Abstract

Above-threshold ionization photoelectron spectra are computed for an exactly solvable model. We predict that there will be no trapping or saturation of the bound–continuum transition and that the ionization rate is independent of the redistribution of the electron between the two continua. We find symmetric peaks about the ionization energy, and these peaks appear only during the ionization process.

© 1990 Optical Society of America

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References

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  1. P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979);P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988), and references therein.
    [CrossRef]
  2. P. Corkum, C. Rolland, and T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1987).
    [CrossRef]
  3. Z. Deng and J. H. Eberly, Phys. Rev. Lett. 53, 1810 (1984);J. Opt. Soc. Am. B 2, 486 (1985).
    [CrossRef]
  4. H. G. Muller, H. B. van den Heuvell, and M. J. van der Wiel, J. Phys. B 19, L733 (1986).
    [CrossRef]
  5. K. Rza̧żewski, L. Wang, and J. W. Haus, Phys. Rev. A 40, 3453 (1989).
    [CrossRef]
  6. M. Trippenbach, K. Rza̧żewski, M. V. Federov, and A. E. Kazakov, J. Phys. B 22, 1193 (1989).
    [CrossRef]
  7. L. V. Keldysh, Zh. Eksp.Teor. Fiz 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].
  8. F. H. M. Faisal, J. Phys B 6, L312 (1973);H. R. Reiss, Phys. Rev. A 22, 1786 (1980).
    [CrossRef]
  9. D. M. Volkov, Z. Phys. 94, 250 (1935).
    [CrossRef]
  10. J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988);L. A. Collins and A. L. Merts, Phys. Rev. A 37, 2415 (1988).
    [CrossRef] [PubMed]
  11. P. W. Milonni, Phys. Rev. A 38, 2682 (1988).
    [CrossRef] [PubMed]
  12. L. Roso-Franco, K. Rza̧żewski, and J. H. Eberly, in Technical Digest of Optical Society of America 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), paper FM3.
  13. C. Leone, S. Bivona, R. Burlon, and G. Ferrante, Phys. Rev. A 38, 5642 (1988).
    [CrossRef] [PubMed]

1989 (2)

K. Rza̧żewski, L. Wang, and J. W. Haus, Phys. Rev. A 40, 3453 (1989).
[CrossRef]

M. Trippenbach, K. Rza̧żewski, M. V. Federov, and A. E. Kazakov, J. Phys. B 22, 1193 (1989).
[CrossRef]

1988 (3)

J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988);L. A. Collins and A. L. Merts, Phys. Rev. A 37, 2415 (1988).
[CrossRef] [PubMed]

P. W. Milonni, Phys. Rev. A 38, 2682 (1988).
[CrossRef] [PubMed]

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, Phys. Rev. A 38, 5642 (1988).
[CrossRef] [PubMed]

1987 (1)

P. Corkum, C. Rolland, and T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1987).
[CrossRef]

1986 (1)

H. G. Muller, H. B. van den Heuvell, and M. J. van der Wiel, J. Phys. B 19, L733 (1986).
[CrossRef]

1984 (1)

Z. Deng and J. H. Eberly, Phys. Rev. Lett. 53, 1810 (1984);J. Opt. Soc. Am. B 2, 486 (1985).
[CrossRef]

1979 (1)

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979);P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988), and references therein.
[CrossRef]

1973 (1)

F. H. M. Faisal, J. Phys B 6, L312 (1973);H. R. Reiss, Phys. Rev. A 22, 1786 (1980).
[CrossRef]

1964 (1)

L. V. Keldysh, Zh. Eksp.Teor. Fiz 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].

1935 (1)

D. M. Volkov, Z. Phys. 94, 250 (1935).
[CrossRef]

Agostini, P.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979);P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988), and references therein.
[CrossRef]

Bivona, S.

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, Phys. Rev. A 38, 5642 (1988).
[CrossRef] [PubMed]

Burlon, R.

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, Phys. Rev. A 38, 5642 (1988).
[CrossRef] [PubMed]

Corkum, P.

P. Corkum, C. Rolland, and T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1987).
[CrossRef]

Deng, Z.

Z. Deng and J. H. Eberly, Phys. Rev. Lett. 53, 1810 (1984);J. Opt. Soc. Am. B 2, 486 (1985).
[CrossRef]

Eberly, J. H.

J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988);L. A. Collins and A. L. Merts, Phys. Rev. A 37, 2415 (1988).
[CrossRef] [PubMed]

Z. Deng and J. H. Eberly, Phys. Rev. Lett. 53, 1810 (1984);J. Opt. Soc. Am. B 2, 486 (1985).
[CrossRef]

L. Roso-Franco, K. Rza̧żewski, and J. H. Eberly, in Technical Digest of Optical Society of America 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), paper FM3.

Fabre, F.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979);P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988), and references therein.
[CrossRef]

Faisal, F. H. M.

F. H. M. Faisal, J. Phys B 6, L312 (1973);H. R. Reiss, Phys. Rev. A 22, 1786 (1980).
[CrossRef]

Federov, M. V.

M. Trippenbach, K. Rza̧żewski, M. V. Federov, and A. E. Kazakov, J. Phys. B 22, 1193 (1989).
[CrossRef]

Ferrante, G.

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, Phys. Rev. A 38, 5642 (1988).
[CrossRef] [PubMed]

Haus, J. W.

K. Rza̧żewski, L. Wang, and J. W. Haus, Phys. Rev. A 40, 3453 (1989).
[CrossRef]

Javanainen, J.

J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988);L. A. Collins and A. L. Merts, Phys. Rev. A 37, 2415 (1988).
[CrossRef] [PubMed]

Kazakov, A. E.

M. Trippenbach, K. Rza̧żewski, M. V. Federov, and A. E. Kazakov, J. Phys. B 22, 1193 (1989).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, Zh. Eksp.Teor. Fiz 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].

Leone, C.

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, Phys. Rev. A 38, 5642 (1988).
[CrossRef] [PubMed]

Mainfray, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979);P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988), and references therein.
[CrossRef]

Milonni, P. W.

P. W. Milonni, Phys. Rev. A 38, 2682 (1988).
[CrossRef] [PubMed]

Muller, H. G.

H. G. Muller, H. B. van den Heuvell, and M. J. van der Wiel, J. Phys. B 19, L733 (1986).
[CrossRef]

Petite, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979);P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988), and references therein.
[CrossRef]

Rahman, N. K.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979);P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988), and references therein.
[CrossRef]

Rolland, C.

P. Corkum, C. Rolland, and T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1987).
[CrossRef]

Roso-Franco, L.

L. Roso-Franco, K. Rza̧żewski, and J. H. Eberly, in Technical Digest of Optical Society of America 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), paper FM3.

Rza¸zewski, K.

M. Trippenbach, K. Rza̧żewski, M. V. Federov, and A. E. Kazakov, J. Phys. B 22, 1193 (1989).
[CrossRef]

K. Rza̧żewski, L. Wang, and J. W. Haus, Phys. Rev. A 40, 3453 (1989).
[CrossRef]

L. Roso-Franco, K. Rza̧żewski, and J. H. Eberly, in Technical Digest of Optical Society of America 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), paper FM3.

Srinivasan-Rao, T.

P. Corkum, C. Rolland, and T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1987).
[CrossRef]

Trippenbach, M.

M. Trippenbach, K. Rza̧żewski, M. V. Federov, and A. E. Kazakov, J. Phys. B 22, 1193 (1989).
[CrossRef]

van den Heuvell, H. B.

H. G. Muller, H. B. van den Heuvell, and M. J. van der Wiel, J. Phys. B 19, L733 (1986).
[CrossRef]

van der Wiel, M. J.

H. G. Muller, H. B. van den Heuvell, and M. J. van der Wiel, J. Phys. B 19, L733 (1986).
[CrossRef]

Volkov, D. M.

D. M. Volkov, Z. Phys. 94, 250 (1935).
[CrossRef]

Wang, L.

K. Rza̧żewski, L. Wang, and J. W. Haus, Phys. Rev. A 40, 3453 (1989).
[CrossRef]

J. Phys B (1)

F. H. M. Faisal, J. Phys B 6, L312 (1973);H. R. Reiss, Phys. Rev. A 22, 1786 (1980).
[CrossRef]

J. Phys. B (3)

M. Trippenbach, K. Rza̧żewski, M. V. Federov, and A. E. Kazakov, J. Phys. B 22, 1193 (1989).
[CrossRef]

H. G. Muller, H. B. van den Heuvell, and M. J. van der Wiel, J. Phys. B 19, L733 (1986).
[CrossRef]

J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988);L. A. Collins and A. L. Merts, Phys. Rev. A 37, 2415 (1988).
[CrossRef] [PubMed]

Phys. Rev. A (3)

P. W. Milonni, Phys. Rev. A 38, 2682 (1988).
[CrossRef] [PubMed]

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, Phys. Rev. A 38, 5642 (1988).
[CrossRef] [PubMed]

K. Rza̧żewski, L. Wang, and J. W. Haus, Phys. Rev. A 40, 3453 (1989).
[CrossRef]

Phys. Rev. Lett. (3)

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, Phys. Rev. Lett. 42, 1127 (1979);P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988), and references therein.
[CrossRef]

P. Corkum, C. Rolland, and T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1987).
[CrossRef]

Z. Deng and J. H. Eberly, Phys. Rev. Lett. 53, 1810 (1984);J. Opt. Soc. Am. B 2, 486 (1985).
[CrossRef]

Z. Phys. (1)

D. M. Volkov, Z. Phys. 94, 250 (1935).
[CrossRef]

Zh. Eksp.Teor. Fiz (1)

L. V. Keldysh, Zh. Eksp.Teor. Fiz 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].

Other (1)

L. Roso-Franco, K. Rza̧żewski, and J. H. Eberly, in Technical Digest of Optical Society of America 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), paper FM3.

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Figures (4)

Fig. 1
Fig. 1

R = 10−4, B = 5, T0 = 400π/ωL1, and T1 = T0/2. The inset in each figure shows the ground-state population (dashed curve) and the redistribution pulse envelope (solid curve). The window extends over the time range (−T0/2, T0/2). (a) t0 = −T0/2, (b) t0 = −T0/4, (c) t0 = 0, (d) t0 = T0/4.

Fig. 2
Fig. 2

R = 0.1, B = 5, T0 = 400π/ωL1, and T1 = T0/2. The insets are as in Fig. 1: (a) t0 = −T0/2, (b) t0 = −T0/4, (c) t0 = 0.

Fig. 3
Fig. 3

As for Fig. 2 except that R = 0.1, B = 5, T1 = T0/4.

Fig. 4
Fig. 4

B = 5, T0 = 40π/ωL1, and T1 = T0. (a) R = 10−4, (b) R = 0.1, (c) R = 1. In (a) the population of the ground state is not noticeably changed from unity.

Equations (26)

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| ψ ( t ) = α ( t ) | 0 + d ω C 1 ( ω , t ) | ω , + d ω C 2 ( ω , t ) | ω , + .
= E 0 | 0 0 | + d ω ω { | ω , , ω | + | ω , + + , ω | } + { V i ( t ) exp ( i ω L 0 t ) | 0 d ω , ω | + V 1 ( t ) cos ( ω L 1 t ) × d ω d ω D ( ω ω ) | ω , + , ω | + H . c . } ,
d α ( t ) d t = i V i ( t ) d ω C 1 ( ω , t ) ,
d C 1 ( ω , t ) d t = i ω C 1 ( ω , t ) i V i ( t ) α ( t ) i V 1 ( t ) cos ( ω L 1 t ) × d ω D ( ω ω ) C 2 ( ω , t ) ,
d C 2 ( ω , t ) d t = i ω C 2 ( ω , t ) i V 1 ( t ) cos ( ω L 1 t ) d ω D ( ω ω ) C 1 ( ω , t ) .
α ( 0 ) = 1 .
Ĉ i ( x , t ) = d ω exp ( i x ω ) C i ( ω , t ) .
E p 0 2 2 m + p 0 Δ p m .
Ĉ 1 ( x , t ) t = x Ĉ 1 ( x , t ) i 2 π V i ( t ) α ( t ) δ ( x ) i V 1 ( t ) cos ( ω L 1 t ) D ̂ ( x ) Ĉ 2 ( x , t ) ,
Ĉ 2 ( x , t ) t = x Ĉ 2 ( x , t ) i V 1 ( t ) cos ( ω L 1 t ) D ̂ ( x ) Ĉ 1 ( x , t ) ,
d α ( t ) d t = i V i ( t ) Ĉ 1 ( 0 , t ) ,
d d η Ĉ 1 ( η , ζ ) = i 2 π V i ( ζ + η ) α ( ζ + η ) δ ( η ) i V 1 ( ζ + η ) cos ω L 1 ( ζ + η ) D ̂ ( η ) C 2 ( η , ζ ) , d d η C 2 ( η , ζ ) = i V 1 ( ζ + η ) cos ω L 1 ( ζ + η ) D ̂ ( η ) C 2 ( η , ζ ) .
d S ( ζ , η ) d η = i 2 π V i ( ζ + η ) α ( ζ + η ) δ ( η ) i V 1 ( ζ + η ) cos ω L 1 ( ζ + η ) D ̂ ( η ) S ( ζ , η )
d Δ ( ζ , η ) d η = i 2 π V i ( ζ + η ) α ( ζ + η ) δ ( η ) + i V 1 ( ζ + η ) cos ω L 1 ( ζ + η ) D ̂ ( η ) Δ ( ζ , η ) .
S ( x , t ) = i 2 π V i ( t x ) α ( t x ) [ θ ( x t ) θ ( x ) ] × exp { i 0 x D ̂ ( u ) V i ( u + t x ) cos [ ω L 1 ( u + t x ) ] d u }
Δ ( x , t ) = i 2 π V i ( t x ) α ( t x ) [ θ ( x t ) θ ( x ) ] × exp { i 0 x D ̂ ( u ) V i ( u + t x ) cos [ ω L 1 ( u + t x ) ] du } .
Ĉ 1 ( 0 , t ) = i π V i ( t ) α ( t ) .
α ( t ) = exp [ π t V i 2 ( u ) d u ] .
C 1 ( ω , t ) = i 0 t d x exp ( i ω x ) V i ( t x ) exp [ π t x d u V i 2 ( u ) ] × cos [ t x t d u D ̂ ( u t + x ) V 1 ( u ) cos ( ω L 1 u ) ]
C 2 ( ω , t ) = 0 t d x exp ( i ω x ) V i ( t x ) exp [ π t x d u V i 2 ( u ) ] × sin [ t x t d u D ̂ ( u t + x ) V 1 ( u ) cos ( ω L 1 u ) ] .
V i ( t ) = V 0 f 0 ( t ) ,
R = π V 0 2 .
f 0 ( t ) = { cos 2 ( π t T 0 ) T 0 2 < t < T 0 2 0 otherwise .
V 1 ( t ) = { A cos 2 [ π T 1 ( t + t 0 ) ] T 1 2 < t + t 0 < T 1 2 0 otherwise .
D ( ω ) = d 2 π [ 1 ( ω + i ) 2 + c . c . ] .
S ( ω ) = | C 1 ( ω , t ) | 2 + | C 2 ( ω , t ) | 2

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