electron wave packet is not affected by electromagnetic forces of laser electric field (no laser field polarized alone this direction), the free expansion of the wave function reflects directly the information of the bound states they set free from. Hence, we infer that this interference structure in y direction is originated from coherent superposition states, i.e., the interference among different bound states. Moreover, forϕ=0.5π, more bound states wave functions are included than that forϕ=0. Both 2D and 1D results support the above physical picture of bound state electron dynamics. From the analysis of population dynamics (see Fig. 2), we know that forϕ=0, only electrons on C2 and C3 are ionized by ABI when the first peak of laser electric field comes, that means only two states are involved in the interference in y direction, hence the interference finger is quite clear. However, forϕ=0.5π, the electrons on all the excited states C1-Cn are ionized by ABI. Since the interference structure involves many bound states which results in the complicated in the case ofϕ=0.5π. This is consistent with our previous analysis. Moreover, our further calculation shows that the interference structure in y direction can occur even if the system is initially partially populated in the excited state.

 

Fig. 4 The real part of electron wave function (a) and (c), and momentum distribution of ABI electrons ((b) and (d), as a function of the CEP. For CEPs ϕ=0 ((a) and (b)), ϕ=0.5π ((c) and (d)). The laser intensity is I=9.5×1013W/cm2.

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For comparison, in Fig. 5 , we further show the wave function after the interaction and the momentum distribution when the initial wave function is in the field-free ground state. The laser intensity is increased to achieve about the same ionization rate with that in Fig. 4. It can be seen that, in this case, though there is some distribution of the wave function in other states, which is quite weak compared with that of ground state. As a result, the electron wave packet is still mainly populated in ground state after the interaction. ATI dominates the whole dynamical process and no ABI occurs. Electron populated in ground state is bound by the binding potential and tunnelling is the only channel for electron to escape. Therefore, in the electron momentum distribution, there is only the asymmetry along x direction, but without the interference phenomenon along y direction (see Fig. 5(b)). This further confirms our previous analysis that the interference structure in y direction is indeed originated from the interference among different repopulated bound states. It has been known that the interference of transitions from the repopulated Rydberg levels to the continuum can induce a novel multipeak structure of the photoelectron spectra and the interference stabilization, which has been demonstrated both in theoretical and experimental works [4447]. In our work, it is found that the interference of repopulated low excited states can induce a spatial interference structure in the momentum distribution. These interference phenomena offer new possibilities for getting insight into the electron bound states wave packet dynamical process in atoms and molecules.

 

Fig. 5 The real part of wave function after the interaction and electron momentum distribution in ATI scheme. The laser intensity is I=4.7×1014W/cm2.

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4. Conclusions

In summary, few-cycle probe pulse combining with resonant xuv pump pulse has been introduced to study bound-state electron dynamics. The pump-probe scheme populates electron on the excited states which has eigen energy higher than the energy of potential barrier of atom. The ABI electron escapes from atom directly and carries the information of the excited states, which results in a new interference effect in the direction perpendicular to the laser polarization in electron momentum map. The dependence of interference structure on the CEP of few-cycle pulse implies that steering initially population distribution of bound states can be achieved by controlling the CEP. Moreover, the information of coherent states and bound states in atom can be extracted from the electron momentum distribution and the photoelectron spectra. Therefore, the ABI spectrum provides a new way to imaging and controlling the electron bound states wave packet in atoms and molecules.

Acknowledgments

We would like to thank Prof. Z. Zeng, Prof. J. Zhang, Prof. R. Li, and Prof. Z. Xu for their valuable discussion of the physics. The work was supported by the National Basic Research Program of China (Grant Nos. 2006CB806000 and 2010CB923200), the National Natural Science Foundation of China (Grant No. 61008061), and the Open Fund of the State Key Laboratory of High Field Laser Physics (Shanghai Institute of Optics and Fine Mechanics). W. Yang, X. Song, and Z. Chen were also supported by STU Scientific Research Foundation for Talents, respectively.

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References

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  1. T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
    [CrossRef]
  2. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
    [CrossRef]
  3. P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
    [CrossRef]
  4. P. H. Bucksbaum, “The future of attosecond spectroscopy,” Science 317(5839), 766–769 (2007).
    [CrossRef] [PubMed]
  5. E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317(5839), 769–775 (2007).
    [CrossRef] [PubMed]
  6. H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent x-rays,” Science 317(5839), 775–778 (2007).
    [CrossRef] [PubMed]
  7. M. Lein, “Molecular imaging using recolliding electrons,” J. Phys. At. Mol. Opt. Phys. 40(16), R135–R173 (2007).
    [CrossRef]
  8. W. Yang, X. Song, Z. Zeng, R. Li, and Z. Xu, “Quantum path interferences of electron trajectories in two-center molecules,” Opt. Express 18(3), 2558–2565 (2010).
    [CrossRef] [PubMed]
  9. A. Palacios, T. N. Rescigno, and C. W. McCurdy, “Two-electron time-delay interference in atomic double ionization by attosecond pulses,” Phys. Rev. Lett. 103(25), 253001 (2009).
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  10. M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
    [CrossRef] [PubMed]
  11. M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419(6909), 803–807 (2002).
    [CrossRef] [PubMed]
  12. H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
    [CrossRef] [PubMed]
  13. E. Gagnon, P. Ranitovic, X. M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317(5843), 1374–1378 (2007).
    [CrossRef] [PubMed]
  14. O. Smirnova, “Spectroscopy: Attosecond prints of electrons,” Nature 466(7307), 700–702 (2010).
    [CrossRef] [PubMed]
  15. 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(5883), 1614–1617 (2008).
    [CrossRef] [PubMed]
  16. E. Goulielmakis, Z. H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466(7307), 739–743 (2010).
    [CrossRef] [PubMed]
  17. X. Song, W. Yang, Z. Zeng, R. Li, and Z. Xu, “Unipolar half-cycle pulse generation in asymmetrical media with a periodic subwavelength structure,” Phys. Rev. A 82(5), 053821 (2010).
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  18. A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334(6053), 195–200 (2011).
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  19. G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett. 91(25), 253004 (2003).
    [CrossRef] [PubMed]
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  21. W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express 14(16), 7216–7223 (2006).
    [CrossRef] [PubMed]
  22. W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007).
    [CrossRef] [PubMed]
  23. S. Zherebtsov, T. Fennel, J. Plenge, E. Antonsson, I. Znakovskaya, A. Wirth, O. Herrwerth, F. Süßmann, C. Peltz, I. Ahmad, S. A. Trushin, V. Pervak, S. Karsch, M. J. J. Vrakking, B. Langer, C. Graf, M. I. Stockman, F. Krausz, E. Rühl, and M. F. Kling, “Controlled near-field enhanced electron acceleration from dielectric nanospheres with intense few-cycle laser fields,” Nat. Phys. 7(8), 656–662 (2011).
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  24. W. Yang, X. Song, R. Li, and Z. Xu, “Generation of intense extreme supercontinuum radiation via resonant propagation effects,” Phys. Rev. A 78(2), 023836 (2008).
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  25. W. Yang, X. Song, C. Zhang, and Z. Xu, “Carrier-envelope phase dependent transmitted spectra in inversion-asymmetric media with permanent dipole moments,” J. Phys. At. Mol. Opt. Phys. 42(17), 175601 (2009).
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    [CrossRef] [PubMed]
  28. J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
    [CrossRef] [PubMed]
  29. Y. Zheng, Z. Zeng, P. Zou, L. Zhang, X. Li, P. Liu, R. Li, and Z. Xu, “Dynamic chirp control and pulse compression for attosecond high-order harmonic emission,” Phys. Rev. Lett. 103(4), 043904 (2009).
    [CrossRef] [PubMed]
  30. X. M. Tong, K. Hino, and N. Toshima, “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74(3), 031405 (2006).
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  31. D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. At. Mol. Opt. Phys. 39(14), R203–R262 (2006).
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  32. W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103(9), 093001 (2009).
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  33. H. Mashiko, A. Suda, and K. Midorikawa, “Focusing coherent soft-x-ray radiation to a micrometer spot size with an intensity of 1014 W/cm2.,” Opt. Lett. 29(16), 1927–1929 (2004).
    [CrossRef] [PubMed]
  34. O. Smirnova, S. Patchkovskii, and M. Spanner, “Direct XUV probing of attosecond electron recollision,” Phys. Rev. Lett. 98(12), 123001 (2007).
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  35. Q. Liao, P. Lu, P. Lan, W. Cao, and Y. Li, “Phase dependence of high-order above-threshold ionization in asymmetric molecules,” Phys. Rev. A 77(1), 013408 (2008).
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  36. S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H2+ dissociative ionization in intense laser fields,” Phys. Rev. A 57(2), 1176–1185 (1998).
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  37. M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60(4), 389–486 (1997).
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  38. S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18(21), 908–911 (1967).
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  39. S. L. McCall and E. L. Hahn, “Self-induced transparency,” Phys. Rev. 183(2), 457–485 (1969).
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  40. D. Yoshitomi, T. Shimizu, T. Sekikawa, and S. Watanabe, “Generation and focusing of submilliwatt-average-power 50-nm pulses by the fifth harmonic of a KrF laser,” Opt. Lett. 27(24), 2170–2172 (2002).
    [CrossRef] [PubMed]
  41. C. Valentin, D. Douillet, S. Kazamias, Th. Lefrou, G. Grillon, F. Augé, G. Mullot, Ph. Balcou, P. Mercère, and Ph. Zeitoun, “Imaging and quality assessment of high-harmonic focal spots,” Opt. Lett. 28(12), 1049–1051 (2003).
    [CrossRef] [PubMed]
  42. M. Swoboda, T. Fordell, K. Klünder, J. M. Dahlström, M. Miranda, C. Buth, K. J. Schafer, J. Mauritsson, A. L’Huillier, and M. Gisselbrecht, “Phase measurement of resonant two-photon ionization in Helium,” Phys. Rev. Lett. 104(10), 103003 (2010).
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  44. M. V. Fedorov, N. P. Poluektov, A. M. Popov, O. V. Tikhonova, V. Yu. Kharin, and E. A. Volkova, “Interference stabilization revisited,” IEEE J. Sel. Top. Quantum Electron. 18(1), 42–53 (2012).
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  45. M. V. Fedorov and A. M. Movsesian, “Field-induced effects of narrowing of photoelectron spectra and stabilization of Rydberg atom,” J. Phys. At. Mol. Opt. Phys. 21(7), L155–L158 (1988).
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  46. M. V. Fedorov, M. M. Tehranchi, and S. M. Fedorov, “Interference stabilization of Rydberg atom: numerical calculations and physical models,” J. Phys. At. Mol. Opt. Phys. 29(13), 2907–2924 (1996).
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2012 (1)

M. V. Fedorov, N. P. Poluektov, A. M. Popov, O. V. Tikhonova, V. Yu. Kharin, and E. A. Volkova, “Interference stabilization revisited,” IEEE J. Sel. Top. Quantum Electron. 18(1), 42–53 (2012).
[CrossRef]

2011 (2)

A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334(6053), 195–200 (2011).
[CrossRef] [PubMed]

S. Zherebtsov, T. Fennel, J. Plenge, E. Antonsson, I. Znakovskaya, A. Wirth, O. Herrwerth, F. Süßmann, C. Peltz, I. Ahmad, S. A. Trushin, V. Pervak, S. Karsch, M. J. J. Vrakking, B. Langer, C. Graf, M. I. Stockman, F. Krausz, E. Rühl, and M. F. Kling, “Controlled near-field enhanced electron acceleration from dielectric nanospheres with intense few-cycle laser fields,” Nat. Phys. 7(8), 656–662 (2011).
[CrossRef]

2010 (5)

E. Goulielmakis, Z. H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466(7307), 739–743 (2010).
[CrossRef] [PubMed]

X. Song, W. Yang, Z. Zeng, R. Li, and Z. Xu, “Unipolar half-cycle pulse generation in asymmetrical media with a periodic subwavelength structure,” Phys. Rev. A 82(5), 053821 (2010).
[CrossRef]

O. Smirnova, “Spectroscopy: Attosecond prints of electrons,” Nature 466(7307), 700–702 (2010).
[CrossRef] [PubMed]

M. Swoboda, T. Fordell, K. Klünder, J. M. Dahlström, M. Miranda, C. Buth, K. J. Schafer, J. Mauritsson, A. L’Huillier, and M. Gisselbrecht, “Phase measurement of resonant two-photon ionization in Helium,” Phys. Rev. Lett. 104(10), 103003 (2010).
[CrossRef] [PubMed]

W. Yang, X. Song, Z. Zeng, R. Li, and Z. Xu, “Quantum path interferences of electron trajectories in two-center molecules,” Opt. Express 18(3), 2558–2565 (2010).
[CrossRef] [PubMed]

2009 (5)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[CrossRef]

A. Palacios, T. N. Rescigno, and C. W. McCurdy, “Two-electron time-delay interference in atomic double ionization by attosecond pulses,” Phys. Rev. Lett. 103(25), 253001 (2009).
[CrossRef] [PubMed]

W. Yang, X. Song, C. Zhang, and Z. Xu, “Carrier-envelope phase dependent transmitted spectra in inversion-asymmetric media with permanent dipole moments,” J. Phys. At. Mol. Opt. Phys. 42(17), 175601 (2009).
[CrossRef]

Y. Zheng, Z. Zeng, P. Zou, L. Zhang, X. Li, P. Liu, R. Li, and Z. Xu, “Dynamic chirp control and pulse compression for attosecond high-order harmonic emission,” Phys. Rev. Lett. 103(4), 043904 (2009).
[CrossRef] [PubMed]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103(9), 093001 (2009).
[CrossRef] [PubMed]

2008 (3)

Q. Liao, P. Lu, P. Lan, W. Cao, and Y. Li, “Phase dependence of high-order above-threshold ionization in asymmetric molecules,” Phys. Rev. A 77(1), 013408 (2008).
[CrossRef]

W. Yang, X. Song, R. Li, and Z. Xu, “Generation of intense extreme supercontinuum radiation via resonant propagation effects,” Phys. Rev. A 78(2), 023836 (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(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

2007 (9)

E. Gagnon, P. Ranitovic, X. M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317(5843), 1374–1378 (2007).
[CrossRef] [PubMed]

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[CrossRef]

P. H. Bucksbaum, “The future of attosecond spectroscopy,” Science 317(5839), 766–769 (2007).
[CrossRef] [PubMed]

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317(5839), 769–775 (2007).
[CrossRef] [PubMed]

H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent x-rays,” Science 317(5839), 775–778 (2007).
[CrossRef] [PubMed]

M. Lein, “Molecular imaging using recolliding electrons,” J. Phys. At. Mol. Opt. Phys. 40(16), R135–R173 (2007).
[CrossRef]

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007).
[CrossRef] [PubMed]

O. Smirnova, S. Patchkovskii, and M. Spanner, “Direct XUV probing of attosecond electron recollision,” Phys. Rev. Lett. 98(12), 123001 (2007).
[CrossRef] [PubMed]

2006 (3)

X. M. Tong, K. Hino, and N. Toshima, “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74(3), 031405 (2006).
[CrossRef]

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. At. Mol. Opt. Phys. 39(14), R203–R262 (2006).
[CrossRef]

W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express 14(16), 7216–7223 (2006).
[CrossRef] [PubMed]

2005 (1)

G. L. Kamta and A. D. Bandrauk, “Phase dependence of enhanced ionization in asymmetric molecules,” Phys. Rev. Lett. 94(20), 203003 (2005).
[CrossRef] [PubMed]

2004 (2)

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

H. Mashiko, A. Suda, and K. Midorikawa, “Focusing coherent soft-x-ray radiation to a micrometer spot size with an intensity of 1014 W/cm2.,” Opt. Lett. 29(16), 1927–1929 (2004).
[CrossRef] [PubMed]

2003 (3)

C. Valentin, D. Douillet, S. Kazamias, Th. Lefrou, G. Grillon, F. Augé, G. Mullot, Ph. Balcou, P. Mercère, and Ph. Zeitoun, “Imaging and quality assessment of high-harmonic focal spots,” Opt. Lett. 28(12), 1049–1051 (2003).
[CrossRef] [PubMed]

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett. 91(25), 253004 (2003).
[CrossRef] [PubMed]

2002 (3)

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419(6909), 803–807 (2002).
[CrossRef] [PubMed]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[CrossRef] [PubMed]

D. Yoshitomi, T. Shimizu, T. Sekikawa, and S. Watanabe, “Generation and focusing of submilliwatt-average-power 50-nm pulses by the fifth harmonic of a KrF laser,” Opt. Lett. 27(24), 2170–2172 (2002).
[CrossRef] [PubMed]

2000 (1)

T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[CrossRef]

1998 (1)

S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H2+ dissociative ionization in intense laser fields,” Phys. Rev. A 57(2), 1176–1185 (1998).
[CrossRef]

1997 (1)

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60(4), 389–486 (1997).
[CrossRef]

1996 (1)

M. V. Fedorov, M. M. Tehranchi, and S. M. Fedorov, “Interference stabilization of Rydberg atom: numerical calculations and physical models,” J. Phys. At. Mol. Opt. Phys. 29(13), 2907–2924 (1996).
[CrossRef]

1994 (1)

J. H. Hoogenraad, R. B. Vrijen, and L. D. Noordam, “Ionization suppression of Rydberg atoms by short laser pulses,” Phys. Rev. A 50(5), 4133–4138 (1994).
[CrossRef] [PubMed]

1993 (1)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[CrossRef] [PubMed]

1988 (1)

M. V. Fedorov and A. M. Movsesian, “Field-induced effects of narrowing of photoelectron spectra and stabilization of Rydberg atom,” J. Phys. At. Mol. Opt. Phys. 21(7), L155–L158 (1988).
[CrossRef]

1969 (1)

S. L. McCall and E. L. Hahn, “Self-induced transparency,” Phys. Rev. 183(2), 457–485 (1969).
[CrossRef]

1967 (1)

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18(21), 908–911 (1967).
[CrossRef]

Ahmad, I.

S. Zherebtsov, T. Fennel, J. Plenge, E. Antonsson, I. Znakovskaya, A. Wirth, O. Herrwerth, F. Süßmann, C. Peltz, I. Ahmad, S. A. Trushin, V. Pervak, S. Karsch, M. J. J. Vrakking, B. Langer, C. Graf, M. I. Stockman, F. Krausz, E. Rühl, and M. F. Kling, “Controlled near-field enhanced electron acceleration from dielectric nanospheres with intense few-cycle laser fields,” Nat. Phys. 7(8), 656–662 (2011).
[CrossRef]

Alahmed, Z. A.

A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334(6053), 195–200 (2011).
[CrossRef] [PubMed]

Antonsson, E.

S. Zherebtsov, T. Fennel, J. Plenge, E. Antonsson, I. Znakovskaya, A. Wirth, O. Herrwerth, F. Süßmann, C. Peltz, I. Ahmad, S. A. Trushin, V. Pervak, S. Karsch, M. J. J. Vrakking, B. Langer, C. Graf, M. I. Stockman, F. Krausz, E. Rühl, and M. F. Kling, “Controlled near-field enhanced electron acceleration from dielectric nanospheres with intense few-cycle laser fields,” Nat. Phys. 7(8), 656–662 (2011).
[CrossRef]

Apolonski, A.

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317(5839), 769–775 (2007).
[CrossRef] [PubMed]

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(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

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(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Augé, F.

Azzeer, A. M.

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S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H2+ dissociative ionization in intense laser fields,” Phys. Rev. A 57(2), 1176–1185 (1998).
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W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103(9), 093001 (2009).
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A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334(6053), 195–200 (2011).
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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(5883), 1614–1617 (2008).
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Gisselbrecht, M.

M. Swoboda, T. Fordell, K. Klünder, J. M. Dahlström, M. Miranda, C. Buth, K. J. Schafer, J. Mauritsson, A. L’Huillier, and M. Gisselbrecht, “Phase measurement of resonant two-photon ionization in Helium,” Phys. Rev. Lett. 104(10), 103003 (2010).
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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
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Gong, S.

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007).
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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(5883), 1614–1617 (2008).
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E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317(5839), 769–775 (2007).
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G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett. 91(25), 253004 (2003).
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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
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S. Zherebtsov, T. Fennel, J. Plenge, E. Antonsson, I. Znakovskaya, A. Wirth, O. Herrwerth, F. Süßmann, C. Peltz, I. Ahmad, S. A. Trushin, V. Pervak, S. Karsch, M. J. J. Vrakking, B. Langer, C. Graf, M. I. Stockman, F. Krausz, E. Rühl, and M. F. Kling, “Controlled near-field enhanced electron acceleration from dielectric nanospheres with intense few-cycle laser fields,” Nat. Phys. 7(8), 656–662 (2011).
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A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334(6053), 195–200 (2011).
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Gullikson, E. 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(5883), 1614–1617 (2008).
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Hasbani, R.

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
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A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334(6053), 195–200 (2011).
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W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103(9), 093001 (2009).
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M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
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M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419(6909), 803–807 (2002).
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M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
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M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419(6909), 803–807 (2002).
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Herrwerth, O.

S. Zherebtsov, T. Fennel, J. Plenge, E. Antonsson, I. Znakovskaya, A. Wirth, O. Herrwerth, F. Süßmann, C. Peltz, I. Ahmad, S. A. Trushin, V. Pervak, S. Karsch, M. J. J. Vrakking, B. Langer, C. Graf, M. I. Stockman, F. Krausz, E. Rühl, and M. F. Kling, “Controlled near-field enhanced electron acceleration from dielectric nanospheres with intense few-cycle laser fields,” Nat. Phys. 7(8), 656–662 (2011).
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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
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H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
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M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
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G. L. Kamta and A. D. Bandrauk, “Phase dependence of enhanced ionization in asymmetric molecules,” Phys. Rev. Lett. 94(20), 203003 (2005).
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W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103(9), 093001 (2009).
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H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent x-rays,” Science 317(5839), 775–778 (2007).
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Kapteyn, H. C.

E. Gagnon, P. Ranitovic, X. M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317(5843), 1374–1378 (2007).
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http://physics.nist.gov/PhysRefData/handbook/element_name.htm .

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Figures (5)

Fig. 1
Fig. 1

(a) The time-dependent population of different bound states. (b) Electric field E(t) as a function of time in optical cycles for the CEP ( ϕ=0 ) of the few-cycle pulse.

Fig. 2
Fig. 2

The time-dependent population of different bound states for CEPs (a) ϕ=0 and (b) ϕ=0.5π .

Fig. 3
Fig. 3

Ionization yields to the left and right sides as a function of the CEP of few-cycle pulse. Plots (a)-(d) are for CEPs ϕ=0,0.3π,0.5πand0.8π , respectively. The peak intensity of the few-cycle pulse is I=2.0× 10 14 W/cm2.

Fig. 4
Fig. 4

The real part of electron wave function (a) and (c), and momentum distribution of ABI electrons ((b) and (d), as a function of the CEP. For CEPs ϕ=0 ((a) and (b)), ϕ=0.5π ((c) and (d)). The laser intensity is I=9.5× 10 13 W/cm2.

Fig. 5
Fig. 5

The real part of wave function after the interaction and electron momentum distribution in ATI scheme. The laser intensity is I=4.7× 10 14 W/cm2.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

i t Ψ(r,t)=( p 2 2 + p x A(t)+V(r) )Ψ(r,t)
Ψ( t i )=Ψ( t i )[ 1 F s ( R c ) ]+Ψ( t i ) F s ( R c )= Ψ I ( t i )+ Ψ II ( t i )
C(p, t i )= Ψ II ( t i ) e i[pA( t i )]r 2π d 2 r,
Ψ II (, t i )= C ¯ (p, t i ) e ipr 2π d 2 p,
dP(p) dE = 2E | i C ¯ (p, t i ) | 2 .
E(t,ϕ)= E 0 sin 2 ( ω l t/8)cos[ ω l (t T p /2)+ϕ],
d P L (p) dE = 2E | i C ¯ (p, t i ) | 2
d P R (p) dE = 2E | i C ¯ + (p, t i ) | 2 .

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