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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 11 — May. 21, 2012
  • pp: 12067–12075
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Phase-dependent above-barrier ionization of excited-state electrons

Weifeng Yang, Xiaohong Song, and Zhangjin Chen  »View Author Affiliations


Optics Express, Vol. 20, Issue 11, pp. 12067-12075 (2012)
http://dx.doi.org/10.1364/OE.20.012067


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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 [1

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

9

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). [CrossRef] [PubMed]

]. The ultrafast pump-probe technology allows tracking of microscopic electronic dynamic process, such as real-time observation of electron tunnelling in atoms [10

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]

], retrieval of atomic inner-shell electron motion [11

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]

], probing sub-cycle molecular dynamics [12

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]

], ultrafast molecular nuclear dynamics [13

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]

], 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

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

]. 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 [15

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]

18

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). [CrossRef] [PubMed]

]. 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 [19

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]

25

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). [CrossRef]

]. 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.

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)
(1)
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 [35

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). [CrossRef]

37

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). [CrossRef]

]
Ψ(ti)=Ψ(ti)[1Fs(Rc)]+Ψ(ti)Fs(Rc)=ΨI(ti)+ΨII(ti)
(2)
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

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). [CrossRef]

]. We calculate
C(p,ti)=ΨII(ti)ei[pA(ti)]r2πd2r,
(3)
then ΨII is propagated to the final time as
ΨII(,ti)=C¯(p,ti)eipr2πd2p,
(4)
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.
(5)
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],
(6)
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

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

, 39

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

], 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

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). [CrossRef]

,40

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]

42

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). [CrossRef] [PubMed]

], 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
(7)
and
dPR(p)dE=2E|iC¯+(p,ti)|2.
(8)
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
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.
). 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.

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

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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OCIS Codes
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.7150) Ultrafast optics : Ultrafast spectroscopy

ToC Category:
Ultrafast Optics

History
Original Manuscript: March 26, 2012
Revised Manuscript: April 27, 2012
Manuscript Accepted: April 28, 2012
Published: May 11, 2012

Citation
Weifeng Yang, Xiaohong Song, and Zhangjin Chen, "Phase-dependent above-barrier ionization of excited-state electrons," Opt. Express 20, 12067-12075 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-12067


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References

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