Abstract

We propose a straightforward approach to directly probe the tunneling time by observing the transition of photoelectron wave packets in strong-field ionization processes, where Coulomb potentials do not affect the results. A circularly polarized laser pulse is used to avoid the impact of scattering electrons on the direct ionization electrons, and a pure transmission photoelectron wave packet can be obtained. Then, a positive tunneling time is extracted. The results demonstrate that the tunneling time is dominated mainly by the laser frequency in some laser intensity range. At the same time, we also investigate the tunneling time by analyzing the instantaneous ionization rate, and the consentaneous results are obtained.

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

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  10. A. I. Baz, “Lifetime of intermediate states,” Sov. J. Nucl. Physics-USSR 4, 182 (1967).
  11. M. Büttiker and R. Landauer, “Traversal time for tunneling,” Phys. Rev. Lett. 49, 1739–1742 (1982).
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  12. E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145–147 (1955).
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  13. E. Pollak and W. H. Miller, “New physical interpretation for time in scattering theory,” Phys. Rev. Lett. 53, 115–118 (1984).
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  14. H. A. Fertig, “Traversal-time distribution and the uncertainty principle in quantum tunneling,” Phys. Rev. Lett. 65, 2321–2324 (1990).
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    [Crossref]
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    [Crossref]
  26. M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Under-the-tunneling-barrier recollisions in strong-field ionization,” Phys. Rev. Lett. 120, 013201 (2018).
    [Crossref] [PubMed]
  27. X. Wang and J. H. Eberly, “Elliptical polarization and probability of double ionization,” Phys. Rev. Lett. 105, 083001 (2010).
    [Crossref] [PubMed]
  28. M. H. Yuan and T. S. Chu, “Solution to a 3d atom-laser interaction problem by sine-dvr and split-operator propagator,” Chem. Phys. 435, 9 (2014).
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  29. L. Feng and T. S. Chu, “Role of excited states in asymmetric harmonic emission,” Commun. Comput. Chem. 1, 52 (2013).
  30. L. Feng and H. Liu, “Plasmonic nanostructures assisted generation of x-ray sources,” Commun. Comput. Chem. 2, 47 (2014).
  31. M. Yuan, R. Lü, L. Feng, and T. Chu, “Computational efficiency improvement with wigner rotation technique in studying atoms in intense few-cycle circularly polarized pulses,” J. Chem. Phys. 140, 074108 (2014).
    [Crossref] [PubMed]
  32. R.-F. Lu, P.-Y. Zhang, and K.-L. Han, “Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields,” Phys. Rev. E 77, 066701 (2008).
    [Crossref]
  33. M. H. Beck, A. Jackle, G. A. Worth, and H. D. Meyer, “The multiconfiguration time-dependent hartree (mctdh) method: a highly efficient algorithm for propagating wavepackets,” Phys. Reports-Review Sect. Phys. Lett. 324, 1–105 (2000).
  34. J. Hu, K.-L. Han, and G.-Z. He, “Correlation quantum dynamics between an electron and d2+ molecule with attosecond resolution,” Phys. Rev. Lett. 95, 123001 (2005).
    [Crossref]
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    [Crossref]
  38. D. Farrelly and T. Uzer, “Ionization mechanism of rydberg atoms in a circularly polarized microwave field,” Phys. Rev. Lett. 74, 1720–1723 (1995).
    [Crossref] [PubMed]
  39. A. D. Bandrauk and H. Lu, “Controlling harmonic generation in molecules with intense laser and static magnetic fields: Orientation effects,” Phys. Rev. A 68, 043408 (2003).
    [Crossref]
  40. 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]
  41. M. Yuan, P. Xin, T. Chu, and H. Liu, “Exploring tunneling time by instantaneous ionization rate in strong-field ionization,” Opt. Express 25, 23493–23501 (2017).
    [Crossref] [PubMed]

2018 (1)

M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Under-the-tunneling-barrier recollisions in strong-field ionization,” Phys. Rev. Lett. 120, 013201 (2018).
[Crossref] [PubMed]

2017 (3)

N. Camus, E. Yakaboylu, L. Fechner, M. Klaiber, M. Laux, Y. Mi, K. Z. Hatsagortsyan, T. Pfeifer, C. H. Keitel, and R. Moshammer, “Experimental evidence for quantum tunneling time,” Phys. Rev. Lett. 119, 023201 (2017).
[Crossref] [PubMed]

M. Yuan, P. Xin, T. Chu, and H. Liu, “Investigating tunneling process of atom exposed in circularly polarized strong-laser field,” J. Phys. B: At. Mol. Opt. Phys. 50, 055006 (2017).
[Crossref]

M. Yuan, P. Xin, T. Chu, and H. Liu, “Exploring tunneling time by instantaneous ionization rate in strong-field ionization,” Opt. Express 25, 23493–23501 (2017).
[Crossref] [PubMed]

2016 (2)

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]

T. Zimmermann, S. Mishra, B. R. Doran, D. F. Gordon, and A. S. Landsman, “Tunneling time and weak measurement in strong field ionization,” Phys. Rev. Lett. 116, 233603 (2016).
[Crossref] [PubMed]

2015 (3)

L. Torlina, F. Morales, J. Kaushal, I. Ivanov, A. Kheifets, A. Zielinski, A. Scrinzi, H. G. Muller, S. Sukiasyan, M. Ivanov, and O. Smirnova, “Interpreting attoclock measurements of tunnelling times,” Nat. Phys. 11, 503 (2015).
[Crossref]

A. S. Landsman and U. Keller, “Attosecond science and the tunnelling time problem,” Phys. Reports-Review Sect. Phys. Lett. 547, 1–24 (2015).

M. Yuan, G. Zhao, and H. Liu, “Influence of wavelength on nonadiabatic effects in circularly polarized strong-field ionization,” Phys. Rev. A 92, 053405 (2015).
[Crossref]

2014 (4)

A. S. Landsman, M. Weger, J. Maurer, R. Boge, A. Ludwig, S. Heuser, C. Cirelli, L. Gallmann, and U. Keller, “Ultrafast resolution of tunneling delay time,” Optica 1, 343–349 (2014).
[Crossref]

M. H. Yuan and T. S. Chu, “Solution to a 3d atom-laser interaction problem by sine-dvr and split-operator propagator,” Chem. Phys. 435, 9 (2014).
[Crossref]

L. Feng and H. Liu, “Plasmonic nanostructures assisted generation of x-ray sources,” Commun. Comput. Chem. 2, 47 (2014).

M. Yuan, R. Lü, L. Feng, and T. Chu, “Computational efficiency improvement with wigner rotation technique in studying atoms in intense few-cycle circularly polarized pulses,” J. Chem. Phys. 140, 074108 (2014).
[Crossref] [PubMed]

2013 (2)

L. Feng and T. S. Chu, “Role of excited states in asymmetric harmonic emission,” Commun. Comput. Chem. 1, 52 (2013).

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]

2012 (1)

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nat Phys 8, 76–80 (2012).
[Crossref]

2011 (1)

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

2010 (1)

X. Wang and J. H. Eberly, “Elliptical polarization and probability of double ionization,” Phys. Rev. Lett. 105, 083001 (2010).
[Crossref] [PubMed]

2008 (3)

R.-F. Lu, P.-Y. Zhang, and K.-L. Han, “Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields,” Phys. Rev. E 77, 066701 (2008).
[Crossref]

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schoeffler, H. G. Muller, R. Doerner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4, 565–570 (2008).
[Crossref]

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

2007 (2)

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. 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]

T. K. Kjeldsen, L. A. A. Nikolopoulos, and L. B. Madsen, “Solving the m-mixing problem for the three-dimensional time-dependent Schrödinger equation by rotations: Application to strong-field ionization of h2+,” Phys. Rev. A 75, 063427 (2007).
[Crossref]

2005 (1)

J. Hu, K.-L. Han, and G.-Z. He, “Correlation quantum dynamics between an electron and d2+ molecule with attosecond resolution,” Phys. Rev. Lett. 95, 123001 (2005).
[Crossref]

2004 (1)

N. Yamada, “Unified derivation of tunneling times from decoherence functionals,” Phys. Rev. Lett. 93, 170401 (2004).
[Crossref] [PubMed]

2003 (1)

A. D. Bandrauk and H. Lu, “Controlling harmonic generation in molecules with intense laser and static magnetic fields: Orientation effects,” Phys. Rev. A 68, 043408 (2003).
[Crossref]

2000 (1)

M. H. Beck, A. Jackle, G. A. Worth, and H. D. Meyer, “The multiconfiguration time-dependent hartree (mctdh) method: a highly efficient algorithm for propagating wavepackets,” Phys. Reports-Review Sect. Phys. Lett. 324, 1–105 (2000).

1995 (1)

D. Farrelly and T. Uzer, “Ionization mechanism of rydberg atoms in a circularly polarized microwave field,” Phys. Rev. Lett. 74, 1720–1723 (1995).
[Crossref] [PubMed]

1994 (1)

R. Landauer and T. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys. 66, 217–228 (1994).
[Crossref]

1990 (1)

H. A. Fertig, “Traversal-time distribution and the uncertainty principle in quantum tunneling,” Phys. Rev. Lett. 65, 2321–2324 (1990).
[Crossref] [PubMed]

1989 (1)

E. H. Hauge and J. A. Støvneng, “Tunneling times: a critical review,” Rev. Mod. Phys. 61, 917–936 (1989).
[Crossref]

1988 (1)

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

1984 (1)

E. Pollak and W. H. Miller, “New physical interpretation for time in scattering theory,” Phys. Rev. Lett. 53, 115–118 (1984).
[Crossref]

1982 (1)

M. Büttiker and R. Landauer, “Traversal time for tunneling,” Phys. Rev. Lett. 49, 1739–1742 (1982).
[Crossref]

1967 (2)

V. F. Rybachen, “Time of penetration of a particle through a potential barrier,” Sov. J. Nucl. Physics-USSR 5, 635 (1967).

A. I. Baz, “Lifetime of intermediate states,” Sov. J. Nucl. Physics-USSR 4, 182 (1967).

1965 (1)

L. V. Keldysh, “Ionization in field of a strong electromagnetic wave,” Sov. Phys. Jetp-Ussr 20, 1307 (1965).

1955 (1)

E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145–147 (1955).
[Crossref]

1932 (1)

L. A. MacColl, “Note on the transmission and reflection of wave packets by potential barriers,” Phys. Rev. 40, 621–626 (1932).
[Crossref]

Abu-samha, M.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nat Phys 8, 76–80 (2012).
[Crossref]

Aharonov, Y.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

Atia-Tul-Noor,

U. S. Sainadh, H. Xu, X. Wang, Atia-Tul-Noor, W. C. Wallace, N. Douguet, A. W. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. T. Sang, and I. V. Litvinyuk, “Attosecond angular streaking and tunnelling time in atomic hydrogen,” ArXiv e-prints 1707 (2017).

Bandrauk, A. D.

A. D. Bandrauk and H. Lu, “Controlling harmonic generation in molecules with intense laser and static magnetic fields: Orientation effects,” Phys. Rev. A 68, 043408 (2003).
[Crossref]

Bartschat, K.

U. S. Sainadh, H. Xu, X. Wang, Atia-Tul-Noor, W. C. Wallace, N. Douguet, A. W. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. T. Sang, and I. V. Litvinyuk, “Attosecond angular streaking and tunnelling time in atomic hydrogen,” ArXiv e-prints 1707 (2017).

Bauke, H.

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]

Baz, A. I.

A. I. Baz, “Lifetime of intermediate states,” Sov. J. Nucl. Physics-USSR 4, 182 (1967).

Beck, M. H.

M. H. Beck, A. Jackle, G. A. Worth, and H. D. Meyer, “The multiconfiguration time-dependent hartree (mctdh) method: a highly efficient algorithm for propagating wavepackets,” Phys. Reports-Review Sect. Phys. Lett. 324, 1–105 (2000).

Biegert, J.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schoeffler, H. G. Muller, R. Doerner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4, 565–570 (2008).
[Crossref]

Boge, R.

A. S. Landsman, M. Weger, J. Maurer, R. Boge, A. Ludwig, S. Heuser, C. Cirelli, L. Gallmann, and U. Keller, “Ultrafast resolution of tunneling delay time,” Optica 1, 343–349 (2014).
[Crossref]

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]

Bray, A. W.

U. S. Sainadh, H. Xu, X. Wang, Atia-Tul-Noor, W. C. Wallace, N. Douguet, A. W. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. T. Sang, and I. V. Litvinyuk, “Attosecond angular streaking and tunnelling time in atomic hydrogen,” ArXiv e-prints 1707 (2017).

Buettiker, M.

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

Büttiker, M.

M. Büttiker and R. Landauer, “Traversal time for tunneling,” Phys. Rev. Lett. 49, 1739–1742 (1982).
[Crossref]

Camus, N.

N. Camus, E. Yakaboylu, L. Fechner, M. Klaiber, M. Laux, Y. Mi, K. Z. Hatsagortsyan, T. Pfeifer, C. H. Keitel, and R. Moshammer, “Experimental evidence for quantum tunneling time,” Phys. Rev. Lett. 119, 023201 (2017).
[Crossref] [PubMed]

Chu, T.

M. Yuan, P. Xin, T. Chu, and H. Liu, “Investigating tunneling process of atom exposed in circularly polarized strong-laser field,” J. Phys. B: At. Mol. Opt. Phys. 50, 055006 (2017).
[Crossref]

M. Yuan, P. Xin, T. Chu, and H. Liu, “Exploring tunneling time by instantaneous ionization rate in strong-field ionization,” Opt. Express 25, 23493–23501 (2017).
[Crossref] [PubMed]

M. Yuan, R. Lü, L. Feng, and T. Chu, “Computational efficiency improvement with wigner rotation technique in studying atoms in intense few-cycle circularly polarized pulses,” J. Chem. Phys. 140, 074108 (2014).
[Crossref] [PubMed]

Chu, T. S.

M. H. Yuan and T. S. Chu, “Solution to a 3d atom-laser interaction problem by sine-dvr and split-operator propagator,” Chem. Phys. 435, 9 (2014).
[Crossref]

L. Feng and T. S. Chu, “Role of excited states in asymmetric harmonic emission,” Commun. Comput. Chem. 1, 52 (2013).

Cirelli, C.

A. S. Landsman, M. Weger, J. Maurer, R. Boge, A. Ludwig, S. Heuser, C. Cirelli, L. Gallmann, and U. Keller, “Ultrafast resolution of tunneling delay time,” Optica 1, 343–349 (2014).
[Crossref]

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]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nat Phys 8, 76–80 (2012).
[Crossref]

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

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

Dimitrovski, D.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nat Phys 8, 76–80 (2012).
[Crossref]

Doerner, R.

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

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schoeffler, H. G. Muller, R. Doerner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4, 565–570 (2008).
[Crossref]

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

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N. Camus, E. Yakaboylu, L. Fechner, M. Klaiber, M. Laux, Y. Mi, K. Z. Hatsagortsyan, T. Pfeifer, C. H. Keitel, and R. Moshammer, “Experimental evidence for quantum tunneling time,” Phys. Rev. Lett. 119, 023201 (2017).
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N. Camus, E. Yakaboylu, L. Fechner, M. Klaiber, M. Laux, Y. Mi, K. Z. Hatsagortsyan, T. Pfeifer, C. H. Keitel, and R. Moshammer, “Experimental evidence for quantum tunneling time,” Phys. Rev. Lett. 119, 023201 (2017).
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N. Camus, E. Yakaboylu, L. Fechner, M. Klaiber, M. Laux, Y. Mi, K. Z. Hatsagortsyan, T. Pfeifer, C. H. Keitel, and R. Moshammer, “Experimental evidence for quantum tunneling time,” Phys. Rev. Lett. 119, 023201 (2017).
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A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nat Phys 8, 76–80 (2012).
[Crossref]

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

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

Pollak, E.

E. Pollak and W. H. Miller, “New physical interpretation for time in scattering theory,” Phys. Rev. Lett. 53, 115–118 (1984).
[Crossref]

Rauschenberger, J.

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. 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]

Rybachen, V. F.

V. F. Rybachen, “Time of penetration of a particle through a potential barrier,” Sov. J. Nucl. Physics-USSR 5, 635 (1967).

Sainadh, U. S.

U. S. Sainadh, H. Xu, X. Wang, Atia-Tul-Noor, W. C. Wallace, N. Douguet, A. W. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. T. Sang, and I. V. Litvinyuk, “Attosecond angular streaking and tunnelling time in atomic hydrogen,” ArXiv e-prints 1707 (2017).

Sang, R. T.

U. S. Sainadh, H. Xu, X. Wang, Atia-Tul-Noor, W. C. Wallace, N. Douguet, A. W. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. T. Sang, and I. V. Litvinyuk, “Attosecond angular streaking and tunnelling time in atomic hydrogen,” ArXiv e-prints 1707 (2017).

Schlup, P.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schoeffler, H. G. Muller, R. Doerner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4, 565–570 (2008).
[Crossref]

Schoeffler, M.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schoeffler, H. G. Muller, R. Doerner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4, 565–570 (2008).
[Crossref]

Schroder, H.

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. 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]

Schultze, M.

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. 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]

Scrinzi, A.

L. Torlina, F. Morales, J. Kaushal, I. Ivanov, A. Kheifets, A. Zielinski, A. Scrinzi, H. G. Muller, S. Sukiasyan, M. Ivanov, and O. Smirnova, “Interpreting attoclock measurements of tunnelling times,” Nat. Phys. 11, 503 (2015).
[Crossref]

Smirnova, O.

L. Torlina, F. Morales, J. Kaushal, I. Ivanov, A. Kheifets, A. Zielinski, A. Scrinzi, H. G. Muller, S. Sukiasyan, M. Ivanov, and O. Smirnova, “Interpreting attoclock measurements of tunnelling times,” Nat. Phys. 11, 503 (2015).
[Crossref]

Smolarski, M.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nat Phys 8, 76–80 (2012).
[Crossref]

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

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schoeffler, H. G. Muller, R. Doerner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4, 565–570 (2008).
[Crossref]

Staudte, A.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schoeffler, H. G. Muller, R. Doerner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4, 565–570 (2008).
[Crossref]

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

Støvneng, J. A.

E. H. Hauge and J. A. Støvneng, “Tunneling times: a critical review,” Rev. Mod. Phys. 61, 917–936 (1989).
[Crossref]

Sukiasyan, S.

L. Torlina, F. Morales, J. Kaushal, I. Ivanov, A. Kheifets, A. Zielinski, A. Scrinzi, H. G. Muller, S. Sukiasyan, M. Ivanov, and O. Smirnova, “Interpreting attoclock measurements of tunnelling times,” Nat. Phys. 11, 503 (2015).
[Crossref]

Teeny, N.

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]

Torlina, L.

L. Torlina, F. Morales, J. Kaushal, I. Ivanov, A. Kheifets, A. Zielinski, A. Scrinzi, H. G. Muller, S. Sukiasyan, M. Ivanov, and O. Smirnova, “Interpreting attoclock measurements of tunnelling times,” Nat. Phys. 11, 503 (2015).
[Crossref]

Uiberacker, M.

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. 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]

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. 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]

Uzer, T.

D. Farrelly and T. Uzer, “Ionization mechanism of rydberg atoms in a circularly polarized microwave field,” Phys. Rev. Lett. 74, 1720–1723 (1995).
[Crossref] [PubMed]

Vaidman, L.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

Verhoef, A. J.

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. 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]

Vrakking, M. J. J.

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. 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]

Wallace, W. C.

U. S. Sainadh, H. Xu, X. Wang, Atia-Tul-Noor, W. C. Wallace, N. Douguet, A. W. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. T. Sang, and I. V. Litvinyuk, “Attosecond angular streaking and tunnelling time in atomic hydrogen,” ArXiv e-prints 1707 (2017).

Wang, X.

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

X. Wang and J. H. Eberly, “Elliptical polarization and probability of double ionization,” Phys. Rev. Lett. 105, 083001 (2010).
[Crossref] [PubMed]

U. S. Sainadh, H. Xu, X. Wang, Atia-Tul-Noor, W. C. Wallace, N. Douguet, A. W. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. T. Sang, and I. V. Litvinyuk, “Attosecond angular streaking and tunnelling time in atomic hydrogen,” ArXiv e-prints 1707 (2017).

Weger, M.

A. S. Landsman, M. Weger, J. Maurer, R. Boge, A. Ludwig, S. Heuser, C. Cirelli, L. Gallmann, and U. Keller, “Ultrafast resolution of tunneling delay time,” Optica 1, 343–349 (2014).
[Crossref]

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]

Wigner, E. P.

E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145–147 (1955).
[Crossref]

Worth, G. A.

M. H. Beck, A. Jackle, G. A. Worth, and H. D. Meyer, “The multiconfiguration time-dependent hartree (mctdh) method: a highly efficient algorithm for propagating wavepackets,” Phys. Reports-Review Sect. Phys. Lett. 324, 1–105 (2000).

Xin, P.

M. Yuan, P. Xin, T. Chu, and H. Liu, “Investigating tunneling process of atom exposed in circularly polarized strong-laser field,” J. Phys. B: At. Mol. Opt. Phys. 50, 055006 (2017).
[Crossref]

M. Yuan, P. Xin, T. Chu, and H. Liu, “Exploring tunneling time by instantaneous ionization rate in strong-field ionization,” Opt. Express 25, 23493–23501 (2017).
[Crossref] [PubMed]

Xu, H.

U. S. Sainadh, H. Xu, X. Wang, Atia-Tul-Noor, W. C. Wallace, N. Douguet, A. W. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. T. Sang, and I. V. Litvinyuk, “Attosecond angular streaking and tunnelling time in atomic hydrogen,” ArXiv e-prints 1707 (2017).

Yakaboylu, E.

N. Camus, E. Yakaboylu, L. Fechner, M. Klaiber, M. Laux, Y. Mi, K. Z. Hatsagortsyan, T. Pfeifer, C. H. Keitel, and R. Moshammer, “Experimental evidence for quantum tunneling time,” Phys. Rev. Lett. 119, 023201 (2017).
[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]

Yakovlev, V.

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. 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]

Yamada, N.

N. Yamada, “Unified derivation of tunneling times from decoherence functionals,” Phys. Rev. Lett. 93, 170401 (2004).
[Crossref] [PubMed]

Yuan, M.

M. Yuan, P. Xin, T. Chu, and H. Liu, “Exploring tunneling time by instantaneous ionization rate in strong-field ionization,” Opt. Express 25, 23493–23501 (2017).
[Crossref] [PubMed]

M. Yuan, P. Xin, T. Chu, and H. Liu, “Investigating tunneling process of atom exposed in circularly polarized strong-laser field,” J. Phys. B: At. Mol. Opt. Phys. 50, 055006 (2017).
[Crossref]

M. Yuan, G. Zhao, and H. Liu, “Influence of wavelength on nonadiabatic effects in circularly polarized strong-field ionization,” Phys. Rev. A 92, 053405 (2015).
[Crossref]

M. Yuan, R. Lü, L. Feng, and T. Chu, “Computational efficiency improvement with wigner rotation technique in studying atoms in intense few-cycle circularly polarized pulses,” J. Chem. Phys. 140, 074108 (2014).
[Crossref] [PubMed]

Yuan, M. H.

M. H. Yuan and T. S. Chu, “Solution to a 3d atom-laser interaction problem by sine-dvr and split-operator propagator,” Chem. Phys. 435, 9 (2014).
[Crossref]

Zhang, P.-Y.

R.-F. Lu, P.-Y. Zhang, and K.-L. Han, “Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields,” Phys. Rev. E 77, 066701 (2008).
[Crossref]

Zhao, G.

M. Yuan, G. Zhao, and H. Liu, “Influence of wavelength on nonadiabatic effects in circularly polarized strong-field ionization,” Phys. Rev. A 92, 053405 (2015).
[Crossref]

Zielinski, A.

L. Torlina, F. Morales, J. Kaushal, I. Ivanov, A. Kheifets, A. Zielinski, A. Scrinzi, H. G. Muller, S. Sukiasyan, M. Ivanov, and O. Smirnova, “Interpreting attoclock measurements of tunnelling times,” Nat. Phys. 11, 503 (2015).
[Crossref]

Zimmermann, T.

T. Zimmermann, S. Mishra, B. R. Doran, D. F. Gordon, and A. S. Landsman, “Tunneling time and weak measurement in strong field ionization,” Phys. Rev. Lett. 116, 233603 (2016).
[Crossref] [PubMed]

Chem. Phys. (1)

M. H. Yuan and T. S. Chu, “Solution to a 3d atom-laser interaction problem by sine-dvr and split-operator propagator,” Chem. Phys. 435, 9 (2014).
[Crossref]

Commun. Comput. Chem. (2)

L. Feng and T. S. Chu, “Role of excited states in asymmetric harmonic emission,” Commun. Comput. Chem. 1, 52 (2013).

L. Feng and H. Liu, “Plasmonic nanostructures assisted generation of x-ray sources,” Commun. Comput. Chem. 2, 47 (2014).

J. Chem. Phys. (1)

M. Yuan, R. Lü, L. Feng, and T. Chu, “Computational efficiency improvement with wigner rotation technique in studying atoms in intense few-cycle circularly polarized pulses,” J. Chem. Phys. 140, 074108 (2014).
[Crossref] [PubMed]

J. Phys. B: At. Mol. Opt. Phys. (1)

M. Yuan, P. Xin, T. Chu, and H. Liu, “Investigating tunneling process of atom exposed in circularly polarized strong-laser field,” J. Phys. B: At. Mol. Opt. Phys. 50, 055006 (2017).
[Crossref]

Nat Phys (1)

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nat Phys 8, 76–80 (2012).
[Crossref]

Nat. Phys. (2)

L. Torlina, F. Morales, J. Kaushal, I. Ivanov, A. Kheifets, A. Zielinski, A. Scrinzi, H. G. Muller, S. Sukiasyan, M. Ivanov, and O. Smirnova, “Interpreting attoclock measurements of tunnelling times,” Nat. Phys. 11, 503 (2015).
[Crossref]

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schoeffler, H. G. Muller, R. Doerner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4, 565–570 (2008).
[Crossref]

Nature (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. 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]

New J. Phys. (1)

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

Opt. Express (1)

Optica (1)

Phys. Reports-Review Sect. Phys. Lett. (2)

A. S. Landsman and U. Keller, “Attosecond science and the tunnelling time problem,” Phys. Reports-Review Sect. Phys. Lett. 547, 1–24 (2015).

M. H. Beck, A. Jackle, G. A. Worth, and H. D. Meyer, “The multiconfiguration time-dependent hartree (mctdh) method: a highly efficient algorithm for propagating wavepackets,” Phys. Reports-Review Sect. Phys. Lett. 324, 1–105 (2000).

Phys. Rev. (2)

L. A. MacColl, “Note on the transmission and reflection of wave packets by potential barriers,” Phys. Rev. 40, 621–626 (1932).
[Crossref]

E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145–147 (1955).
[Crossref]

Phys. Rev. A (3)

T. K. Kjeldsen, L. A. A. Nikolopoulos, and L. B. Madsen, “Solving the m-mixing problem for the three-dimensional time-dependent Schrödinger equation by rotations: Application to strong-field ionization of h2+,” Phys. Rev. A 75, 063427 (2007).
[Crossref]

M. Yuan, G. Zhao, and H. Liu, “Influence of wavelength on nonadiabatic effects in circularly polarized strong-field ionization,” Phys. Rev. A 92, 053405 (2015).
[Crossref]

A. D. Bandrauk and H. Lu, “Controlling harmonic generation in molecules with intense laser and static magnetic fields: Orientation effects,” Phys. Rev. A 68, 043408 (2003).
[Crossref]

Phys. Rev. E (1)

R.-F. Lu, P.-Y. Zhang, and K.-L. Han, “Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields,” Phys. Rev. E 77, 066701 (2008).
[Crossref]

Phys. Rev. Lett. (13)

N. Camus, E. Yakaboylu, L. Fechner, M. Klaiber, M. Laux, Y. Mi, K. Z. Hatsagortsyan, T. Pfeifer, C. H. Keitel, and R. Moshammer, “Experimental evidence for quantum tunneling time,” Phys. Rev. Lett. 119, 023201 (2017).
[Crossref] [PubMed]

D. Farrelly and T. Uzer, “Ionization mechanism of rydberg atoms in a circularly polarized microwave field,” Phys. Rev. Lett. 74, 1720–1723 (1995).
[Crossref] [PubMed]

J. Hu, K.-L. Han, and G.-Z. He, “Correlation quantum dynamics between an electron and d2+ molecule with attosecond resolution,” Phys. Rev. Lett. 95, 123001 (2005).
[Crossref]

M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Under-the-tunneling-barrier recollisions in strong-field ionization,” Phys. Rev. Lett. 120, 013201 (2018).
[Crossref] [PubMed]

X. Wang and J. H. Eberly, “Elliptical polarization and probability of double ionization,” Phys. Rev. Lett. 105, 083001 (2010).
[Crossref] [PubMed]

E. Pollak and W. H. Miller, “New physical interpretation for time in scattering theory,” Phys. Rev. Lett. 53, 115–118 (1984).
[Crossref]

H. A. Fertig, “Traversal-time distribution and the uncertainty principle in quantum tunneling,” Phys. Rev. Lett. 65, 2321–2324 (1990).
[Crossref] [PubMed]

N. Yamada, “Unified derivation of tunneling times from decoherence functionals,” Phys. Rev. Lett. 93, 170401 (2004).
[Crossref] [PubMed]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

T. Zimmermann, S. Mishra, B. R. Doran, D. F. Gordon, and A. S. Landsman, “Tunneling time and weak measurement in strong field ionization,” Phys. Rev. Lett. 116, 233603 (2016).
[Crossref] [PubMed]

M. Büttiker and R. Landauer, “Traversal time for tunneling,” Phys. Rev. Lett. 49, 1739–1742 (1982).
[Crossref]

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]

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]

Rev. Mod. Phys. (2)

R. Landauer and T. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys. 66, 217–228 (1994).
[Crossref]

E. H. Hauge and J. A. Støvneng, “Tunneling times: a critical review,” Rev. Mod. Phys. 61, 917–936 (1989).
[Crossref]

Science (1)

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

Sov. J. Nucl. Physics-USSR (2)

V. F. Rybachen, “Time of penetration of a particle through a potential barrier,” Sov. J. Nucl. Physics-USSR 5, 635 (1967).

A. I. Baz, “Lifetime of intermediate states,” Sov. J. Nucl. Physics-USSR 4, 182 (1967).

Sov. Phys. Jetp-Ussr (1)

L. V. Keldysh, “Ionization in field of a strong electromagnetic wave,” Sov. Phys. Jetp-Ussr 20, 1307 (1965).

Other (2)

T. K. Kjeldsen, Wave packet dynamics studied by ab initio methods: Applications to strong-field ionization of atoms and molecules, University of Arhus (University of Arhus, Arhus, 2007).

U. S. Sainadh, H. Xu, X. Wang, Atia-Tul-Noor, W. C. Wallace, N. Douguet, A. W. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. T. Sang, and I. V. Litvinyuk, “Attosecond angular streaking and tunnelling time in atomic hydrogen,” ArXiv e-prints 1707 (2017).

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Figures (8)

Fig. 1
Fig. 1 (a) Tunnel ionization in circularly polarized laser field. An electron may tunnel out of atoms through the potential barrier instantaneously (red dash line) or taking a finite time (blue wavy line) in this process. xin and xexit are the entry and exit of the barrier. (b) Calculated momentum distribution from tunnel ionization of hydrogen with circularly polarized pulse.
Fig. 2
Fig. 2 The photoelectron momentum angular distribution which are obtained by integrating the momentum distributions over the radial direction as shown in Fig. 1(b). The different intensities are 1.0 × 1014 W/cm2 (F0 = 0.0534 a.u.), 1.5 × 1014 W/cm2 (F0 = 0.0654 a.u.) and 2.0 × 1014 W/cm2 (F0 = 0.0755 a.u.), respectively. The wavelength is 800 nm and the total duration is 3 optical cycles.
Fig. 3
Fig. 3 (a) The density of wave function (|ψ(r, t)|2) in the radial and time coordinate. (b) The transmission density of wave function (|ψ(r, t)|2 − |ψ(r, t = 0)|2) in the radial and time coordinate. The blue curve indicates the moment when the peaks appear for different radial location. The wavelength is 800 nm, duration is 3 optical cycles, and laser intensity is 1.0 × 1014 W/cm2.
Fig. 4
Fig. 4 The photoelectron density as a function of radial coordinate at different times. The wavelength and pulse duration are the same as those in Fig. 3. But the different intensities are 1.0 × 1014 W/cm2 (a), 1.5 × 1014 W/cm2 (b) and 2.0 × 1014 W/cm2 (c), respectively. For the three cases, we extract the photoelectron density at the moment of (105, 115, 125, 135, 145, 155 and 165) a.u. in the time propagation. And all the density peaks appear at the entry (xin) of the barrier.
Fig. 5
Fig. 5 The peak of transmission electron density as a function of radial coordinate and propagation time. The laser intensities are 1.0 × 1014 W/cm2 (a), 1.5 × 1014 W/cm2 (b) and 2.0 × 1014 W/cm2 (c), respectively. And the other laser parameters are the same as those used in Fig. 4. The slash shadow zones indicate the barrier for the three cases.
Fig. 6
Fig. 6 The peak of transmission electron density with different barriers, where an absorption function of CP is attached starting at 3, 8, 14, 20, 30 a.u., respectively. The laser intensity is 1.5 × 1014W/cm2.
Fig. 7
Fig. 7 Instantaneous ionization rate of hydrogen exposed in circularly polarized laser fields with different intensities. The delay time indicates the lag of the maximum ionization rate behind the moment when the electric field is the strongest. The laser parameters are the same as those used in Fig. 5.
Fig. 8
Fig. 8 The peak of transmission electron density as a function of radial coordinate and propagation time. The wavelengths are 1200 nm (a,b,c) and 1600 nm (d,e,f), and the laser intensities are 1.0 × 1014 W/cm2 (a,d), 1.5 × 1014 W/cm2 (b,e) and 2.0 × 1014 W/cm2 (c,f), respectively. The slash shadow zones indicate the barrier for the three cases.

Equations (6)

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ψ ( r , t ) = l = 0 l max m = l l 1 r χ l , m ( r , t ) Y l , m ( θ , ϕ )
i t ψ ( r , t ) = ( H 0 + V ( F ) ( r , t ) ) ψ ( r , t )
P ion = 1 j | ψ j ( r ) | ψ ( r , t ) | 2 .
P k ( k ) = | ψ k ( ) ( r ) | ψ ( r , t = T ) | 2
ψ k ( ) ( r ) = l = 0 l max m = l e i ( l π / 2 σ l ( k ) δ l ( k ) ) F k , l ( r ) k r Y l , m * ( θ k , ϕ k ) Y l , m ( θ , ϕ )
P k ( k ) = | l = 0 l max m = l l e i ( l π / 2 σ l ( k ) δ l ( k ) ) r min r max F k , l ( r ) k χ l , m ( t , T ) d r Y ( θ k , ϕ k ) | 2

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