Abstract

We present wave functions of helium atoms exposed to an intense 800-nm laser, calculated by numerical integration of the time-dependent Schrödinger equation. Around 600 TW/cm2 strong resonance enhancements of high-energy electrons occur, each leading to the appearance of specific quasi-periodic charge distribution patterns around the atom. The time-dependence of several such states is presented and discussed.

© 2001 Optical Society of America

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  1. B. Yang, K.J. Schafer, B. Walker, K.C. Kulander, P. Agostini, and L.F. DiMauro, “Intensity - dependent scattering ring in above-threshold ionization,” Phys. Rev. Lett. 71, 3770 (1993).
    [Crossref] [PubMed]
  2. P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N.K. Rahman, “Free-free transitions following six photon ionization of xenon,” Phys. Rev. Lett. 42, 1127 (1979).
    [Crossref]
  3. K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, Academic (1992) p.247; K.J. Schafer and K.C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A42 (1990) 5794.
  4. H.G. Muller, “Tunneling excitation to resonant states in helium as the main source of super-ponderomotive electrons in the tunneling regime,” Phys. Rev. Lett. 83, 3158–61 (1999).
    [Crossref]
  5. H.G. Muller and M.V. Fedorov, Super-Intense Laser-Atom Physics V proceedings, NATO series, p. ix Wolters-Kluwer Academic Publishing, (1996).
    [Crossref]
  6. H.G. Muller, “An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge,” Laser Phys. 9, 138 (1999).
  7. H.B. van Linden van den Heuvell and H.G. Muller, “Limiting cases of excess-photon ionization,” in S.J. Smith and P.L. Knight (eds.), “Studies in Modern Optics No. 8, Multiphoton processes”, p. 25–34, Cambridge University Press, Cambridge, (1988).
  8. G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
    [Crossref] [PubMed]
  9. P.B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71 (1993) 1994.
    [Crossref] [PubMed]
  10. H.G. Muller, “Numerical simulation of high-order above-threshold-ionization enhancement in argon,” Phys. Rev. A 60, 1341–50 (1999).
    [Crossref]
  11. M. Pont, N. Walet, M. Gavrila, and C.W. McCurdy, “Dichotomy of the hydrogen atom in superintense, high-frequency laser fields,” Phys. Rev. Lett. 61, 939 (1988)
    [Crossref] [PubMed]
  12. T. Brabec, M.Yu. Ivanov, and P.B. Corkum, “Coulomb focusing in intense field atomic processes,” Phys. Rev. A 54, R2551–R2554 (1996).
    [Crossref] [PubMed]

1999 (3)

H.G. Muller, “Tunneling excitation to resonant states in helium as the main source of super-ponderomotive electrons in the tunneling regime,” Phys. Rev. Lett. 83, 3158–61 (1999).
[Crossref]

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

H.G. Muller, “Numerical simulation of high-order above-threshold-ionization enhancement in argon,” Phys. Rev. A 60, 1341–50 (1999).
[Crossref]

1996 (1)

T. Brabec, M.Yu. Ivanov, and P.B. Corkum, “Coulomb focusing in intense field atomic processes,” Phys. Rev. A 54, R2551–R2554 (1996).
[Crossref] [PubMed]

1994 (1)

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

1993 (2)

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

B. Yang, K.J. Schafer, B. Walker, K.C. Kulander, P. Agostini, and L.F. DiMauro, “Intensity - dependent scattering ring in above-threshold ionization,” Phys. Rev. Lett. 71, 3770 (1993).
[Crossref] [PubMed]

1988 (1)

M. Pont, N. Walet, M. Gavrila, and C.W. McCurdy, “Dichotomy of the hydrogen atom in superintense, high-frequency laser fields,” Phys. Rev. Lett. 61, 939 (1988)
[Crossref] [PubMed]

1979 (1)

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N.K. Rahman, “Free-free transitions following six photon ionization of xenon,” Phys. Rev. Lett. 42, 1127 (1979).
[Crossref]

Agostini, P.

B. Yang, K.J. Schafer, B. Walker, K.C. Kulander, P. Agostini, and L.F. DiMauro, “Intensity - dependent scattering ring in above-threshold ionization,” Phys. Rev. Lett. 71, 3770 (1993).
[Crossref] [PubMed]

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N.K. Rahman, “Free-free transitions following six photon ionization of xenon,” Phys. Rev. Lett. 42, 1127 (1979).
[Crossref]

Brabec, T.

T. Brabec, M.Yu. Ivanov, and P.B. Corkum, “Coulomb focusing in intense field atomic processes,” Phys. Rev. A 54, R2551–R2554 (1996).
[Crossref] [PubMed]

Corkum, P.B.

T. Brabec, M.Yu. Ivanov, and P.B. Corkum, “Coulomb focusing in intense field atomic processes,” Phys. Rev. A 54, R2551–R2554 (1996).
[Crossref] [PubMed]

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

DiMauro, L.F.

B. Yang, K.J. Schafer, B. Walker, K.C. Kulander, P. Agostini, and L.F. DiMauro, “Intensity - dependent scattering ring in above-threshold ionization,” Phys. Rev. Lett. 71, 3770 (1993).
[Crossref] [PubMed]

Fabre, F.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N.K. Rahman, “Free-free transitions following six photon ionization of xenon,” Phys. Rev. Lett. 42, 1127 (1979).
[Crossref]

Fedorov, M.V.

H.G. Muller and M.V. Fedorov, Super-Intense Laser-Atom Physics V proceedings, NATO series, p. ix Wolters-Kluwer Academic Publishing, (1996).
[Crossref]

Gavrila, M.

M. Pont, N. Walet, M. Gavrila, and C.W. McCurdy, “Dichotomy of the hydrogen atom in superintense, high-frequency laser fields,” Phys. Rev. Lett. 61, 939 (1988)
[Crossref] [PubMed]

Ivanov, M.Yu.

T. Brabec, M.Yu. Ivanov, and P.B. Corkum, “Coulomb focusing in intense field atomic processes,” Phys. Rev. A 54, R2551–R2554 (1996).
[Crossref] [PubMed]

Krause, J.L.

K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, Academic (1992) p.247; K.J. Schafer and K.C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A42 (1990) 5794.

Kulander, K.C.

B. Yang, K.J. Schafer, B. Walker, K.C. Kulander, P. Agostini, and L.F. DiMauro, “Intensity - dependent scattering ring in above-threshold ionization,” Phys. Rev. Lett. 71, 3770 (1993).
[Crossref] [PubMed]

K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, Academic (1992) p.247; K.J. Schafer and K.C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A42 (1990) 5794.

K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, Academic (1992) p.247; K.J. Schafer and K.C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A42 (1990) 5794.

Lambropoulos, P.

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

Mainfray, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N.K. Rahman, “Free-free transitions following six photon ionization of xenon,” Phys. Rev. Lett. 42, 1127 (1979).
[Crossref]

McCurdy, C.W.

M. Pont, N. Walet, M. Gavrila, and C.W. McCurdy, “Dichotomy of the hydrogen atom in superintense, high-frequency laser fields,” Phys. Rev. Lett. 61, 939 (1988)
[Crossref] [PubMed]

Muller, H.G.

H.G. Muller, “Numerical simulation of high-order above-threshold-ionization enhancement in argon,” Phys. Rev. A 60, 1341–50 (1999).
[Crossref]

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

H.G. Muller, “Tunneling excitation to resonant states in helium as the main source of super-ponderomotive electrons in the tunneling regime,” Phys. Rev. Lett. 83, 3158–61 (1999).
[Crossref]

H.G. Muller and M.V. Fedorov, Super-Intense Laser-Atom Physics V proceedings, NATO series, p. ix Wolters-Kluwer Academic Publishing, (1996).
[Crossref]

H.B. van Linden van den Heuvell and H.G. Muller, “Limiting cases of excess-photon ionization,” in S.J. Smith and P.L. Knight (eds.), “Studies in Modern Optics No. 8, Multiphoton processes”, p. 25–34, Cambridge University Press, Cambridge, (1988).

Nicklich, W.

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

Paulus, G.G.

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

Petite, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N.K. Rahman, “Free-free transitions following six photon ionization of xenon,” Phys. Rev. Lett. 42, 1127 (1979).
[Crossref]

Pont, M.

M. Pont, N. Walet, M. Gavrila, and C.W. McCurdy, “Dichotomy of the hydrogen atom in superintense, high-frequency laser fields,” Phys. Rev. Lett. 61, 939 (1988)
[Crossref] [PubMed]

Rahman, N.K.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N.K. Rahman, “Free-free transitions following six photon ionization of xenon,” Phys. Rev. Lett. 42, 1127 (1979).
[Crossref]

Schafer, K.J.

B. Yang, K.J. Schafer, B. Walker, K.C. Kulander, P. Agostini, and L.F. DiMauro, “Intensity - dependent scattering ring in above-threshold ionization,” Phys. Rev. Lett. 71, 3770 (1993).
[Crossref] [PubMed]

K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, Academic (1992) p.247; K.J. Schafer and K.C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A42 (1990) 5794.

K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, Academic (1992) p.247; K.J. Schafer and K.C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A42 (1990) 5794.

van Linden van den Heuvell, H.B.

H.B. van Linden van den Heuvell and H.G. Muller, “Limiting cases of excess-photon ionization,” in S.J. Smith and P.L. Knight (eds.), “Studies in Modern Optics No. 8, Multiphoton processes”, p. 25–34, Cambridge University Press, Cambridge, (1988).

Walet, N.

M. Pont, N. Walet, M. Gavrila, and C.W. McCurdy, “Dichotomy of the hydrogen atom in superintense, high-frequency laser fields,” Phys. Rev. Lett. 61, 939 (1988)
[Crossref] [PubMed]

Walker, B.

B. Yang, K.J. Schafer, B. Walker, K.C. Kulander, P. Agostini, and L.F. DiMauro, “Intensity - dependent scattering ring in above-threshold ionization,” Phys. Rev. Lett. 71, 3770 (1993).
[Crossref] [PubMed]

Walther, H.

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

Xu, Huale

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

Yang, B.

B. Yang, K.J. Schafer, B. Walker, K.C. Kulander, P. Agostini, and L.F. DiMauro, “Intensity - dependent scattering ring in above-threshold ionization,” Phys. Rev. Lett. 71, 3770 (1993).
[Crossref] [PubMed]

Laser Phys. (1)

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

Phys. Rev. A (2)

H.G. Muller, “Numerical simulation of high-order above-threshold-ionization enhancement in argon,” Phys. Rev. A 60, 1341–50 (1999).
[Crossref]

T. Brabec, M.Yu. Ivanov, and P.B. Corkum, “Coulomb focusing in intense field atomic processes,” Phys. Rev. A 54, R2551–R2554 (1996).
[Crossref] [PubMed]

Phys. Rev. Lett. (6)

M. Pont, N. Walet, M. Gavrila, and C.W. McCurdy, “Dichotomy of the hydrogen atom in superintense, high-frequency laser fields,” Phys. Rev. Lett. 61, 939 (1988)
[Crossref] [PubMed]

G.G. Paulus, W. Nicklich, Huale Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72 (1994) 2851.
[Crossref] [PubMed]

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

B. Yang, K.J. Schafer, B. Walker, K.C. Kulander, P. Agostini, and L.F. DiMauro, “Intensity - dependent scattering ring in above-threshold ionization,” Phys. Rev. Lett. 71, 3770 (1993).
[Crossref] [PubMed]

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N.K. Rahman, “Free-free transitions following six photon ionization of xenon,” Phys. Rev. Lett. 42, 1127 (1979).
[Crossref]

H.G. Muller, “Tunneling excitation to resonant states in helium as the main source of super-ponderomotive electrons in the tunneling regime,” Phys. Rev. Lett. 83, 3158–61 (1999).
[Crossref]

Other (3)

H.G. Muller and M.V. Fedorov, Super-Intense Laser-Atom Physics V proceedings, NATO series, p. ix Wolters-Kluwer Academic Publishing, (1996).
[Crossref]

K.C. Kulander, K.J. Schafer, and J.L. Krause, “Time-dependent studies of multiphoton processes,” in Atoms in intense laser fields, ed. M. Gavrila, Academic (1992) p.247; K.J. Schafer and K.C. Kulander, “Energy analysis of time-dependent wave function: Application to above threshold ionization,” Phys. Rev. A42 (1990) 5794.

H.B. van Linden van den Heuvell and H.G. Muller, “Limiting cases of excess-photon ionization,” in S.J. Smith and P.L. Knight (eds.), “Studies in Modern Optics No. 8, Multiphoton processes”, p. 25–34, Cambridge University Press, Cambridge, (1988).

Supplementary Material (5)

» Media 1: MOV (1066 KB)     
» Media 2: MOV (968 KB)     
» Media 3: MOV (957 KB)     
» Media 4: MOV (1077 KB)     
» Media 5: MOV (1132 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Yield of electrons with energies larger than 100 eV as a function of the electric field amplitude E 0.

Fig. 2.
Fig. 2.

Resonance charge distribution at E 0=0.1284 a.u., which is obtained from the total wave function after removal of the ground state and primary continuum electrons. The state quivers over a distance of 40 Bohr in either direction, and avoids contact with the nucleus almost entirely. (Movie size 1.2 MB)

Fig. 3.
Fig. 3.

The resonance charge distribution at E 0=0.1296 a.u., which consists of five on-axis blobs that quiver over a distance of 40 Bohr in either direction. The movie (1.1 MB) shows how the charge density is revived as the lobes are focused on passing the nucleus.

Fig. 4.
Fig. 4.

The same resonance charge distribution as in Fig. 3 (at E 0=0.1296 a.u.), but shown as a contour plot, in which the decay products can be observed more clearly. (Movie size 1 MB.)

Fig. 5.
Fig. 5.

The resonance at E 0=0.1291 a.u., which shows both on-axis and off-axis features, plotted in the same way as Fig. 4. (Movie size 1.2 MB)

Fig. 6.
Fig. 6.

The resonant charge density at E 0=0.1265 a.u., plotted as in Fig. 4. (Movie size 1.3 MB) Note the small packet of fast electrons leaving along the axis.

Equations (2)

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i t Ψ ( t ) = H ( t ) Ψ ( t )
H ( t ) = 1 2 p 2 + V + A ( t ) · p .

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