Abstract

A model of strong bound-free coupling by a stochastic train of delta-function impulses is solved analytically. The model can be used to describe transitions caused by strong isolated collisions. The decay of bound-state population and photoelectron spectra is discussed, and the limits of the applicability of Fermi’s Golden Rule are evaluated. It turns out that the results depend nontrivially on the statistics of the driving signal.

© 1988 Optical Society of America

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References

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  1. N. B. Delone, V. P. Krainov, in Atoms in Strong Light Fields, Vol. 28 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1985).
    [CrossRef]
  2. P. Lambropoulos, Appl. Opt. 19, 3926 (1980).
    [CrossRef] [PubMed]
  3. P. Lambropoulos, P. Zoller, Phys. Rev. A 24, 379 (1981).
    [CrossRef]
  4. K. Rza̧żewski, J. H. Eberly, Phys. Rev. Lett. 47, 408 (1981).
    [CrossRef]
  5. K. Rza̧żewski, J. H. Eberly, Phys. Rev. A 27, 2026 (1983).
    [CrossRef]
  6. G. S. Agarwal, S. L. Haan, K. Burnett, J. Cooper, Phys. Rev. Lett. 48, 1164 (1982).
    [CrossRef]
  7. P. E. Coleman, P. L. Knight, J. Phys. B 15, L235 (1982).
    [CrossRef]
  8. M. Lewenstein, J. Haus, K. Rza̧żewski, Phys. Rev. Lett. 50, 417 (1983).
    [CrossRef]
  9. A. I. Andryushin, A. E. Kazakov, M. V. Fedorov, Zh. Eksp. Teor. Fiz. 82, 91 (1982) [Sov. Phys. JETP 55, 53 (1982)].
  10. K. Rza̧żewski, J. Mostowski, Phys. Rev. A 35, 4414 (1987).
    [CrossRef]
  11. U. Fano, Phys. Rev. 124, 1866 (1961).
    [CrossRef]

1987

K. Rza̧żewski, J. Mostowski, Phys. Rev. A 35, 4414 (1987).
[CrossRef]

1983

M. Lewenstein, J. Haus, K. Rza̧żewski, Phys. Rev. Lett. 50, 417 (1983).
[CrossRef]

K. Rza̧żewski, J. H. Eberly, Phys. Rev. A 27, 2026 (1983).
[CrossRef]

1982

G. S. Agarwal, S. L. Haan, K. Burnett, J. Cooper, Phys. Rev. Lett. 48, 1164 (1982).
[CrossRef]

P. E. Coleman, P. L. Knight, J. Phys. B 15, L235 (1982).
[CrossRef]

A. I. Andryushin, A. E. Kazakov, M. V. Fedorov, Zh. Eksp. Teor. Fiz. 82, 91 (1982) [Sov. Phys. JETP 55, 53 (1982)].

1981

P. Lambropoulos, P. Zoller, Phys. Rev. A 24, 379 (1981).
[CrossRef]

K. Rza̧żewski, J. H. Eberly, Phys. Rev. Lett. 47, 408 (1981).
[CrossRef]

1980

1961

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, S. L. Haan, K. Burnett, J. Cooper, Phys. Rev. Lett. 48, 1164 (1982).
[CrossRef]

Andryushin, A. I.

A. I. Andryushin, A. E. Kazakov, M. V. Fedorov, Zh. Eksp. Teor. Fiz. 82, 91 (1982) [Sov. Phys. JETP 55, 53 (1982)].

Burnett, K.

G. S. Agarwal, S. L. Haan, K. Burnett, J. Cooper, Phys. Rev. Lett. 48, 1164 (1982).
[CrossRef]

Coleman, P. E.

P. E. Coleman, P. L. Knight, J. Phys. B 15, L235 (1982).
[CrossRef]

Cooper, J.

G. S. Agarwal, S. L. Haan, K. Burnett, J. Cooper, Phys. Rev. Lett. 48, 1164 (1982).
[CrossRef]

Delone, N. B.

N. B. Delone, V. P. Krainov, in Atoms in Strong Light Fields, Vol. 28 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1985).
[CrossRef]

Eberly, J. H.

K. Rza̧żewski, J. H. Eberly, Phys. Rev. A 27, 2026 (1983).
[CrossRef]

K. Rza̧żewski, J. H. Eberly, Phys. Rev. Lett. 47, 408 (1981).
[CrossRef]

Fano, U.

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Fedorov, M. V.

A. I. Andryushin, A. E. Kazakov, M. V. Fedorov, Zh. Eksp. Teor. Fiz. 82, 91 (1982) [Sov. Phys. JETP 55, 53 (1982)].

Haan, S. L.

G. S. Agarwal, S. L. Haan, K. Burnett, J. Cooper, Phys. Rev. Lett. 48, 1164 (1982).
[CrossRef]

Haus, J.

M. Lewenstein, J. Haus, K. Rza̧żewski, Phys. Rev. Lett. 50, 417 (1983).
[CrossRef]

Kazakov, A. E.

A. I. Andryushin, A. E. Kazakov, M. V. Fedorov, Zh. Eksp. Teor. Fiz. 82, 91 (1982) [Sov. Phys. JETP 55, 53 (1982)].

Knight, P. L.

P. E. Coleman, P. L. Knight, J. Phys. B 15, L235 (1982).
[CrossRef]

Krainov, V. P.

N. B. Delone, V. P. Krainov, in Atoms in Strong Light Fields, Vol. 28 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1985).
[CrossRef]

Lambropoulos, P.

P. Lambropoulos, P. Zoller, Phys. Rev. A 24, 379 (1981).
[CrossRef]

P. Lambropoulos, Appl. Opt. 19, 3926 (1980).
[CrossRef] [PubMed]

Lewenstein, M.

M. Lewenstein, J. Haus, K. Rza̧żewski, Phys. Rev. Lett. 50, 417 (1983).
[CrossRef]

Mostowski, J.

K. Rza̧żewski, J. Mostowski, Phys. Rev. A 35, 4414 (1987).
[CrossRef]

Rza¸zewski, K.

K. Rza̧żewski, J. Mostowski, Phys. Rev. A 35, 4414 (1987).
[CrossRef]

M. Lewenstein, J. Haus, K. Rza̧żewski, Phys. Rev. Lett. 50, 417 (1983).
[CrossRef]

K. Rza̧żewski, J. H. Eberly, Phys. Rev. A 27, 2026 (1983).
[CrossRef]

K. Rza̧żewski, J. H. Eberly, Phys. Rev. Lett. 47, 408 (1981).
[CrossRef]

Zoller, P.

P. Lambropoulos, P. Zoller, Phys. Rev. A 24, 379 (1981).
[CrossRef]

Appl. Opt.

J. Phys. B

P. E. Coleman, P. L. Knight, J. Phys. B 15, L235 (1982).
[CrossRef]

Phys. Rev.

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Phys. Rev. A

K. Rza̧żewski, J. Mostowski, Phys. Rev. A 35, 4414 (1987).
[CrossRef]

P. Lambropoulos, P. Zoller, Phys. Rev. A 24, 379 (1981).
[CrossRef]

K. Rza̧żewski, J. H. Eberly, Phys. Rev. A 27, 2026 (1983).
[CrossRef]

Phys. Rev. Lett.

G. S. Agarwal, S. L. Haan, K. Burnett, J. Cooper, Phys. Rev. Lett. 48, 1164 (1982).
[CrossRef]

K. Rza̧żewski, J. H. Eberly, Phys. Rev. Lett. 47, 408 (1981).
[CrossRef]

M. Lewenstein, J. Haus, K. Rza̧żewski, Phys. Rev. Lett. 50, 417 (1983).
[CrossRef]

Zh. Eksp. Teor. Fiz.

A. I. Andryushin, A. E. Kazakov, M. V. Fedorov, Zh. Eksp. Teor. Fiz. 82, 91 (1982) [Sov. Phys. JETP 55, 53 (1982)].

Other

N. B. Delone, V. P. Krainov, in Atoms in Strong Light Fields, Vol. 28 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1985).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Bound-state population versus time measured in units of the averaged dead time 1/Γ. Kick strengths are symmetrically distributed with qn) = (1/2)[δn − λ) + δn + λ)]. The solid curves display the approximation by Fermi’s Golden Rule. The parameters are (a) γ/Γ = 1 (i.e., ζ = 1/3) and λ = π/12, (b) γ/Γ = 0.01 (i.e., ζ = 0.98) and λ = π/12, (c) γ/Γ = 0.01 and λ = π/3.

Fig. 2
Fig. 2

Energy spectrum of the photoelectrons for symmetrically distributed kick strengths [see Fig. 1(a)] versus ω measured in units of ω0. The dotted curve represents the bare shape of the continuum |(ω)|2. The parameters are γ/Γ = 0.01 and ω0/Γ = 0.1.

Fig. 3
Fig. 3

Same as Fig. 1(a) for uniform kicks, i.e., qn) = δn − λ). Here, γ/Γ = 0.01, λ = π/12, and ω0/Γ = 2 (exponential curve), ω0/Γ = 0.1 (damped oscillations).

Fig. 4
Fig. 4

Same as Fig. 2 for uniform kicks. Here, γ/Γ = 0.01 and λ = π/12.

Equations (36)

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H 0 0 = E 0 0 ,
H 0 ω = ω ω .
0 0 = 1 ,
ω ω = δ ( ω - ω ) .
H int = - S ( t ) X ^ ,
S ( t ) = n = 0 λ n δ ( t - t n ) ,
X ^ = - + d ω ( ω ) 0 ω + H . c . ,
( ω ) = ( γ π ) 1 / 2 1 ω - ω 0 - i γ
T n t n - t n - 1 ,             n = 1 , 2 , ,
p ( T n ) = Γ exp ( - Γ T n ) .
a n 0 ρ ¯ n 0 ,
W ( ω ) lim n ω ρ ¯ n ω .
ρ n + 1 = U n + 1 · ρ n · U n + 1 + = exp ( i L n + 1 ) ρ n .
U n + 1 = exp ( - i T n + 1 H 0 ) exp ( i λ n X ^ ) ,
exp ( i λ n X ^ ) = cos ( λ n ) 0 0 + i sin ( λ n ) X ^ + d ω d ω { δ ( ω - ω ) + [ cos ( λ n ) - 1 ] × * ( ω ) ( ω ) } ω ω .
ρ ¯ n = a n 0 0 + d ω [ i ( ω ) b n * ( ω ) 0 ω + H . c , ] + d ω d ω * ( ω ) ( ω ) g n ( ω , ω ) ω ω ,
a n + 1 = ( 1 - s 2 ¯ ) a n + s 2 ¯ G n + s c ¯ [ B n + B n * ] ,
b n + 1 ( ω ) = i Γ ω - i Γ ( s c ¯ a n + ( s ¯ - s c ¯ ) G n - s ¯ g n ( ω ) - c ¯ b n ( ω ) + ( c ¯ + c 2 ¯ ) B n + s 2 ¯ B n * ) ,
g n + 1 ( ω , ω ) = - i Γ ω - ω - i Γ { s 2 ¯ a n + ( 1 - c ) 2 ¯ G n - ( 1 - c ¯ ) [ g n ( ω ) + g n * ( ω ) ] + g n ( ω , ω ) + ( s ¯ - s c ¯ ) [ B n + B n * ] - s ¯ [ b n ( ω ) + b n * ( ω ) ] } ,
s k c 1 ¯ = d λ n q ( λ n ) sin ( λ n ) k cos ( λ n ) 1 ,
B n = d ω b n ( ω ) ( ω ) 2 ,
g n ( ω ) = d ω g n ( ω , ω ) ( ω ) 2 ,
G n = d ω g n ( ω ) ( ω ) 2 .
a 0 = 1 ,
b 0 ( ω ) = g 0 ( ω , ω ) = 0 ,
g n + 1 ( ω ) = c ¯ Δ ( ω ) g n ( ω ) + Δ ( ω ) [ s 2 ¯ a n - ( c ¯ - c 2 ¯ ) G n ] ,
Δ ( ω ) = - i Γ ω - ω 0 - i ( Γ + γ ) .
d ω u ( ω ) v ( ω ) ( ω ) 2 = d ω u ( ω ) ( ω ) 2 d ω v ( ω ) ( ω ) 2 ,
G n + 1 = ζ s 2 ¯ a n + ζ c 2 ¯ G n ,
ζ = Γ Γ + 2 γ ,
a n = ( c 2 ¯ - λ - ) 2 ( c 2 ¯ - λ - ) 2 + ( s 2 ¯ ) 2 ζ [ λ + n + ( s 2 ¯ ) 2 ζ ( c 2 ¯ - λ - ) 2 λ - n ] ,
λ + , - = ½ { ( 1 + ζ ) c 2 ¯ ± [ ( c 2 ¯ ) 2 ( 1 - ζ ) 2 + 4 ζ ( s 2 ¯ ) 2 ] 1 / 2 } .
W ( ω ) ( ω ) 2 g ( ω , ω )
g ( ω , ω ) = s 2 ¯ n = 0 ( a n - G n ) + ( 1 - c ¯ ) n = 0 { [ G n - g n ( ω ) ] + c . c . } ,
W ( ω ) = ( ω ) 2 { 1 + Γ ^ γ [ 1 - ( Γ ^ + γ ) ( Γ ^ + 2 γ ) ( ω - ω 0 ) 2 + ( Γ ^ + γ ) 2 ] } ,
Γ ^ = Γ ( 1 - c ¯ ) ,

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