Abstract

Quantitative identification of tunneling ionization (TI) and multiphoton ionization (MPI) with Keldysh parameter γ in intermediate regime is of great importance to better understand various ionization-triggered strong-field phenomena. We theoretically demonstrate that the numerical observable ionization delay time is a more reliable indicator for characterizing the transition from TI to MPI under different laser parameters. Using non-linear iterative curve fitting algorithm (NICFA), the detected time-dependent probability current of ionized electrons can be decoupled into weighted TI and MPI portions. This enables us to confirm that the observed plateau-like structure in ionization delay time picture at the intermediate γ originates from the competition between TI and MPI processes. A hybrid quantum and classical approach (HQCA) is developed to evaluate the weights of TI and MPI electrons in good agreement with NICFA result. Moreover, the well separated TI and MPI electrons using HQCA are further propagated classically for mapping their final momentum, which well reproduces the experimental or ab-initio numerical calculated signatures of ionized electron momentum distribution in a rather broad γ regime.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  4. M. Wickenhauser, X. M. Tong, D. G. Arbó, J. Burgdörfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  28. E. E. Serebryannikov and A. M. Zheltikov, “Strong-Field Photoionization as Excited-State Tunneling,” Phys. Rev. Lett. 116, 123901 (2016).
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    [Crossref] [PubMed]
  30. M. Klaiber, E. Yakaboylu, H. Bauke, K. Z. Hatsagortsyan, and C. H. Keitel, “Under-the-barrier dynamics in laser-induced relativistic tunneling,” Phys. Rev. Lett. 110, 153004 (2013).
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  31. M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Tunneling dynamics in multiphoton ionization and attoclock calibration,” Phys. Rev. Lett. 114, 083001 (2015).
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    [Crossref]
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    [Crossref]
  37. C. W. Clark, “Closed-form solutions of the Schrödinger equation for a class of smoothed Coulomb potentials,” J. Phys. B: At. Mol. Opt. Phys. 30, 2517–2527 (1997).
    [Crossref]
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    [Crossref]
  41. X. Wang, J. Tian, and J. H. Eberly, “Extended Virtual Detector Theory for Strong-Field Atomic Ionization,” Phys. Rev. Lett. 110, 243001 (2013).
    [Crossref] [PubMed]
  42. B. Feuerstein and U. Thumm, “On the computation of momentum distributions within wavepacket propagation calculations,” J. Phys. B 36, 707–716 (2003).
    [Crossref]
  43. S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H2+ dissociative ionization in intense laser fields,” Phys. Rev. A 57, 1176–1185 (1998).
    [Crossref]
  44. M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel Ionization Of Complex Atoms And Atomic Ions In Electromagnetic Field,” Sov. Phys. JETP 64, 1191–1194 (1986).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  52. B. Hu, J. Liu, and Shi-gang Chen, “Plateau in above-threshold-ionization spectra and chaotic behavior in rescattering processes,” Phys. Lett. A 236, 533–542 (1997).
    [Crossref]
  53. J. S. Cohen, “Reexamination of over-the-barrier and tunneling ionization of the hydrogen atom in an intense field,” Phys. Rev. A 64, 043412 (2001).
    [Crossref]
  54. V. Mur, S. Popruzhenko, and V. Popov, “Energy and momentum spectra of photoelectrons under conditions of ionization by strong laser radiation (the case of elliptic polarization),” J. Exp. Theor. Phys. 92, 777–788 (2001).
    [Crossref]
  55. A. Perelomov, V. Popov, and M. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).
  56. D. I. Bondar, “Instantaneous multiphoton ionization rate and initial distribution of electron momentum,” Phys. Rev. A 78, 015405 (2008).
    [Crossref]

2019 (1)

X. Zhang, X. Zhu, D. Wang, L. Li, X. Liu, Q. Liao, P. Lan, and P. Lu, “Ultrafast oscillating-magnetic-field generation based on electronic-current dynamics,” Phys. Rev. A 99, 013414 (2019).
[Crossref]

2018 (5)

C. Qin, L. Yuan, B. Wang, S. Fan, and P. Lu, “Effective electric-field force for a photon in a synthetic frequency lattice created in a waveguide modulator,” Phys. Rev. A 97, 063838 (2018).
[Crossref]

L. He, P. Lan, A. T. Le, B. Wang, B. Wang, X. Zhu, P. Lu, and C. D. Lin, “Real-Time Observation of Molecular Spinning with Angular High-Harmonic Spectroscopy,” Phys. Rev. Lett. 121, 163201 (2018).
[Crossref] [PubMed]

L. Li, P. Lan, X. Liu, L. He, X. Zhu, O. D. Mücke, and P. Lu, “Method for direct observation of Bloch oscillations in semiconductors,” Opt. Express 26, 23844–23853 (2018).
[Crossref] [PubMed]

J. Tan, Y. Zhou, M. He, Y. Chen, Q. Ke, J. Liang, X. Zhu, M. Li, and P. Lu, “Determination of the Ionization Time Using Attosecond Photoelectron Interferometry,” Phys. Rev. Lett. 121, 253203 (2018).
[Crossref]

K. Liu, H. Ni, K. Renziehausen, J. M. Rost, and I. Barth, “Deformation of Atomic p± Orbitals in Strong Elliptically Polarized Laser Fields: Ionization Time Drifts and Spatial Photoelectron Separation,” Phys. Rev. Lett. 121, 203201 (2018).
[Crossref]

2017 (1)

Q. Zhang, G. Basnayake, A. Winney, Y. Lin, D. Debrah, S. K. Lee, and W. Li, “Orbital-resolved nonadiabatic tunneling ionization,” Phys. Rev. A 96, 023422 (2017).
[Crossref]

2016 (4)

M. Klaiber and J. S. Briggs, “Crossover from tunneling to multiphoton ionization of atoms,” Phys. Rev. A 94, 053405 (2016).
[Crossref]

E. E. Serebryannikov and A. M. Zheltikov, “Strong-Field Photoionization as Excited-State Tunneling,” Phys. Rev. Lett. 116, 123901 (2016).
[Crossref] [PubMed]

N. Teeny, E. Yakaboylu, H. Bauke, and C. H. Keitel, “Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization,” Phys. Rev. Lett. 116, 063003 (2016).
[Crossref] [PubMed]

H. Ni, U. Saalmann, and J. M. Rost, “Tunneling Ionization Time Resolved by Backpropagation,” Phys. Rev. Lett. 117, 023002 (2016).
[Crossref] [PubMed]

2015 (1)

M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Tunneling dynamics in multiphoton ionization and attoclock calibration,” Phys. Rev. Lett. 114, 083001 (2015).
[Crossref] [PubMed]

2014 (4)

N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
[Crossref] [PubMed]

Z. Hong, Q. Zhang, P. Lan, and P. Lu, “Generation of few-cycle infrared pulses from a degenerate dual-pump OPCPA,” Opt. Express 22, 5544–5557 (2014).
[Crossref] [PubMed]

E. Yakaboylu, M. Klaiber, and K. Z. Hatsagortsyan, “Wigner time delay for tunneling ionization via the electron propagator,” Phys. Rev. A 90, 012116 (2014).
[Crossref]

G. Orlando, C. R. McDonald, N. H. Protik, G. Vampa, and T. Brabec, “Tunnelling time, what does it mean?” J. Phys. B: At. Mol. Opt. Phys. 47, 204002 (2014).
[Crossref]

2013 (4)

X. Wang, J. Tian, and J. H. Eberly, “Extended Virtual Detector Theory for Strong-Field Atomic Ionization,” Phys. Rev. Lett. 110, 243001 (2013).
[Crossref] [PubMed]

R. Boge, C. Cirelli, A. S. Landsman, S. Heuser, A. Ludwig, J. Maurer, M. Weger, L. Gallmann, and U. Keller, “Probing nonadiabatic effects in strong-field tunnel ionization,” Phys. Rev. Lett. 111, 103003 (2013).
[Crossref]

Z. Hong, Q. Zhang, and P. Lu, “Compact dual-crystal optical parametric amplification for broadband IR pulse generation using a collinear geometry,” Opt. Express 21, 9491–9504 (2013).
[Crossref] [PubMed]

M. Klaiber, E. Yakaboylu, H. Bauke, K. Z. Hatsagortsyan, and C. H. Keitel, “Under-the-barrier dynamics in laser-induced relativistic tunneling,” Phys. Rev. Lett. 110, 153004 (2013).
[Crossref] [PubMed]

2012 (1)

T. Topcu and F. Robicheaux, “Dichotomy between tunneling and multiphoton ionization in atomic photoionization: Keldysh parameter γ versus scaled frequency Ω,” Phys. Rev. A 86, 053407 (2012).
[Crossref]

2011 (2)

T. Marchenko, Y. Huismans, K. J. Schafer, and M. J. J. Vrakking, “Criteria for the observation of strong-field photoelectron holography,” Phys. Rev. A 84, 053427 (2011).
[Crossref]

O. I. Tolstikhin, T. Morishita, and L. B. Madsen, “Theory of tunneling ionization of molecules: Weak-field asymptotics including dipole effects,” Phys. Rev. A 84, 053423 (2011).
[Crossref]

2010 (1)

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]

2009 (3)

R. L. Hall, N. Saad, K. D. Sen, and H. Ciftci, “Energies and wave functions for a soft-core Coulomb potential,” Phys. Rev. A 80, 032507 (2009).
[Crossref]

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

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]

2008 (3)

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

P. Eckle, A. N. Pfeiffer, C. Cirelli, A. Staudte, R. Dörner, H. G. Muller, M. Buttiker, and U. Keller, “Attosecond ionization and tunneling delay time measurements in helium,” Science 322, 1525–1529 (2008).
[Crossref] [PubMed]

D. I. Bondar, “Instantaneous multiphoton ionization rate and initial distribution of electron momentum,” Phys. Rev. A 78, 015405 (2008).
[Crossref]

2007 (1)

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

2006 (1)

M. Wickenhauser, X. M. Tong, D. G. Arbó, J. Burgdörfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
[Crossref]

2005 (1)

F. Lindner, M. G. Schatzel, H. Walther, A. Baltuska, E. Goulielmakis, F. Krausz, D. B. Milosevic, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401 (2005).
[Crossref] [PubMed]

2003 (3)

F. Grasbon, G. G. Paulus, H. Walther, P. Villoresi, G. Sansone, S. Stagira, M. Nisoli, and S. De Silvestri, “Above-threshold ionization at the few-cycle limit,” Phys. Rev. Lett. 91, 173003 (2003).
[Crossref] [PubMed]

K. Ishikawa, “Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003).
[Crossref]

B. Feuerstein and U. Thumm, “On the computation of momentum distributions within wavepacket propagation calculations,” J. Phys. B 36, 707–716 (2003).
[Crossref]

2001 (3)

J. S. Cohen, “Reexamination of over-the-barrier and tunneling ionization of the hydrogen atom in an intense field,” Phys. Rev. A 64, 043412 (2001).
[Crossref]

V. Mur, S. Popruzhenko, and V. Popov, “Energy and momentum spectra of photoelectrons under conditions of ionization by strong laser radiation (the case of elliptic polarization),” J. Exp. Theor. Phys. 92, 777–788 (2001).
[Crossref]

G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
[Crossref]

1998 (2)

N. B. Delone and V. P. Krainov, “Tunneling and barrier-suppression ionization of atoms and ions in a laser radiation field,” Phys. Usp. 41, 469–485 (1998).
[Crossref]

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

1997 (3)

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

B. Hu, J. Liu, and Shi-gang Chen, “Plateau in above-threshold-ionization spectra and chaotic behavior in rescattering processes,” Phys. Lett. A 236, 533–542 (1997).
[Crossref]

C. W. Clark, “Closed-form solutions of the Schrödinger equation for a class of smoothed Coulomb potentials,” J. Phys. B: At. Mol. Opt. Phys. 30, 2517–2527 (1997).
[Crossref]

1993 (1)

D. S. Chemla, “Nonlinear optics in quantum-confined structures,” Phys. Today 46, 46–52 (1993).
[Crossref]

1992 (1)

W.C. Liu and C.W. Clark, “Closed-form solutions of the Schrödinger equation for a model one-dimensional hydrogen atom,” J. Phys. B : At. Mol. Opt. Phys. 25, L517–L524 (1992).
[Crossref]

1991 (1)

Q. Su and J. H. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A 44, 5997–6008 (1991)
[Crossref] [PubMed]

1989 (1)

S. C. Jones, P. Braunlich, R. T. Casper, X. Shen, and P. Kelly, “Recent progress on laser-induced modifications and intrinsic bulk damage of wide-gap optical materials,” Opt. Engineering 28, 281039 (1989).
[Crossref]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel Ionization Of Complex Atoms And Atomic Ions In Electromagnetic Field,” Sov. Phys. JETP 64, 1191–1194 (1986).

1983 (1)

G. Binnig, H. Rohrer, C. Gerber, and E. Weibel, “7 × 7 Reconstruction on Si(111) Resolved in Real Space,” Phys. Rev. Lett. 50, 120–123 (1983).
[Crossref]

1982 (1)

M. D. Feit, J. A. Fleck, and A. Steiger, “Solution of the schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
[Crossref]

1970 (1)

L. Esaki and R. Tsu, “Superlattice and negative differential conductivity in semiconductors,” IBM J. Res. Dev. 14, 61–65 (1970).
[Crossref]

1966 (1)

A. Perelomov, V. Popov, and M. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

1965 (1)

L. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

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]

Ammosov, M. V.

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M. Klaiber and J. S. Briggs, “Crossover from tunneling to multiphoton ionization of atoms,” Phys. Rev. A 94, 053405 (2016).
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N. B. Delone and V. P. Krainov, “Tunneling and barrier-suppression ionization of atoms and ions in a laser radiation field,” Phys. Usp. 41, 469–485 (1998).
[Crossref]

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F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
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Uphues, T.

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

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G. Orlando, C. R. McDonald, N. H. Protik, G. Vampa, and T. Brabec, “Tunnelling time, what does it mean?” J. Phys. B: At. Mol. Opt. Phys. 47, 204002 (2014).
[Crossref]

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

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

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X. Zhang, X. Zhu, D. Wang, L. Li, X. Liu, Q. Liao, P. Lan, and P. Lu, “Ultrafast oscillating-magnetic-field generation based on electronic-current dynamics,” Phys. Rev. A 99, 013414 (2019).
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[Crossref]

M. Wickenhauser, X. M. Tong, D. G. Arbó, J. Burgdörfer, and C. D. Lin, “Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses,” Phys. Rev. A 74, 041402 (2006).
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D. Ye, X. Liu, and J. Liu, “Classical trajectory diagnosis of a fingerlike pattern in the correlated electron momentum distribution in strong field double ionization of helium,” Phys. Rev. Lett. 101, 233003 (2008).
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J. Tan, Y. Zhou, M. He, Y. Chen, Q. Ke, J. Liang, X. Zhu, M. Li, and P. Lu, “Determination of the Ionization Time Using Attosecond Photoelectron Interferometry,” Phys. Rev. Lett. 121, 253203 (2018).
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Figures (6)

Fig. 1
Fig. 1 The probability current j(rd, t) as a function of time at the detector rd, at Keldysh parameters of 0.6, 1.2, 1.6, 1.8. The laser intensity is fixed at 5.9 × 1013 W/cm2. The vertical dashed black line is used to guide the moment when the laser field reaches maximum. The purple arrows and the red arrows represent the pre-peak and post-peak, respectively.
Fig. 2
Fig. 2 The delay time τA plotted as a function of γ in various intensities: I = 5.9 × 1013 W/cm2, I = 7.1 × 1013 W/cm2, and I = 8.4 × 1013 W/cm2.
Fig. 3
Fig. 3 (a) The probability current j(rd, t) as a function of time at the detector rd, where γ = 1.6 and the laser intensity is 5.9 × 1013 W/cm2 (black curve). The red dashed curve is a Gaussian fit to the probability current. The green dotted curve and yellow dash-dotted curve are Gaussian fitting of TI and MPI, respectively. (b) The delay time covering a range of Keldysh parameters from 0.4 to 4 at laser intensity of 5.9 × 1013 W/cm2 (black circles). The red squares and the blue crosses represent the delay time abstracted from the Gaussian fit of probability current of TI and MPI, respectively.
Fig. 4
Fig. 4 The fraction of TI electrons in the total ionization electrons (R) as a function of γ at laser intensities: 8.4 × 1013 W/cm2 (red triangles and curve), 7.1 × 1013 W/cm2 (blue crosses and curve) and 5.9 × 1013 W/cm2 (yellow circles and curve). The green rhombuses represent the R calculated by NICFA at laser intensity of 5.9 × 1013 W/cm2.
Fig. 5
Fig. 5 The two-dimension reconstructed final momentum distribution of tunneling electrons at various Keldysh parameters: (a) γ = 0.84; (b) γ = 0.92; (c) γ = 1.45 and (d) γ = 1.69. The laser intendity is fixed at 7.1 ×1013 W/cm2. The weights of the electrons are counted in a logarithmic scale. Furthermore, the side profile is the integrated signal along the polarization axis which is used to show the feature of py, and the weight is determined by normalization of the integral value.
Fig. 6
Fig. 6 The two-dimension reconstructed final momentum distribution of MPI at various Keldysh parameters: (a) γ = 1.69; (b) γ = 2.03; (c) γ = 2.53; (d) γ = 3.38. The laser intensity is fixed at 7.1 × 1013 W/cm2. The weights of the electrons are in logarithmic scale.

Equations (6)

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

i ψ ( r , t ) / t = [ 2 / 2 + V C ( r ) + V E ( r , t ) ] ψ ( r , t ) ,
E ( t ) = E 0 f ( t ) cos ( ω t ) x ^ .
j ( r d , t ) = i [ ψ ( r d , t ) ψ ( r d , t ) * c . c . ] / 2 ,
fun 1 , 2 = a 1 , 2 exp ( ( t b 1 , 2 ) 2 / c 1 , 2 2 ) ,
p ( r d , t ) = j ( r d , t ) / | ψ ( r d , t ) | 2 .
d 2 r / d t 2 = E ( t ) V C ( r ) .

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