Abstract

The evolution of low excited states of hydrogen in the presence of a strong light field is investigated by using the complex dilatation method with a finite basis of Slater-type functions. The method is applied for wavelengths of 592, 608, and 616 nm, which have been investigated experimentally. The results of the calculation are in agreement with experimental observations as far as comparison is possible.

© 1990 Optical Society of America

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  1. P. Agostini, J. Kupersztych, L. A. Lompré, G. Petite, F. Yergeau, “Direct evidence of ponderomotive effects via laser pulse duration in above-threshold ionization,” Phys. Rev. A 36, 4111–4114 (1987).
    [CrossRef] [PubMed]
  2. M. Crance, “Multiphoton stripping of atoms,” Phys. Rep. 144, 117–185 (1987).
    [CrossRef]
  3. R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, G. M. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
    [CrossRef] [PubMed]
  4. P. Agostini, A. Antonetti, P. Breger, M. Crance, A. Migus, H. G. Muller, G. Petite, “Resonant multiphoton ionization of xenon with high intensity femtosecond pulses,” J. Phys. B 22, 1971–1978 (1989).
    [CrossRef]
  5. P. Agostini, P. Breger, A. L’Huillier, H. G. Muller, G. Petite, A. Antonetti, A. Migus, “Giant Stark shifts in multiphoton ionization,” Phys. Rev. Lett. (to be published).
  6. H. Rottke, B. Wolff, M. Tapernon, D. Feldmann, K. H. Welge, “Resonant multiphoton ionization of xenon and atomic hydrogen in intense sub ps laser pulses,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).
  7. P. Avan, C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, “Effect of high frequency irradiation on the dynamical properties of weakly bound electrons,” J. Phys. (Paris) 37, 993–1009 (1976).
    [CrossRef]
  8. W. E. Cooke, R. R. Freeman, “The complex spatial structure of ion yield arising from high intensity multiphoton ionization,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).
  9. M. Crance, “Multiphoton ionization of hydrogen. A nonperturbative calculation of strong field effects,” J. Phys. B 21, 2697–2708 (1988).
    [CrossRef]
  10. S. I. Chu, W. P. Reinhardt, “Intense field multiphoton ionization via complex dressed states. Application to the hydrogen atom,” Phys. Rev. Lett. 39, 1195–1198 (1977).
    [CrossRef]
  11. R. M. Potvliege, R. Shakeshaft, “Theoretical aspects of multiphoton processes in intense laser fields,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).
  12. A. Maquet, S. I. Chu, W. P. Reinhardt, “Stark ionization in dc and ac fields: an L2 complex coordinate approach,” Phys. Rev. A 27, 2946–2970 (1983).
    [CrossRef]
  13. M. Crance, J. Sinzelle, “Multiphoton ionization of atoms in strong field. A nonperturbative method,” in Fundamentals of Laser InteractionsF. Ehlotzky, ed., Vol. 229 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1985), pp. 290–291.
    [CrossRef]
  14. S. I. Chu, J. Cooper, “Threshold shift and above-threshold ionization of atomic hydrogen in intense laser fields,” Phys. Rev. A 32, 2769–2775 (1985).
    [CrossRef] [PubMed]

1989 (1)

P. Agostini, A. Antonetti, P. Breger, M. Crance, A. Migus, H. G. Muller, G. Petite, “Resonant multiphoton ionization of xenon with high intensity femtosecond pulses,” J. Phys. B 22, 1971–1978 (1989).
[CrossRef]

1988 (1)

M. Crance, “Multiphoton ionization of hydrogen. A nonperturbative calculation of strong field effects,” J. Phys. B 21, 2697–2708 (1988).
[CrossRef]

1987 (3)

P. Agostini, J. Kupersztych, L. A. Lompré, G. Petite, F. Yergeau, “Direct evidence of ponderomotive effects via laser pulse duration in above-threshold ionization,” Phys. Rev. A 36, 4111–4114 (1987).
[CrossRef] [PubMed]

M. Crance, “Multiphoton stripping of atoms,” Phys. Rep. 144, 117–185 (1987).
[CrossRef]

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, G. M. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

1985 (1)

S. I. Chu, J. Cooper, “Threshold shift and above-threshold ionization of atomic hydrogen in intense laser fields,” Phys. Rev. A 32, 2769–2775 (1985).
[CrossRef] [PubMed]

1983 (1)

A. Maquet, S. I. Chu, W. P. Reinhardt, “Stark ionization in dc and ac fields: an L2 complex coordinate approach,” Phys. Rev. A 27, 2946–2970 (1983).
[CrossRef]

1977 (1)

S. I. Chu, W. P. Reinhardt, “Intense field multiphoton ionization via complex dressed states. Application to the hydrogen atom,” Phys. Rev. Lett. 39, 1195–1198 (1977).
[CrossRef]

1976 (1)

P. Avan, C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, “Effect of high frequency irradiation on the dynamical properties of weakly bound electrons,” J. Phys. (Paris) 37, 993–1009 (1976).
[CrossRef]

Agostini, P.

P. Agostini, A. Antonetti, P. Breger, M. Crance, A. Migus, H. G. Muller, G. Petite, “Resonant multiphoton ionization of xenon with high intensity femtosecond pulses,” J. Phys. B 22, 1971–1978 (1989).
[CrossRef]

P. Agostini, J. Kupersztych, L. A. Lompré, G. Petite, F. Yergeau, “Direct evidence of ponderomotive effects via laser pulse duration in above-threshold ionization,” Phys. Rev. A 36, 4111–4114 (1987).
[CrossRef] [PubMed]

P. Agostini, P. Breger, A. L’Huillier, H. G. Muller, G. Petite, A. Antonetti, A. Migus, “Giant Stark shifts in multiphoton ionization,” Phys. Rev. Lett. (to be published).

Antonetti, A.

P. Agostini, A. Antonetti, P. Breger, M. Crance, A. Migus, H. G. Muller, G. Petite, “Resonant multiphoton ionization of xenon with high intensity femtosecond pulses,” J. Phys. B 22, 1971–1978 (1989).
[CrossRef]

P. Agostini, P. Breger, A. L’Huillier, H. G. Muller, G. Petite, A. Antonetti, A. Migus, “Giant Stark shifts in multiphoton ionization,” Phys. Rev. Lett. (to be published).

Avan, P.

P. Avan, C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, “Effect of high frequency irradiation on the dynamical properties of weakly bound electrons,” J. Phys. (Paris) 37, 993–1009 (1976).
[CrossRef]

Breger, P.

P. Agostini, A. Antonetti, P. Breger, M. Crance, A. Migus, H. G. Muller, G. Petite, “Resonant multiphoton ionization of xenon with high intensity femtosecond pulses,” J. Phys. B 22, 1971–1978 (1989).
[CrossRef]

P. Agostini, P. Breger, A. L’Huillier, H. G. Muller, G. Petite, A. Antonetti, A. Migus, “Giant Stark shifts in multiphoton ionization,” Phys. Rev. Lett. (to be published).

Bucksbaum, P. H.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, G. M. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Chu, S. I.

S. I. Chu, J. Cooper, “Threshold shift and above-threshold ionization of atomic hydrogen in intense laser fields,” Phys. Rev. A 32, 2769–2775 (1985).
[CrossRef] [PubMed]

A. Maquet, S. I. Chu, W. P. Reinhardt, “Stark ionization in dc and ac fields: an L2 complex coordinate approach,” Phys. Rev. A 27, 2946–2970 (1983).
[CrossRef]

S. I. Chu, W. P. Reinhardt, “Intense field multiphoton ionization via complex dressed states. Application to the hydrogen atom,” Phys. Rev. Lett. 39, 1195–1198 (1977).
[CrossRef]

Cohen-Tannoudji, C.

P. Avan, C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, “Effect of high frequency irradiation on the dynamical properties of weakly bound electrons,” J. Phys. (Paris) 37, 993–1009 (1976).
[CrossRef]

Cooke, W. E.

W. E. Cooke, R. R. Freeman, “The complex spatial structure of ion yield arising from high intensity multiphoton ionization,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

Cooper, J.

S. I. Chu, J. Cooper, “Threshold shift and above-threshold ionization of atomic hydrogen in intense laser fields,” Phys. Rev. A 32, 2769–2775 (1985).
[CrossRef] [PubMed]

Crance, M.

P. Agostini, A. Antonetti, P. Breger, M. Crance, A. Migus, H. G. Muller, G. Petite, “Resonant multiphoton ionization of xenon with high intensity femtosecond pulses,” J. Phys. B 22, 1971–1978 (1989).
[CrossRef]

M. Crance, “Multiphoton ionization of hydrogen. A nonperturbative calculation of strong field effects,” J. Phys. B 21, 2697–2708 (1988).
[CrossRef]

M. Crance, “Multiphoton stripping of atoms,” Phys. Rep. 144, 117–185 (1987).
[CrossRef]

M. Crance, J. Sinzelle, “Multiphoton ionization of atoms in strong field. A nonperturbative method,” in Fundamentals of Laser InteractionsF. Ehlotzky, ed., Vol. 229 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1985), pp. 290–291.
[CrossRef]

Darack, S.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, G. M. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Dupont-Roc, J.

P. Avan, C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, “Effect of high frequency irradiation on the dynamical properties of weakly bound electrons,” J. Phys. (Paris) 37, 993–1009 (1976).
[CrossRef]

Fabre, C.

P. Avan, C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, “Effect of high frequency irradiation on the dynamical properties of weakly bound electrons,” J. Phys. (Paris) 37, 993–1009 (1976).
[CrossRef]

Feldmann, D.

H. Rottke, B. Wolff, M. Tapernon, D. Feldmann, K. H. Welge, “Resonant multiphoton ionization of xenon and atomic hydrogen in intense sub ps laser pulses,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

Freeman, R. R.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, G. M. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

W. E. Cooke, R. R. Freeman, “The complex spatial structure of ion yield arising from high intensity multiphoton ionization,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

Geusic, G. M.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, G. M. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Kupersztych, J.

P. Agostini, J. Kupersztych, L. A. Lompré, G. Petite, F. Yergeau, “Direct evidence of ponderomotive effects via laser pulse duration in above-threshold ionization,” Phys. Rev. A 36, 4111–4114 (1987).
[CrossRef] [PubMed]

L’Huillier, A.

P. Agostini, P. Breger, A. L’Huillier, H. G. Muller, G. Petite, A. Antonetti, A. Migus, “Giant Stark shifts in multiphoton ionization,” Phys. Rev. Lett. (to be published).

Lompré, L. A.

P. Agostini, J. Kupersztych, L. A. Lompré, G. Petite, F. Yergeau, “Direct evidence of ponderomotive effects via laser pulse duration in above-threshold ionization,” Phys. Rev. A 36, 4111–4114 (1987).
[CrossRef] [PubMed]

Maquet, A.

A. Maquet, S. I. Chu, W. P. Reinhardt, “Stark ionization in dc and ac fields: an L2 complex coordinate approach,” Phys. Rev. A 27, 2946–2970 (1983).
[CrossRef]

Migus, A.

P. Agostini, A. Antonetti, P. Breger, M. Crance, A. Migus, H. G. Muller, G. Petite, “Resonant multiphoton ionization of xenon with high intensity femtosecond pulses,” J. Phys. B 22, 1971–1978 (1989).
[CrossRef]

P. Agostini, P. Breger, A. L’Huillier, H. G. Muller, G. Petite, A. Antonetti, A. Migus, “Giant Stark shifts in multiphoton ionization,” Phys. Rev. Lett. (to be published).

Milchberg, H.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, G. M. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Muller, H. G.

P. Agostini, A. Antonetti, P. Breger, M. Crance, A. Migus, H. G. Muller, G. Petite, “Resonant multiphoton ionization of xenon with high intensity femtosecond pulses,” J. Phys. B 22, 1971–1978 (1989).
[CrossRef]

P. Agostini, P. Breger, A. L’Huillier, H. G. Muller, G. Petite, A. Antonetti, A. Migus, “Giant Stark shifts in multiphoton ionization,” Phys. Rev. Lett. (to be published).

Petite, G.

P. Agostini, A. Antonetti, P. Breger, M. Crance, A. Migus, H. G. Muller, G. Petite, “Resonant multiphoton ionization of xenon with high intensity femtosecond pulses,” J. Phys. B 22, 1971–1978 (1989).
[CrossRef]

P. Agostini, J. Kupersztych, L. A. Lompré, G. Petite, F. Yergeau, “Direct evidence of ponderomotive effects via laser pulse duration in above-threshold ionization,” Phys. Rev. A 36, 4111–4114 (1987).
[CrossRef] [PubMed]

P. Agostini, P. Breger, A. L’Huillier, H. G. Muller, G. Petite, A. Antonetti, A. Migus, “Giant Stark shifts in multiphoton ionization,” Phys. Rev. Lett. (to be published).

Potvliege, R. M.

R. M. Potvliege, R. Shakeshaft, “Theoretical aspects of multiphoton processes in intense laser fields,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

Reinhardt, W. P.

A. Maquet, S. I. Chu, W. P. Reinhardt, “Stark ionization in dc and ac fields: an L2 complex coordinate approach,” Phys. Rev. A 27, 2946–2970 (1983).
[CrossRef]

S. I. Chu, W. P. Reinhardt, “Intense field multiphoton ionization via complex dressed states. Application to the hydrogen atom,” Phys. Rev. Lett. 39, 1195–1198 (1977).
[CrossRef]

Rottke, H.

H. Rottke, B. Wolff, M. Tapernon, D. Feldmann, K. H. Welge, “Resonant multiphoton ionization of xenon and atomic hydrogen in intense sub ps laser pulses,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

Schumacher, D.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, G. M. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Shakeshaft, R.

R. M. Potvliege, R. Shakeshaft, “Theoretical aspects of multiphoton processes in intense laser fields,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

Sinzelle, J.

M. Crance, J. Sinzelle, “Multiphoton ionization of atoms in strong field. A nonperturbative method,” in Fundamentals of Laser InteractionsF. Ehlotzky, ed., Vol. 229 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1985), pp. 290–291.
[CrossRef]

Tapernon, M.

H. Rottke, B. Wolff, M. Tapernon, D. Feldmann, K. H. Welge, “Resonant multiphoton ionization of xenon and atomic hydrogen in intense sub ps laser pulses,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

Welge, K. H.

H. Rottke, B. Wolff, M. Tapernon, D. Feldmann, K. H. Welge, “Resonant multiphoton ionization of xenon and atomic hydrogen in intense sub ps laser pulses,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

Wolff, B.

H. Rottke, B. Wolff, M. Tapernon, D. Feldmann, K. H. Welge, “Resonant multiphoton ionization of xenon and atomic hydrogen in intense sub ps laser pulses,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

Yergeau, F.

P. Agostini, J. Kupersztych, L. A. Lompré, G. Petite, F. Yergeau, “Direct evidence of ponderomotive effects via laser pulse duration in above-threshold ionization,” Phys. Rev. A 36, 4111–4114 (1987).
[CrossRef] [PubMed]

J. Phys. (Paris) (1)

P. Avan, C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, “Effect of high frequency irradiation on the dynamical properties of weakly bound electrons,” J. Phys. (Paris) 37, 993–1009 (1976).
[CrossRef]

J. Phys. B (2)

M. Crance, “Multiphoton ionization of hydrogen. A nonperturbative calculation of strong field effects,” J. Phys. B 21, 2697–2708 (1988).
[CrossRef]

P. Agostini, A. Antonetti, P. Breger, M. Crance, A. Migus, H. G. Muller, G. Petite, “Resonant multiphoton ionization of xenon with high intensity femtosecond pulses,” J. Phys. B 22, 1971–1978 (1989).
[CrossRef]

Phys. Rep. (1)

M. Crance, “Multiphoton stripping of atoms,” Phys. Rep. 144, 117–185 (1987).
[CrossRef]

Phys. Rev. A (3)

A. Maquet, S. I. Chu, W. P. Reinhardt, “Stark ionization in dc and ac fields: an L2 complex coordinate approach,” Phys. Rev. A 27, 2946–2970 (1983).
[CrossRef]

P. Agostini, J. Kupersztych, L. A. Lompré, G. Petite, F. Yergeau, “Direct evidence of ponderomotive effects via laser pulse duration in above-threshold ionization,” Phys. Rev. A 36, 4111–4114 (1987).
[CrossRef] [PubMed]

S. I. Chu, J. Cooper, “Threshold shift and above-threshold ionization of atomic hydrogen in intense laser fields,” Phys. Rev. A 32, 2769–2775 (1985).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, G. M. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

S. I. Chu, W. P. Reinhardt, “Intense field multiphoton ionization via complex dressed states. Application to the hydrogen atom,” Phys. Rev. Lett. 39, 1195–1198 (1977).
[CrossRef]

Other (5)

R. M. Potvliege, R. Shakeshaft, “Theoretical aspects of multiphoton processes in intense laser fields,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

W. E. Cooke, R. R. Freeman, “The complex spatial structure of ion yield arising from high intensity multiphoton ionization,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

P. Agostini, P. Breger, A. L’Huillier, H. G. Muller, G. Petite, A. Antonetti, A. Migus, “Giant Stark shifts in multiphoton ionization,” Phys. Rev. Lett. (to be published).

H. Rottke, B. Wolff, M. Tapernon, D. Feldmann, K. H. Welge, “Resonant multiphoton ionization of xenon and atomic hydrogen in intense sub ps laser pulses,” in Fundamentals of Laser Interactions II, F. Ehlotzky, ed. (Springer-Verlag, Berlin, to be published).

M. Crance, J. Sinzelle, “Multiphoton ionization of atoms in strong field. A nonperturbative method,” in Fundamentals of Laser InteractionsF. Ehlotzky, ed., Vol. 229 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1985), pp. 290–291.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Eigenenergy spectrum for the dressed hydrogen atom. The real part of the eigenenergy is plotted as a solid curve when the imaginary part is smaller than 0.4 × 10−2 hartree and as a dashed curve when the imaginary part is between 0.4 × 10−2 and 10−2 hartree. Dotted–dashed lines indicate the thresholds. States are labeled by continuity with the field-free state from which they are issued. Labels have been written for the strong field in order to identify parts of the spectrum; however they are somewhat arbitrary since field-free basis states are spread over several eigenstates. Energies are in hartrees, their origin being the energy of the field-free state |2p|〉|N〉. The intensities are given in units of 1013 W cm−2. The intensity scale is linear in the field amplitude. The wavelength of the light field is (a) 592 nm; (b) 608 nm; (c) 616 nm.

Fig. 2
Fig. 2

Peaks in the electron energy spectrum as predicted by the present calculation. The net number of absorbed photons, q, is given. Each peak is labeled by the field-free state from which it is issued. The upper part of the diagram shows the major peaks observed by Rottke et al.6 Each group (first four peaks; next three peaks) is seated on a broad background.

Tables (1)

Tables Icon

Table 1 Intensity at Which the Rabi Frequency Equals the Detuning from Resonance (in units of 1013 W cm−2)

Equations (3)

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H = H A + H F + W ,
E 0 + δ I + q ω = + Δ i .
I ( q ) = ( E 0 + q ω E ) / ( Δ δ ) .

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