Abstract

High angular momentum partial waves are indispensable in the numerical calculations of the time-dependent Schrödinger equation (TDSE) for the interaction between atoms and strong long-wavelength laser pulses. In these cases, the widely-applied Lanczos propagator, used to solve the TDSE, requires an extremely small time step to be convergent. By splitting out the centrifugal potential from the whole Hamiltonian, we demonstrate that the stiffness of the TDSE can be reduced and a rather large time step is allowed for the present Split-Lanczos propagator. Compared with the ordinary Lanczos propagator, the efficiency of the propagation can be improved by more than 100 times for large angular momentum in present tests.

© 2017 Optical Society of America

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References

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  1. R. Pazourek, J. Feist, S. Nagele, and J. Burgdörfer, “Attosecond streaking of correlated two-electron transitions in helium,” Phys. Rev. Lett. 108(16), 163001 (2012).
    [Crossref] [PubMed]
  2. W.-C. Jiang, J.-Y. Shan, Q. Gong, and L.-Y. Peng, “Virtual sequential picture for nonsequential two-photon double ionization of helium,” Phys. Rev. Lett. 115(15), 153002 (2015).
    [Crossref] [PubMed]
  3. R. Pazourek, S. Nagele, and J. Burgdörfer, “Attosecond chronoscopy of photoemission,” Rev. Mod. Phys. 87(3), 765 (2015).
    [Crossref]
  4. L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575(3), 1 (2015).
    [Crossref]
  5. V.S. Melezhik, “Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps,” EPJ Web of Conferences 108(10), 01008 (2016).
    [Crossref]
  6. H. Miyagi and L. B. Madsen, “Exterior time scaling with the stiffness-free lanczos time propagator: Formulation and application to atoms interacting with strong midinfrared lasers,” Phys. Rev. A 93(3), 033420 (2016).
    [Crossref]
  7. Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
    [Crossref]
  8. A. Zielinski, V. P. Majety, and A. Scrinzi, “Double photoelectron momentum spectra of helium at infrared wavelength,” Phys. Rev. A 93 (2), 023406 (2016).
    [Crossref]
  9. X. M. Tong, K. Hino, and N. Toshima, “Double photoelectron momentum spectra of helium at infrared wavelength,” “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74(3), 031405 (2006).
    [Crossref]
  10. A. Scrinzi, “t -surff: fully differential two-electron photo-emission spectra,” New J. Phys. 14(8), 085008 (2012).
    [Crossref]
  11. L. Tao and A. Scrinzi, “Photo-electron momentum spectra from minimal volumes: the time-dependent surface flux method,” New J. Phys. 14(1), 013021 (2012).
    [Crossref]
  12. M. Feit, J. Fleck, and A. Steiger, “Solution of the schrödinger equation by a spectral method,” J. Comput. Phys. 47(3), 412 (1982).
    [Crossref]
  13. M. R. Hermann and J. A. Fleck, “Split-operator spectral method for solving the time-dependent schrödinger equation in spherical coordinates,” Phys. Rev. A 38(12), 6000 (1988).
    [Crossref]
  14. E. A. McCullough and R. E. Wyatt, “Quantum dynamics of the collinear (h, h2) reaction,” J. Chem. Phys. 51(3), 1253 (1969).
    [Crossref]
  15. E. A. McCullough and R. E. Wyatt, “Dynamics of the collinear h+h2 reaction. i. probability density and flux,” J. Chem. Phys. 54(8), 3578 (1971).
    [Crossref]
  16. H. Muller, “An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge,” Laser Phys. 9(138), 138 (1999).
  17. A. Castro, Miguel A. L. Marques, and A. Rubio, “Propagators for the time-dependent Kohn-Sham equations,” J. Chem. Phys. 121(8), 3425 (2004).
    [Crossref] [PubMed]
  18. H. Tal-Ezer and R. Kosloff, “An accurate and efficient scheme for propagating the time dependent schrödinger equation,” J. Chem. Phys. 81(9), 3967 (1984).
    [Crossref]
  19. M. Braun, S. Sofianos, D. Papageorgiou, and I. Lagaris, “An Efficient Chebyshev-Lanczos Method for Obtaining. Eigensolutions of the Schrödinger Equation on a Grid,” J. Comput. Phys. 126(2), 315 (1996).
    [Crossref]
  20. U. Peskin and N. Moiseyev, “The solution of the time-dependent Schrödinger equation by the (t, t’) method: Theory, computational algorithm and applications,” J. Chem. Phys. 99(6), 4590 (1993).
    [Crossref]
  21. A. Askar and A. S. Cakmak, “Explicit integration method for the time dependent schrödinger equation for collision problems, ” J. Chem. Phys. 68 (6), 2794 (1978).
    [Crossref]
  22. D. Kosloff and R. Kosloff, “A Fourier method solution for the time dependent schrödinger equation as a tool in molecular dynamics,” J. Comput. Phys. 52(1), 35 (1983).
    [Crossref]
  23. I. Gonoskov and M. Marklund, “Single-step propagators for calculation of time evolution in quantum systems with arbitrary interactions,” Comput. Phys. Commun. 202(5), 211 (2016).
    [Crossref]
  24. T. J. Park and J. C. Light, “Unitary quantum time evolution by iterative lanczos reduction,” J. Chem. Phys. 85(10), 5870 (1986).
    [Crossref]
  25. E. S. Smyth, J. S. Parker, and K. Taylor, “Numerical integration of the time-dependent schrödinger equation for laser-driven helium,” Comput. Phys. Commun. 114(1), 1 (1998).
    [Crossref]
  26. M. Hochbruck and C. Lubich, “On Krylov subspace approximations to the matrix exponential operator,” SIAM J. Numer. Anal. 34(5), 1911 (1997).
    [Crossref]
  27. B. I. Schneider, X. Guan, and K. Bartschat, “Chapter five - time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation,” in Concepts of Mathematical Physics in Chemistry: A Tribute to Frank E. Harris - Part B (Academic, 2016)
  28. C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
    [Crossref]
  29. L.-Y. Peng and A. F. Starace, “Application of coulomb wave function discrete variable representation to atomic systems in strong laser fields,” J. Chem. Phys. 125(15), 154311 (2006).
    [Crossref]
  30. J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
    [Crossref] [PubMed]
  31. J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins, and J. Burgdöerfer, “Nonsequential two-photon double ionization of helium,” Phys. Rev. A 77(4), 043420 (2008).
    [Crossref]
  32. W.-C. Jiang, W.-H. Xiong, T.-S. Zhu, L.-Y. Peng, and Q. Gong, “Double ionization of He by time-delayed attosecond pulses,” J. Phys. B 47(9), 091001 (2014).
    [Crossref]
  33. X. Guan, K. Bartschat, and B. I. Schneider, “Breakup of the aligned H2 molecule by xuv laser pulses: A time-dependent treatment in prolate spheroidal coordinates,” Phys. Rev. A 83(4), 043403 (2011).
    [Crossref]
  34. W.-C. Jiang, L.-Y. Peng, J.-W. Geng, and Q. Gong, “One-photon double ionization of H2 with arbitrary orientation,” Phys. Rev. A 88 (6), 063408 (2013).
    [Crossref]
  35. T. N. Rescigno and C. W. McCurdy, “Numerical grid methods for quantum-mechanical scattering problems,” Phys. Rev. A 62(3), 032706 (2000).
    [Crossref]
  36. J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
    [Crossref] [PubMed]
  37. M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
    [Crossref] [PubMed]
  38. M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
    [Crossref] [PubMed]
  39. S. X. Hu, “Optimizing the fedvr-tdcc code for exploring the quantum dynamics of two-electron systems in intense laser pulses,” Phys. Rev. E 81(5), 056705 (2010).
    [Crossref]
  40. S. Blanes, F. Casas, and A. Murua, “An efficient algorithm based on splitting for the time integration of the Schrödinger equation,” J. Comput. Phys. 303, 396 (2015).
    [Crossref]
  41. D. G. Arbó, J. E. Miraglia, M. S. Gravielle, K. Schiessl, E. Persson, and J. Burgdörfer, “Coulomb-volkov approximation for near-threshold ionization by short laser pulses,” Phys. Rev. A 77(1), 013401 (2008).
    [Crossref]

2016 (4)

V.S. Melezhik, “Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps,” EPJ Web of Conferences 108(10), 01008 (2016).
[Crossref]

H. Miyagi and L. B. Madsen, “Exterior time scaling with the stiffness-free lanczos time propagator: Formulation and application to atoms interacting with strong midinfrared lasers,” Phys. Rev. A 93(3), 033420 (2016).
[Crossref]

A. Zielinski, V. P. Majety, and A. Scrinzi, “Double photoelectron momentum spectra of helium at infrared wavelength,” Phys. Rev. A 93 (2), 023406 (2016).
[Crossref]

I. Gonoskov and M. Marklund, “Single-step propagators for calculation of time evolution in quantum systems with arbitrary interactions,” Comput. Phys. Commun. 202(5), 211 (2016).
[Crossref]

2015 (5)

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

W.-C. Jiang, J.-Y. Shan, Q. Gong, and L.-Y. Peng, “Virtual sequential picture for nonsequential two-photon double ionization of helium,” Phys. Rev. Lett. 115(15), 153002 (2015).
[Crossref] [PubMed]

R. Pazourek, S. Nagele, and J. Burgdörfer, “Attosecond chronoscopy of photoemission,” Rev. Mod. Phys. 87(3), 765 (2015).
[Crossref]

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575(3), 1 (2015).
[Crossref]

S. Blanes, F. Casas, and A. Murua, “An efficient algorithm based on splitting for the time integration of the Schrödinger equation,” J. Comput. Phys. 303, 396 (2015).
[Crossref]

2014 (1)

W.-C. Jiang, W.-H. Xiong, T.-S. Zhu, L.-Y. Peng, and Q. Gong, “Double ionization of He by time-delayed attosecond pulses,” J. Phys. B 47(9), 091001 (2014).
[Crossref]

2013 (1)

W.-C. Jiang, L.-Y. Peng, J.-W. Geng, and Q. Gong, “One-photon double ionization of H2 with arbitrary orientation,” Phys. Rev. A 88 (6), 063408 (2013).
[Crossref]

2012 (4)

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

A. Scrinzi, “t -surff: fully differential two-electron photo-emission spectra,” New J. Phys. 14(8), 085008 (2012).
[Crossref]

L. Tao and A. Scrinzi, “Photo-electron momentum spectra from minimal volumes: the time-dependent surface flux method,” New J. Phys. 14(1), 013021 (2012).
[Crossref]

R. Pazourek, J. Feist, S. Nagele, and J. Burgdörfer, “Attosecond streaking of correlated two-electron transitions in helium,” Phys. Rev. Lett. 108(16), 163001 (2012).
[Crossref] [PubMed]

2011 (3)

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
[Crossref] [PubMed]

X. Guan, K. Bartschat, and B. I. Schneider, “Breakup of the aligned H2 molecule by xuv laser pulses: A time-dependent treatment in prolate spheroidal coordinates,” Phys. Rev. A 83(4), 043403 (2011).
[Crossref]

2010 (1)

S. X. Hu, “Optimizing the fedvr-tdcc code for exploring the quantum dynamics of two-electron systems in intense laser pulses,” Phys. Rev. E 81(5), 056705 (2010).
[Crossref]

2008 (2)

D. G. Arbó, J. E. Miraglia, M. S. Gravielle, K. Schiessl, E. Persson, and J. Burgdörfer, “Coulomb-volkov approximation for near-threshold ionization by short laser pulses,” Phys. Rev. A 77(1), 013401 (2008).
[Crossref]

J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins, and J. Burgdöerfer, “Nonsequential two-photon double ionization of helium,” Phys. Rev. A 77(4), 043420 (2008).
[Crossref]

2006 (3)

L.-Y. Peng and A. F. Starace, “Application of coulomb wave function discrete variable representation to atomic systems in strong laser fields,” J. Chem. Phys. 125(15), 154311 (2006).
[Crossref]

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

X. M. Tong, K. Hino, and N. Toshima, “Double photoelectron momentum spectra of helium at infrared wavelength,” “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74(3), 031405 (2006).
[Crossref]

2004 (1)

A. Castro, Miguel A. L. Marques, and A. Rubio, “Propagators for the time-dependent Kohn-Sham equations,” J. Chem. Phys. 121(8), 3425 (2004).
[Crossref] [PubMed]

2000 (1)

T. N. Rescigno and C. W. McCurdy, “Numerical grid methods for quantum-mechanical scattering problems,” Phys. Rev. A 62(3), 032706 (2000).
[Crossref]

1999 (1)

H. Muller, “An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge,” Laser Phys. 9(138), 138 (1999).

1998 (1)

E. S. Smyth, J. S. Parker, and K. Taylor, “Numerical integration of the time-dependent schrödinger equation for laser-driven helium,” Comput. Phys. Commun. 114(1), 1 (1998).
[Crossref]

1997 (1)

M. Hochbruck and C. Lubich, “On Krylov subspace approximations to the matrix exponential operator,” SIAM J. Numer. Anal. 34(5), 1911 (1997).
[Crossref]

1996 (1)

M. Braun, S. Sofianos, D. Papageorgiou, and I. Lagaris, “An Efficient Chebyshev-Lanczos Method for Obtaining. Eigensolutions of the Schrödinger Equation on a Grid,” J. Comput. Phys. 126(2), 315 (1996).
[Crossref]

1993 (1)

U. Peskin and N. Moiseyev, “The solution of the time-dependent Schrödinger equation by the (t, t’) method: Theory, computational algorithm and applications,” J. Chem. Phys. 99(6), 4590 (1993).
[Crossref]

1991 (1)

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

1988 (1)

M. R. Hermann and J. A. Fleck, “Split-operator spectral method for solving the time-dependent schrödinger equation in spherical coordinates,” Phys. Rev. A 38(12), 6000 (1988).
[Crossref]

1986 (1)

T. J. Park and J. C. Light, “Unitary quantum time evolution by iterative lanczos reduction,” J. Chem. Phys. 85(10), 5870 (1986).
[Crossref]

1984 (1)

H. Tal-Ezer and R. Kosloff, “An accurate and efficient scheme for propagating the time dependent schrödinger equation,” J. Chem. Phys. 81(9), 3967 (1984).
[Crossref]

1983 (1)

D. Kosloff and R. Kosloff, “A Fourier method solution for the time dependent schrödinger equation as a tool in molecular dynamics,” J. Comput. Phys. 52(1), 35 (1983).
[Crossref]

1982 (1)

M. Feit, J. Fleck, and A. Steiger, “Solution of the schrödinger equation by a spectral method,” J. Comput. Phys. 47(3), 412 (1982).
[Crossref]

1978 (1)

A. Askar and A. S. Cakmak, “Explicit integration method for the time dependent schrödinger equation for collision problems, ” J. Chem. Phys. 68 (6), 2794 (1978).
[Crossref]

1971 (1)

E. A. McCullough and R. E. Wyatt, “Dynamics of the collinear h+h2 reaction. i. probability density and flux,” J. Chem. Phys. 54(8), 3578 (1971).
[Crossref]

1969 (1)

E. A. McCullough and R. E. Wyatt, “Quantum dynamics of the collinear (h, h2) reaction,” J. Chem. Phys. 51(3), 1253 (1969).
[Crossref]

Arbó, D. G.

D. G. Arbó, J. E. Miraglia, M. S. Gravielle, K. Schiessl, E. Persson, and J. Burgdörfer, “Coulomb-volkov approximation for near-threshold ionization by short laser pulses,” Phys. Rev. A 77(1), 013401 (2008).
[Crossref]

Askar, A.

A. Askar and A. S. Cakmak, “Explicit integration method for the time dependent schrödinger equation for collision problems, ” J. Chem. Phys. 68 (6), 2794 (1978).
[Crossref]

Bakker, J. M.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Bartschat, K.

X. Guan, K. Bartschat, and B. I. Schneider, “Breakup of the aligned H2 molecule by xuv laser pulses: A time-dependent treatment in prolate spheroidal coordinates,” Phys. Rev. A 83(4), 043403 (2011).
[Crossref]

B. I. Schneider, X. Guan, and K. Bartschat, “Chapter five - time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation,” in Concepts of Mathematical Physics in Chemistry: A Tribute to Frank E. Harris - Part B (Academic, 2016)

Bauer, D.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Berden, G.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Bisseling, R.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Blaga, C. I.

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

Blanes, S.

S. Blanes, F. Casas, and A. Murua, “An efficient algorithm based on splitting for the time integration of the Schrödinger equation,” J. Comput. Phys. 303, 396 (2015).
[Crossref]

Braun, M.

M. Braun, S. Sofianos, D. Papageorgiou, and I. Lagaris, “An Efficient Chebyshev-Lanczos Method for Obtaining. Eigensolutions of the Schrödinger Equation on a Grid,” J. Comput. Phys. 126(2), 315 (1996).
[Crossref]

Burgdöerfer, J.

J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins, and J. Burgdöerfer, “Nonsequential two-photon double ionization of helium,” Phys. Rev. A 77(4), 043420 (2008).
[Crossref]

Burgdörfer, J.

R. Pazourek, S. Nagele, and J. Burgdörfer, “Attosecond chronoscopy of photoemission,” Rev. Mod. Phys. 87(3), 765 (2015).
[Crossref]

R. Pazourek, J. Feist, S. Nagele, and J. Burgdörfer, “Attosecond streaking of correlated two-electron transitions in helium,” Phys. Rev. Lett. 108(16), 163001 (2012).
[Crossref] [PubMed]

D. G. Arbó, J. E. Miraglia, M. S. Gravielle, K. Schiessl, E. Persson, and J. Burgdörfer, “Coulomb-volkov approximation for near-threshold ionization by short laser pulses,” Phys. Rev. A 77(1), 013401 (2008).
[Crossref]

Cakmak, A. S.

A. Askar and A. S. Cakmak, “Explicit integration method for the time dependent schrödinger equation for collision problems, ” J. Chem. Phys. 68 (6), 2794 (1978).
[Crossref]

Casas, F.

S. Blanes, F. Casas, and A. Murua, “An efficient algorithm based on splitting for the time integration of the Schrödinger equation,” J. Comput. Phys. 303, 396 (2015).
[Crossref]

Castro, A.

A. Castro, Miguel A. L. Marques, and A. Rubio, “Propagators for the time-dependent Kohn-Sham equations,” J. Chem. Phys. 121(8), 3425 (2004).
[Crossref] [PubMed]

Cauchy, C.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Cerjan, C.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Collins, L. A.

J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins, and J. Burgdöerfer, “Nonsequential two-photon double ionization of helium,” Phys. Rev. A 77(4), 043420 (2008).
[Crossref]

DiMauro, L. F.

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

Doherty, B. J. S.

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

Feist, J.

R. Pazourek, J. Feist, S. Nagele, and J. Burgdörfer, “Attosecond streaking of correlated two-electron transitions in helium,” Phys. Rev. Lett. 108(16), 163001 (2012).
[Crossref] [PubMed]

J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins, and J. Burgdöerfer, “Nonsequential two-photon double ionization of helium,” Phys. Rev. A 77(4), 043420 (2008).
[Crossref]

Feit, M.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

M. Feit, J. Fleck, and A. Steiger, “Solution of the schrödinger equation by a spectral method,” J. Comput. Phys. 47(3), 412 (1982).
[Crossref]

Fleck, J.

M. Feit, J. Fleck, and A. Steiger, “Solution of the schrödinger equation by a spectral method,” J. Comput. Phys. 47(3), 412 (1982).
[Crossref]

Fleck, J. A.

M. R. Hermann and J. A. Fleck, “Split-operator spectral method for solving the time-dependent schrödinger equation in spherical coordinates,” Phys. Rev. A 38(12), 6000 (1988).
[Crossref]

Friesner, R.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Frolov, M. V.

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

Geng, J.-W.

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575(3), 1 (2015).
[Crossref]

W.-C. Jiang, L.-Y. Peng, J.-W. Geng, and Q. Gong, “One-photon double ionization of H2 with arbitrary orientation,” Phys. Rev. A 88 (6), 063408 (2013).
[Crossref]

Gijsbertsen, A.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Gong, Q.

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575(3), 1 (2015).
[Crossref]

W.-C. Jiang, J.-Y. Shan, Q. Gong, and L.-Y. Peng, “Virtual sequential picture for nonsequential two-photon double ionization of helium,” Phys. Rev. Lett. 115(15), 153002 (2015).
[Crossref] [PubMed]

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

W.-C. Jiang, W.-H. Xiong, T.-S. Zhu, L.-Y. Peng, and Q. Gong, “Double ionization of He by time-delayed attosecond pulses,” J. Phys. B 47(9), 091001 (2014).
[Crossref]

W.-C. Jiang, L.-Y. Peng, J.-W. Geng, and Q. Gong, “One-photon double ionization of H2 with arbitrary orientation,” Phys. Rev. A 88 (6), 063408 (2013).
[Crossref]

M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
[Crossref] [PubMed]

Gonoskov, I.

I. Gonoskov and M. Marklund, “Single-step propagators for calculation of time evolution in quantum systems with arbitrary interactions,” Comput. Phys. Commun. 202(5), 211 (2016).
[Crossref]

Gravielle, M. S.

D. G. Arbó, J. E. Miraglia, M. S. Gravielle, K. Schiessl, E. Persson, and J. Burgdörfer, “Coulomb-volkov approximation for near-threshold ionization by short laser pulses,” Phys. Rev. A 77(1), 013401 (2008).
[Crossref]

Guan, X.

X. Guan, K. Bartschat, and B. I. Schneider, “Breakup of the aligned H2 molecule by xuv laser pulses: A time-dependent treatment in prolate spheroidal coordinates,” Phys. Rev. A 83(4), 043403 (2011).
[Crossref]

B. I. Schneider, X. Guan, and K. Bartschat, “Chapter five - time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation,” in Concepts of Mathematical Physics in Chemistry: A Tribute to Frank E. Harris - Part B (Academic, 2016)

Guldberg, A.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Hammerich, A.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Hermann, M. R.

M. R. Hermann and J. A. Fleck, “Split-operator spectral method for solving the time-dependent schrödinger equation in spherical coordinates,” Phys. Rev. A 38(12), 6000 (1988).
[Crossref]

Hino, K.

X. M. Tong, K. Hino, and N. Toshima, “Double photoelectron momentum spectra of helium at infrared wavelength,” “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74(3), 031405 (2006).
[Crossref]

Hochbruck, M.

M. Hochbruck and C. Lubich, “On Krylov subspace approximations to the matrix exponential operator,” SIAM J. Numer. Anal. 34(5), 1911 (1997).
[Crossref]

Hu, S. X.

S. X. Hu, “Optimizing the fedvr-tdcc code for exploring the quantum dynamics of two-electron systems in intense laser pulses,” Phys. Rev. E 81(5), 056705 (2010).
[Crossref]

Huismans, Y.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Ivanov, M. Y.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Jiang, W.-C.

W.-C. Jiang, J.-Y. Shan, Q. Gong, and L.-Y. Peng, “Virtual sequential picture for nonsequential two-photon double ionization of helium,” Phys. Rev. Lett. 115(15), 153002 (2015).
[Crossref] [PubMed]

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575(3), 1 (2015).
[Crossref]

W.-C. Jiang, W.-H. Xiong, T.-S. Zhu, L.-Y. Peng, and Q. Gong, “Double ionization of He by time-delayed attosecond pulses,” J. Phys. B 47(9), 091001 (2014).
[Crossref]

W.-C. Jiang, L.-Y. Peng, J.-W. Geng, and Q. Gong, “One-photon double ionization of H2 with arbitrary orientation,” Phys. Rev. A 88 (6), 063408 (2013).
[Crossref]

Jolicard, G.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Jungmann, J. H.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Karrlein, W.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Knyazeva, D. V.

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

Kosloff, D.

D. Kosloff and R. Kosloff, “A Fourier method solution for the time dependent schrödinger equation as a tool in molecular dynamics,” J. Comput. Phys. 52(1), 35 (1983).
[Crossref]

Kosloff, R.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

H. Tal-Ezer and R. Kosloff, “An accurate and efficient scheme for propagating the time dependent schrödinger equation,” J. Chem. Phys. 81(9), 3967 (1984).
[Crossref]

D. Kosloff and R. Kosloff, “A Fourier method solution for the time dependent schrödinger equation as a tool in molecular dynamics,” J. Comput. Phys. 52(1), 35 (1983).
[Crossref]

Lagaris, I.

M. Braun, S. Sofianos, D. Papageorgiou, and I. Lagaris, “An Efficient Chebyshev-Lanczos Method for Obtaining. Eigensolutions of the Schrödinger Equation on a Grid,” J. Comput. Phys. 126(2), 315 (1996).
[Crossref]

Leforestier, C.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Lépine, F.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Light, J. C.

T. J. Park and J. C. Light, “Unitary quantum time evolution by iterative lanczos reduction,” J. Chem. Phys. 85(10), 5870 (1986).
[Crossref]

Lipkin, N.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Logman, P. S. W. M.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Lubich, C.

M. Hochbruck and C. Lubich, “On Krylov subspace approximations to the matrix exponential operator,” SIAM J. Numer. Anal. 34(5), 1911 (1997).
[Crossref]

Madsen, L. B.

H. Miyagi and L. B. Madsen, “Exterior time scaling with the stiffness-free lanczos time propagator: Formulation and application to atoms interacting with strong midinfrared lasers,” Phys. Rev. A 93(3), 033420 (2016).
[Crossref]

Majety, V. P.

A. Zielinski, V. P. Majety, and A. Scrinzi, “Double photoelectron momentum spectra of helium at infrared wavelength,” Phys. Rev. A 93 (2), 023406 (2016).
[Crossref]

Manakov, N. L.

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

Marchenko, T.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Marklund, M.

I. Gonoskov and M. Marklund, “Single-step propagators for calculation of time evolution in quantum systems with arbitrary interactions,” Comput. Phys. Commun. 202(5), 211 (2016).
[Crossref]

Marques, Miguel A. L.

A. Castro, Miguel A. L. Marques, and A. Rubio, “Propagators for the time-dependent Kohn-Sham equations,” J. Chem. Phys. 121(8), 3425 (2004).
[Crossref] [PubMed]

McCullough, E. A.

E. A. McCullough and R. E. Wyatt, “Dynamics of the collinear h+h2 reaction. i. probability density and flux,” J. Chem. Phys. 54(8), 3578 (1971).
[Crossref]

E. A. McCullough and R. E. Wyatt, “Quantum dynamics of the collinear (h, h2) reaction,” J. Chem. Phys. 51(3), 1253 (1969).
[Crossref]

McCurdy, C. W.

T. N. Rescigno and C. W. McCurdy, “Numerical grid methods for quantum-mechanical scattering problems,” Phys. Rev. A 62(3), 032706 (2000).
[Crossref]

Melezhik, V.S.

V.S. Melezhik, “Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps,” EPJ Web of Conferences 108(10), 01008 (2016).
[Crossref]

Meyer, H.-D.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Miraglia, J. E.

D. G. Arbó, J. E. Miraglia, M. S. Gravielle, K. Schiessl, E. Persson, and J. Burgdörfer, “Coulomb-volkov approximation for near-threshold ionization by short laser pulses,” Phys. Rev. A 77(1), 013401 (2008).
[Crossref]

Miyagi, H.

H. Miyagi and L. B. Madsen, “Exterior time scaling with the stiffness-free lanczos time propagator: Formulation and application to atoms interacting with strong midinfrared lasers,” Phys. Rev. A 93(3), 033420 (2016).
[Crossref]

Moiseyev, N.

U. Peskin and N. Moiseyev, “The solution of the time-dependent Schrödinger equation by the (t, t’) method: Theory, computational algorithm and applications,” J. Chem. Phys. 99(6), 4590 (1993).
[Crossref]

Muller, H.

H. Muller, “An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge,” Laser Phys. 9(138), 138 (1999).

Muller, H. G.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Murua, A.

S. Blanes, F. Casas, and A. Murua, “An efficient algorithm based on splitting for the time integration of the Schrödinger equation,” J. Comput. Phys. 303, 396 (2015).
[Crossref]

Nagele, S.

R. Pazourek, S. Nagele, and J. Burgdörfer, “Attosecond chronoscopy of photoemission,” Rev. Mod. Phys. 87(3), 765 (2015).
[Crossref]

R. Pazourek, J. Feist, S. Nagele, and J. Burgdörfer, “Attosecond streaking of correlated two-electron transitions in helium,” Phys. Rev. Lett. 108(16), 163001 (2012).
[Crossref] [PubMed]

J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins, and J. Burgdöerfer, “Nonsequential two-photon double ionization of helium,” Phys. Rev. A 77(4), 043420 (2008).
[Crossref]

Papageorgiou, D.

M. Braun, S. Sofianos, D. Papageorgiou, and I. Lagaris, “An Efficient Chebyshev-Lanczos Method for Obtaining. Eigensolutions of the Schrödinger Equation on a Grid,” J. Comput. Phys. 126(2), 315 (1996).
[Crossref]

Park, T. J.

T. J. Park and J. C. Light, “Unitary quantum time evolution by iterative lanczos reduction,” J. Chem. Phys. 85(10), 5870 (1986).
[Crossref]

Parker, J. S.

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

E. S. Smyth, J. S. Parker, and K. Taylor, “Numerical integration of the time-dependent schrödinger equation for laser-driven helium,” Comput. Phys. Commun. 114(1), 1 (1998).
[Crossref]

Pazourek, R.

R. Pazourek, S. Nagele, and J. Burgdörfer, “Attosecond chronoscopy of photoemission,” Rev. Mod. Phys. 87(3), 765 (2015).
[Crossref]

R. Pazourek, J. Feist, S. Nagele, and J. Burgdörfer, “Attosecond streaking of correlated two-electron transitions in helium,” Phys. Rev. Lett. 108(16), 163001 (2012).
[Crossref] [PubMed]

J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins, and J. Burgdöerfer, “Nonsequential two-photon double ionization of helium,” Phys. Rev. A 77(4), 043420 (2008).
[Crossref]

Peng, L.-Y.

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

W.-C. Jiang, J.-Y. Shan, Q. Gong, and L.-Y. Peng, “Virtual sequential picture for nonsequential two-photon double ionization of helium,” Phys. Rev. Lett. 115(15), 153002 (2015).
[Crossref] [PubMed]

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575(3), 1 (2015).
[Crossref]

W.-C. Jiang, W.-H. Xiong, T.-S. Zhu, L.-Y. Peng, and Q. Gong, “Double ionization of He by time-delayed attosecond pulses,” J. Phys. B 47(9), 091001 (2014).
[Crossref]

W.-C. Jiang, L.-Y. Peng, J.-W. Geng, and Q. Gong, “One-photon double ionization of H2 with arbitrary orientation,” Phys. Rev. A 88 (6), 063408 (2013).
[Crossref]

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
[Crossref] [PubMed]

L.-Y. Peng and A. F. Starace, “Application of coulomb wave function discrete variable representation to atomic systems in strong laser fields,” J. Chem. Phys. 125(15), 154311 (2006).
[Crossref]

Persson, E.

J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins, and J. Burgdöerfer, “Nonsequential two-photon double ionization of helium,” Phys. Rev. A 77(4), 043420 (2008).
[Crossref]

D. G. Arbó, J. E. Miraglia, M. S. Gravielle, K. Schiessl, E. Persson, and J. Burgdörfer, “Coulomb-volkov approximation for near-threshold ionization by short laser pulses,” Phys. Rev. A 77(1), 013401 (2008).
[Crossref]

Peskin, U.

U. Peskin and N. Moiseyev, “The solution of the time-dependent Schrödinger equation by the (t, t’) method: Theory, computational algorithm and applications,” J. Chem. Phys. 99(6), 4590 (1993).
[Crossref]

Pi, L.-W.

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

Popov, A. M.

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

Popruzhenko, S. V.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Pronin, E. A.

M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
[Crossref] [PubMed]

Redlich, B.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Rescigno, T. N.

T. N. Rescigno and C. W. McCurdy, “Numerical grid methods for quantum-mechanical scattering problems,” Phys. Rev. A 62(3), 032706 (2000).
[Crossref]

Roncero, O.

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

Rouzée, A.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Rubio, A.

A. Castro, Miguel A. L. Marques, and A. Rubio, “Propagators for the time-dependent Kohn-Sham equations,” J. Chem. Phys. 121(8), 3425 (2004).
[Crossref] [PubMed]

Schafer, K. J.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Schiessl, K.

D. G. Arbó, J. E. Miraglia, M. S. Gravielle, K. Schiessl, E. Persson, and J. Burgdörfer, “Coulomb-volkov approximation for near-threshold ionization by short laser pulses,” Phys. Rev. A 77(1), 013401 (2008).
[Crossref]

Schneider, B. I.

X. Guan, K. Bartschat, and B. I. Schneider, “Breakup of the aligned H2 molecule by xuv laser pulses: A time-dependent treatment in prolate spheroidal coordinates,” Phys. Rev. A 83(4), 043403 (2011).
[Crossref]

J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins, and J. Burgdöerfer, “Nonsequential two-photon double ionization of helium,” Phys. Rev. A 77(4), 043420 (2008).
[Crossref]

B. I. Schneider, X. Guan, and K. Bartschat, “Chapter five - time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation,” in Concepts of Mathematical Physics in Chemistry: A Tribute to Frank E. Harris - Part B (Academic, 2016)

Schultz, K. D.

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

Scrinzi, A.

A. Zielinski, V. P. Majety, and A. Scrinzi, “Double photoelectron momentum spectra of helium at infrared wavelength,” Phys. Rev. A 93 (2), 023406 (2016).
[Crossref]

A. Scrinzi, “t -surff: fully differential two-electron photo-emission spectra,” New J. Phys. 14(8), 085008 (2012).
[Crossref]

L. Tao and A. Scrinzi, “Photo-electron momentum spectra from minimal volumes: the time-dependent surface flux method,” New J. Phys. 14(1), 013021 (2012).
[Crossref]

Shan, J.-Y.

W.-C. Jiang, J.-Y. Shan, Q. Gong, and L.-Y. Peng, “Virtual sequential picture for nonsequential two-photon double ionization of helium,” Phys. Rev. Lett. 115(15), 153002 (2015).
[Crossref] [PubMed]

Smirnova, O.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Smolkowska, A. S.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Smyth, E. S.

E. S. Smyth, J. S. Parker, and K. Taylor, “Numerical integration of the time-dependent schrödinger equation for laser-driven helium,” Comput. Phys. Commun. 114(1), 1 (1998).
[Crossref]

Sofianos, S.

M. Braun, S. Sofianos, D. Papageorgiou, and I. Lagaris, “An Efficient Chebyshev-Lanczos Method for Obtaining. Eigensolutions of the Schrödinger Equation on a Grid,” J. Comput. Phys. 126(2), 315 (1996).
[Crossref]

Spanner, M.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Starace, A. F.

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
[Crossref] [PubMed]

L.-Y. Peng and A. F. Starace, “Application of coulomb wave function discrete variable representation to atomic systems in strong laser fields,” J. Chem. Phys. 125(15), 154311 (2006).
[Crossref]

Steiger, A.

M. Feit, J. Fleck, and A. Steiger, “Solution of the schrödinger equation by a spectral method,” J. Comput. Phys. 47(3), 412 (1982).
[Crossref]

Tal-Ezer, H.

H. Tal-Ezer and R. Kosloff, “An accurate and efficient scheme for propagating the time dependent schrödinger equation,” J. Chem. Phys. 81(9), 3967 (1984).
[Crossref]

Tao, L.

L. Tao and A. Scrinzi, “Photo-electron momentum spectra from minimal volumes: the time-dependent surface flux method,” New J. Phys. 14(1), 013021 (2012).
[Crossref]

Taylor, K.

E. S. Smyth, J. S. Parker, and K. Taylor, “Numerical integration of the time-dependent schrödinger equation for laser-driven helium,” Comput. Phys. Commun. 114(1), 1 (1998).
[Crossref]

Taylor, K. T.

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

Tikhonova, O. V.

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

Tong, X. M.

X. M. Tong, K. Hino, and N. Toshima, “Double photoelectron momentum spectra of helium at infrared wavelength,” “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74(3), 031405 (2006).
[Crossref]

Tong, X.-M.

M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
[Crossref] [PubMed]

Toshima, N.

X. M. Tong, K. Hino, and N. Toshima, “Double photoelectron momentum spectra of helium at infrared wavelength,” “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74(3), 031405 (2006).
[Crossref]

van der Meer, A. F. G.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Vermin, W.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Volkova, E. A.

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

Vrakking, M. J. J.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Wyatt, R. E.

E. A. McCullough and R. E. Wyatt, “Dynamics of the collinear h+h2 reaction. i. probability density and flux,” J. Chem. Phys. 54(8), 3578 (1971).
[Crossref]

E. A. McCullough and R. E. Wyatt, “Quantum dynamics of the collinear (h, h2) reaction,” J. Chem. Phys. 51(3), 1253 (1969).
[Crossref]

Xiao, X.-R.

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

Xiong, W.-H.

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575(3), 1 (2015).
[Crossref]

W.-C. Jiang, W.-H. Xiong, T.-S. Zhu, L.-Y. Peng, and Q. Gong, “Double ionization of He by time-delayed attosecond pulses,” J. Phys. B 47(9), 091001 (2014).
[Crossref]

Xu, M.-H.

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
[Crossref] [PubMed]

Zamith, S.

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

Zhang, Z.

M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
[Crossref] [PubMed]

Zhu, T.-S.

W.-C. Jiang, W.-H. Xiong, T.-S. Zhu, L.-Y. Peng, and Q. Gong, “Double ionization of He by time-delayed attosecond pulses,” J. Phys. B 47(9), 091001 (2014).
[Crossref]

Zielinski, A.

A. Zielinski, V. P. Majety, and A. Scrinzi, “Double photoelectron momentum spectra of helium at infrared wavelength,” Phys. Rev. A 93 (2), 023406 (2016).
[Crossref]

Comput. Phys. Commun. (2)

I. Gonoskov and M. Marklund, “Single-step propagators for calculation of time evolution in quantum systems with arbitrary interactions,” Comput. Phys. Commun. 202(5), 211 (2016).
[Crossref]

E. S. Smyth, J. S. Parker, and K. Taylor, “Numerical integration of the time-dependent schrödinger equation for laser-driven helium,” Comput. Phys. Commun. 114(1), 1 (1998).
[Crossref]

EPJ Web of Conferences (1)

V.S. Melezhik, “Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps,” EPJ Web of Conferences 108(10), 01008 (2016).
[Crossref]

J. Chem. Phys. (8)

E. A. McCullough and R. E. Wyatt, “Quantum dynamics of the collinear (h, h2) reaction,” J. Chem. Phys. 51(3), 1253 (1969).
[Crossref]

E. A. McCullough and R. E. Wyatt, “Dynamics of the collinear h+h2 reaction. i. probability density and flux,” J. Chem. Phys. 54(8), 3578 (1971).
[Crossref]

A. Castro, Miguel A. L. Marques, and A. Rubio, “Propagators for the time-dependent Kohn-Sham equations,” J. Chem. Phys. 121(8), 3425 (2004).
[Crossref] [PubMed]

H. Tal-Ezer and R. Kosloff, “An accurate and efficient scheme for propagating the time dependent schrödinger equation,” J. Chem. Phys. 81(9), 3967 (1984).
[Crossref]

U. Peskin and N. Moiseyev, “The solution of the time-dependent Schrödinger equation by the (t, t’) method: Theory, computational algorithm and applications,” J. Chem. Phys. 99(6), 4590 (1993).
[Crossref]

A. Askar and A. S. Cakmak, “Explicit integration method for the time dependent schrödinger equation for collision problems, ” J. Chem. Phys. 68 (6), 2794 (1978).
[Crossref]

T. J. Park and J. C. Light, “Unitary quantum time evolution by iterative lanczos reduction,” J. Chem. Phys. 85(10), 5870 (1986).
[Crossref]

L.-Y. Peng and A. F. Starace, “Application of coulomb wave function discrete variable representation to atomic systems in strong laser fields,” J. Chem. Phys. 125(15), 154311 (2006).
[Crossref]

J. Comput. Phys. (5)

C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94(1), 59 (1991).
[Crossref]

S. Blanes, F. Casas, and A. Murua, “An efficient algorithm based on splitting for the time integration of the Schrödinger equation,” J. Comput. Phys. 303, 396 (2015).
[Crossref]

D. Kosloff and R. Kosloff, “A Fourier method solution for the time dependent schrödinger equation as a tool in molecular dynamics,” J. Comput. Phys. 52(1), 35 (1983).
[Crossref]

M. Braun, S. Sofianos, D. Papageorgiou, and I. Lagaris, “An Efficient Chebyshev-Lanczos Method for Obtaining. Eigensolutions of the Schrödinger Equation on a Grid,” J. Comput. Phys. 126(2), 315 (1996).
[Crossref]

M. Feit, J. Fleck, and A. Steiger, “Solution of the schrödinger equation by a spectral method,” J. Comput. Phys. 47(3), 412 (1982).
[Crossref]

J. Phys. B (1)

W.-C. Jiang, W.-H. Xiong, T.-S. Zhu, L.-Y. Peng, and Q. Gong, “Double ionization of He by time-delayed attosecond pulses,” J. Phys. B 47(9), 091001 (2014).
[Crossref]

Laser Phys. (1)

H. Muller, “An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge,” Laser Phys. 9(138), 138 (1999).

New J. Phys. (2)

A. Scrinzi, “t -surff: fully differential two-electron photo-emission spectra,” New J. Phys. 14(8), 085008 (2012).
[Crossref]

L. Tao and A. Scrinzi, “Photo-electron momentum spectra from minimal volumes: the time-dependent surface flux method,” New J. Phys. 14(1), 013021 (2012).
[Crossref]

Phys. Rep. (1)

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575(3), 1 (2015).
[Crossref]

Phys. Rev. A (9)

X. Guan, K. Bartschat, and B. I. Schneider, “Breakup of the aligned H2 molecule by xuv laser pulses: A time-dependent treatment in prolate spheroidal coordinates,” Phys. Rev. A 83(4), 043403 (2011).
[Crossref]

W.-C. Jiang, L.-Y. Peng, J.-W. Geng, and Q. Gong, “One-photon double ionization of H2 with arbitrary orientation,” Phys. Rev. A 88 (6), 063408 (2013).
[Crossref]

T. N. Rescigno and C. W. McCurdy, “Numerical grid methods for quantum-mechanical scattering problems,” Phys. Rev. A 62(3), 032706 (2000).
[Crossref]

D. G. Arbó, J. E. Miraglia, M. S. Gravielle, K. Schiessl, E. Persson, and J. Burgdörfer, “Coulomb-volkov approximation for near-threshold ionization by short laser pulses,” Phys. Rev. A 77(1), 013401 (2008).
[Crossref]

J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins, and J. Burgdöerfer, “Nonsequential two-photon double ionization of helium,” Phys. Rev. A 77(4), 043420 (2008).
[Crossref]

A. Zielinski, V. P. Majety, and A. Scrinzi, “Double photoelectron momentum spectra of helium at infrared wavelength,” Phys. Rev. A 93 (2), 023406 (2016).
[Crossref]

X. M. Tong, K. Hino, and N. Toshima, “Double photoelectron momentum spectra of helium at infrared wavelength,” “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74(3), 031405 (2006).
[Crossref]

H. Miyagi and L. B. Madsen, “Exterior time scaling with the stiffness-free lanczos time propagator: Formulation and application to atoms interacting with strong midinfrared lasers,” Phys. Rev. A 93(3), 033420 (2016).
[Crossref]

M. R. Hermann and J. A. Fleck, “Split-operator spectral method for solving the time-dependent schrödinger equation in spherical coordinates,” Phys. Rev. A 38(12), 6000 (1988).
[Crossref]

Phys. Rev. E (1)

S. X. Hu, “Optimizing the fedvr-tdcc code for exploring the quantum dynamics of two-electron systems in intense laser pulses,” Phys. Rev. E 81(5), 056705 (2010).
[Crossref]

Phys. Rev. Lett. (6)

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

M. V. Frolov, D. V. Knyazeva, N. L. Manakov, A. M. Popov, O. V. Tikhonova, E. A. Volkova, M.-H. Xu, L.-Y. Peng, L.-W. Pi, and A. F. Starace, “Validity of Factorization of the High-Energy Photoelectron Yield in Above-Threshold Ionization of an Atom by a Short Laser Pulse,” Phys. Rev. Lett. 108(21), 213002 (2012).
[Crossref] [PubMed]

M.-H. Xu, L.-Y. Peng, Z. Zhang, Q. Gong, X.-M. Tong, E. A. Pronin, and A. F. Starace, “Attosecond Streaking in the Low-Energy Region as a Probe of Rescattering,” Phys. Rev. Lett. 107(18), 183001 (2011).
[Crossref] [PubMed]

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96(13), 133001 (2006).
[Crossref] [PubMed]

R. Pazourek, J. Feist, S. Nagele, and J. Burgdörfer, “Attosecond streaking of correlated two-electron transitions in helium,” Phys. Rev. Lett. 108(16), 163001 (2012).
[Crossref] [PubMed]

W.-C. Jiang, J.-Y. Shan, Q. Gong, and L.-Y. Peng, “Virtual sequential picture for nonsequential two-photon double ionization of helium,” Phys. Rev. Lett. 115(15), 153002 (2015).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

R. Pazourek, S. Nagele, and J. Burgdörfer, “Attosecond chronoscopy of photoemission,” Rev. Mod. Phys. 87(3), 765 (2015).
[Crossref]

Science (1)

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B. Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y. Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking, “Time-resolved holography with photoelectrons,” Science 331(6031), 61 (2011).
[Crossref]

SIAM J. Numer. Anal. (1)

M. Hochbruck and C. Lubich, “On Krylov subspace approximations to the matrix exponential operator,” SIAM J. Numer. Anal. 34(5), 1911 (1997).
[Crossref]

Other (1)

B. I. Schneider, X. Guan, and K. Bartschat, “Chapter five - time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation,” in Concepts of Mathematical Physics in Chemistry: A Tribute to Frank E. Harris - Part B (Academic, 2016)

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Figures (4)

Fig. 1
Fig. 1 The angular integrated energy spectrum for single ionization of H, He+ and He in various of laser conditions. The targets and main laser parameters are given at the top of each panel. The black dash-dot lines come from independent finite-difference (FD) codes [36–38]. The solid red lines are calculated with present split-Lanczos propagator. The time step of the whole split-Lanczos propagator is fixed to be 0.01 a.u., but in (d) the time adaptive scheme [see Eq. (22)] is used. In the panels, Up represents the ponderomotive potential, and the cut-off positions of 2Up and 10Up are marked.
Fig. 2
Fig. 2 The maximal eigenvalues of Hr (a) or H (b) in the Krylov sub-space during propagation [For definations of Hr and H, see Eq. (20)]. The target and laser parameters are the same with Fig. 1(b). Three different maximal angular momentums are used.
Fig. 3
Fig. 3 The maximal eigenvalues of Hr in the Krylov sub-space. The target and laser parameters are the same with Fig. 1(d). The vector potential of the laser pulse is also shown with a scaling (labeled by |A| × 500). The label 5 – 0.001 (25 – 0.01) means the order of the Krylov sub-space is 5 (25) and the time step is 0.001 a.u. (0.01 a.u.).
Fig. 4
Fig. 4 The number of Krylov propagation [Ns(t)] in each split-Lanczos propagation. The target and laser parameters are the same with Fig. 1(d).

Equations (35)

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i t Ψ ( r , t ) = H Ψ ( r , t ) .
Ψ ( r , t ) = l , m R l m ( r , t ) r | l m ,
l m | T | l m = ( T 0 + V d ) δ l l δ m m ,
T 0 = 1 2 2 r 2 ,
V c = l ( l + 1 ) 2 r 2 .
Ψ ( t + Δ t ) = U ( t , t + Δ t ) Ψ ( t ) ,
U ( t , t + Δ t ) = e i H ( t ) Δ t .
K N + 1 = { | Ψ 0 , H | Ψ 0 , H 2 | Ψ 0 , , H N | Ψ 0 } ,
Q N + 1 = { | q 0 , | q 1 , | q 2 , , | q N } .
| q 0 = | Ψ 0
β 0 | q 1 = H | q 0 α 0 | q 0
β j | q j + 1 = H | q j α j | q j β j 1 | q   j 1 ,
α j = q j | H | q j
β j = H | q j α j | q j β j 1 | q j 1 = q j 1 | H | q j = q j + 1 | H | q j .
H i j ( Q ) = q i | H | q j = ( α 0 β 0 0 0 β 0 0 0 β N 1 0 0 β N 1 α N ) .
U ( Q ) = exp ( i H ( Q ) Δ t )
= l exp ( i h l Δ t ) | Z l Z l |
| Ψ ( t + Δ t ) = l Z l | q 0 exp ( i h l Δ t ) | Z l = k = 0 N a k | q k ,
a k = l Z l | q 0 exp ( i h l Δ t ) q k | Z l .
H ( t ) = H r ( t ) + V c ,
U ( t , t + Δ t ) = e i V c Δ t 2 e i H r ( t ) Δ t e i V c Δ t 2 + o ( Δ t 3 ) .
U ( t , t + Δ t ) = e i V c Δ t 2 [ i = 1 N s ( t ) e i H r ( t + Δ t i 1 ) Δ t i ] e i V c Δ t 2 + o ( Δ t 3 ) ,
i = 1 N s ( t ) Δ t i = Δ t ,
l m | H I z | l m R ( r ) r = 1 r i A ( t ) [ r + l r ] a l 1 , m l 1 , l m , m R ( r ) 1 r i A ( t ) [ r + ( l + 1 ) r ] a l , m l + 1 , l l + 1 , l m , m R ( r )
l m | H I   z | l m = r E ( t ) a l 1 , m l 1 , l m , m + r E ( t ) a l , m l + 1 , l m , m
a l , m = ( l + 1 ) 2 m 2 ( 2 l + 1 ) ( 2 l + 3 ) .
f ( k ) = Ψ k ( r ) | Ψ ( r , t f ) .
Ψ k ( r ) = 1 k 1 2 π l , m i l e i ( σ l + σ l ) Y l m * ( k ^ ) R k l ( r ) Y l m ( r ^ ) ,
R k l ( r ) = 2 r 2 l e π Z / 2 k | Γ ( l + 1 i Z / k ) | ( 2 l + 1 ) ! e i k r ( k r ) ( l + 1 ) × 1 F 1 ( l + 1 + i Z / k , 2 l + 2 , 2 i k r ) .
0 r 2 R k l ( r ) R k l ( r ) d r = 2 π δ ( k k ) .
f ( k ) = 1 2 π k l , m Y l m ( k ^ ) M l , m ( k ) ,
M l , m ( k ) = ( i ) l e i σ l ( k ) r R k l ( r ) R l m ( r , t f ) d r .
F keep ( r ) = 1 1 / ( 1 + e ( r R c ) / Δ ) .
U k ( t i , t i + 1 ) = e i t i t i + 1 [ k 2 2 + A ( τ ) ( k ) ] d τ .
f ( k , t i + 1 ) = U k ( t i , t i + 1 ) f ( k , t i ) + f ( k , t i + 1 ) .

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