Abstract

Two analytical methods for computing ionization by high-frequency fields are compared. Predicted ionization rates compare well, but energy predictions for the onset of ionization differ radically. The difference is shown to arise from the use of a transformation in one of the methods that alters the zero from which energy is measured. This alteration leads to an apparent energy threshold for ionization that can, especially in the stabilization regime, differ strongly from the laboratory measurement. It is concluded that channel closings in intense-field ionization can occur at high as well as low frequencies. It is also found that the stabilization phenomenon at high frequencies, very prominent for hydrogen, is absent in a short-range potential.

© 1996 Optical Society of America

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References

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  1. M. Gavrila, “Atomic structure and decay in high-frequency fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), pp. 435–510.
  2. R. M. Potvliege and R. Shakeshaft, “Nonperturbative treatment of multiphoton ionization within the Floquet framework,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), pp. 373–433.
  3. H. R. Reiss, Phys. Rev. A 22, 1786 (1980).
    [Crossref]
  4. H. R. Reiss, Prog. Quantum Electron. 16, 1 (1992).
    [Crossref]
  5. W. Gordon, Z. Phys. 40, 117 (1926).
    [Crossref]
  6. D. M. Volkov, Z. Phys. 94, 250 (1935).
    [Crossref]
  7. L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).
  8. H. G. Muller, FOM Institute for Atomic and Molecular Physics, Amsterdam, The Netherlands (personal communication, 1993).
  9. P. Kruit, J. Kimman, and M. J. van der Wiel, J. Phys. B 14, L597 (1981).
    [Crossref]
  10. H. G. Muller, A. Tip, and M. J. van der Wiel, J. Phys. B 16, L679 (1983).
    [Crossref]
  11. M. Dörr, R. M. Potvliege, D. Proulx, and R. Shakeshaft, Phys. Rev. A 43, 3729 (1991).
    [Crossref]
  12. H. R. Reiss and N. Hatzilambrou, “Atomic state effects in stabilization,” in Super-Intense Laser–Atom Physics, B. Piraux, A. L.’Huillier, and K. Rzażewski, eds. (Plenum, New York, 1993), pp. 213–224.
    [Crossref]
  13. V. P. Krainov and M. A. Preobrazhenskii, Sov. Phys. JETP 76, 559 (1993).
  14. M. Pont and M. Gavrila, Phys. Rev. Lett. 65, 2362 (1990).
    [Crossref] [PubMed]
  15. H. R. Reiss, Phys. Rev. A 46, 391 (1992).
    [Crossref] [PubMed]
  16. H. R. Reiss and V. P. Krainov, Phys. Rev. A 50, R910 (1994).
    [Crossref]
  17. W. C. Henneberger, Phys. Rev. Lett. 21, 838 (1968).
    [Crossref]
  18. E. J. Konopinski, Electromagnetic Fields and Relativistic Particles (McGraw-Hill, New York, 1981), Chap. 6.
  19. H. R. Reiss, “Stabilization from the tunneling limit to the Kramers–Henneberger limit,” in Multiphoton Processes, D. K. Evans and S. L. Chin, eds. (World Scientific, Singapore, 1994), pp. 197–202.
  20. H. R. Reiss, “The Keldysh theory of strong-field ionization and its extensions,” in Atoms in Strong Fields, C. A. Nicolaides, C. W. Clark, and M. H. Nayfeh, eds. (Plenum, New York, 1990), pp. 425–446.
    [Crossref]

1994 (1)

H. R. Reiss and V. P. Krainov, Phys. Rev. A 50, R910 (1994).
[Crossref]

1993 (1)

V. P. Krainov and M. A. Preobrazhenskii, Sov. Phys. JETP 76, 559 (1993).

1992 (2)

H. R. Reiss, Phys. Rev. A 46, 391 (1992).
[Crossref] [PubMed]

H. R. Reiss, Prog. Quantum Electron. 16, 1 (1992).
[Crossref]

1991 (1)

M. Dörr, R. M. Potvliege, D. Proulx, and R. Shakeshaft, Phys. Rev. A 43, 3729 (1991).
[Crossref]

1990 (1)

M. Pont and M. Gavrila, Phys. Rev. Lett. 65, 2362 (1990).
[Crossref] [PubMed]

1983 (1)

H. G. Muller, A. Tip, and M. J. van der Wiel, J. Phys. B 16, L679 (1983).
[Crossref]

1981 (1)

P. Kruit, J. Kimman, and M. J. van der Wiel, J. Phys. B 14, L597 (1981).
[Crossref]

1980 (1)

H. R. Reiss, Phys. Rev. A 22, 1786 (1980).
[Crossref]

1968 (1)

W. C. Henneberger, Phys. Rev. Lett. 21, 838 (1968).
[Crossref]

1965 (1)

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

1935 (1)

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

1926 (1)

W. Gordon, Z. Phys. 40, 117 (1926).
[Crossref]

Dörr, M.

M. Dörr, R. M. Potvliege, D. Proulx, and R. Shakeshaft, Phys. Rev. A 43, 3729 (1991).
[Crossref]

Gavrila, M.

M. Pont and M. Gavrila, Phys. Rev. Lett. 65, 2362 (1990).
[Crossref] [PubMed]

M. Gavrila, “Atomic structure and decay in high-frequency fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), pp. 435–510.

Gordon, W.

W. Gordon, Z. Phys. 40, 117 (1926).
[Crossref]

Hatzilambrou, N.

H. R. Reiss and N. Hatzilambrou, “Atomic state effects in stabilization,” in Super-Intense Laser–Atom Physics, B. Piraux, A. L.’Huillier, and K. Rzażewski, eds. (Plenum, New York, 1993), pp. 213–224.
[Crossref]

Henneberger, W. C.

W. C. Henneberger, Phys. Rev. Lett. 21, 838 (1968).
[Crossref]

Keldysh, L. V.

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Kimman, J.

P. Kruit, J. Kimman, and M. J. van der Wiel, J. Phys. B 14, L597 (1981).
[Crossref]

Konopinski, E. J.

E. J. Konopinski, Electromagnetic Fields and Relativistic Particles (McGraw-Hill, New York, 1981), Chap. 6.

Krainov, V. P.

H. R. Reiss and V. P. Krainov, Phys. Rev. A 50, R910 (1994).
[Crossref]

V. P. Krainov and M. A. Preobrazhenskii, Sov. Phys. JETP 76, 559 (1993).

Kruit, P.

P. Kruit, J. Kimman, and M. J. van der Wiel, J. Phys. B 14, L597 (1981).
[Crossref]

Muller, H. G.

H. G. Muller, A. Tip, and M. J. van der Wiel, J. Phys. B 16, L679 (1983).
[Crossref]

H. G. Muller, FOM Institute for Atomic and Molecular Physics, Amsterdam, The Netherlands (personal communication, 1993).

Pont, M.

M. Pont and M. Gavrila, Phys. Rev. Lett. 65, 2362 (1990).
[Crossref] [PubMed]

Potvliege, R. M.

M. Dörr, R. M. Potvliege, D. Proulx, and R. Shakeshaft, Phys. Rev. A 43, 3729 (1991).
[Crossref]

R. M. Potvliege and R. Shakeshaft, “Nonperturbative treatment of multiphoton ionization within the Floquet framework,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), pp. 373–433.

Preobrazhenskii, M. A.

V. P. Krainov and M. A. Preobrazhenskii, Sov. Phys. JETP 76, 559 (1993).

Proulx, D.

M. Dörr, R. M. Potvliege, D. Proulx, and R. Shakeshaft, Phys. Rev. A 43, 3729 (1991).
[Crossref]

Reiss, H. R.

H. R. Reiss and V. P. Krainov, Phys. Rev. A 50, R910 (1994).
[Crossref]

H. R. Reiss, Phys. Rev. A 46, 391 (1992).
[Crossref] [PubMed]

H. R. Reiss, Prog. Quantum Electron. 16, 1 (1992).
[Crossref]

H. R. Reiss, Phys. Rev. A 22, 1786 (1980).
[Crossref]

H. R. Reiss and N. Hatzilambrou, “Atomic state effects in stabilization,” in Super-Intense Laser–Atom Physics, B. Piraux, A. L.’Huillier, and K. Rzażewski, eds. (Plenum, New York, 1993), pp. 213–224.
[Crossref]

H. R. Reiss, “Stabilization from the tunneling limit to the Kramers–Henneberger limit,” in Multiphoton Processes, D. K. Evans and S. L. Chin, eds. (World Scientific, Singapore, 1994), pp. 197–202.

H. R. Reiss, “The Keldysh theory of strong-field ionization and its extensions,” in Atoms in Strong Fields, C. A. Nicolaides, C. W. Clark, and M. H. Nayfeh, eds. (Plenum, New York, 1990), pp. 425–446.
[Crossref]

Shakeshaft, R.

M. Dörr, R. M. Potvliege, D. Proulx, and R. Shakeshaft, Phys. Rev. A 43, 3729 (1991).
[Crossref]

R. M. Potvliege and R. Shakeshaft, “Nonperturbative treatment of multiphoton ionization within the Floquet framework,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), pp. 373–433.

Tip, A.

H. G. Muller, A. Tip, and M. J. van der Wiel, J. Phys. B 16, L679 (1983).
[Crossref]

van der Wiel, M. J.

H. G. Muller, A. Tip, and M. J. van der Wiel, J. Phys. B 16, L679 (1983).
[Crossref]

P. Kruit, J. Kimman, and M. J. van der Wiel, J. Phys. B 14, L597 (1981).
[Crossref]

Volkov, D. M.

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

J. Phys. B (2)

P. Kruit, J. Kimman, and M. J. van der Wiel, J. Phys. B 14, L597 (1981).
[Crossref]

H. G. Muller, A. Tip, and M. J. van der Wiel, J. Phys. B 16, L679 (1983).
[Crossref]

Phys. Rev. A (4)

M. Dörr, R. M. Potvliege, D. Proulx, and R. Shakeshaft, Phys. Rev. A 43, 3729 (1991).
[Crossref]

H. R. Reiss, Phys. Rev. A 46, 391 (1992).
[Crossref] [PubMed]

H. R. Reiss and V. P. Krainov, Phys. Rev. A 50, R910 (1994).
[Crossref]

H. R. Reiss, Phys. Rev. A 22, 1786 (1980).
[Crossref]

Phys. Rev. Lett. (2)

W. C. Henneberger, Phys. Rev. Lett. 21, 838 (1968).
[Crossref]

M. Pont and M. Gavrila, Phys. Rev. Lett. 65, 2362 (1990).
[Crossref] [PubMed]

Prog. Quantum Electron. (1)

H. R. Reiss, Prog. Quantum Electron. 16, 1 (1992).
[Crossref]

Sov. Phys. JETP (2)

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

V. P. Krainov and M. A. Preobrazhenskii, Sov. Phys. JETP 76, 559 (1993).

Z. Phys. (2)

W. Gordon, Z. Phys. 40, 117 (1926).
[Crossref]

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

Other (7)

H. G. Muller, FOM Institute for Atomic and Molecular Physics, Amsterdam, The Netherlands (personal communication, 1993).

M. Gavrila, “Atomic structure and decay in high-frequency fields,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), pp. 435–510.

R. M. Potvliege and R. Shakeshaft, “Nonperturbative treatment of multiphoton ionization within the Floquet framework,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), pp. 373–433.

E. J. Konopinski, Electromagnetic Fields and Relativistic Particles (McGraw-Hill, New York, 1981), Chap. 6.

H. R. Reiss, “Stabilization from the tunneling limit to the Kramers–Henneberger limit,” in Multiphoton Processes, D. K. Evans and S. L. Chin, eds. (World Scientific, Singapore, 1994), pp. 197–202.

H. R. Reiss, “The Keldysh theory of strong-field ionization and its extensions,” in Atoms in Strong Fields, C. A. Nicolaides, C. W. Clark, and M. H. Nayfeh, eds. (Plenum, New York, 1990), pp. 425–446.
[Crossref]

H. R. Reiss and N. Hatzilambrou, “Atomic state effects in stabilization,” in Super-Intense Laser–Atom Physics, B. Piraux, A. L.’Huillier, and K. Rzażewski, eds. (Plenum, New York, 1993), pp. 213–224.
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

Transition rates for photoionization from the ground state of hydrogen by a laser field of frequency ω = 2 a.u. The solid curve is the SFA (Ref. 15), and the dashed curve is the HFA.14 The vertical line marks the intensity at which z1 = 1, where z1 is defined in Eq. (12).

Fig. 2
Fig. 2

Same as Fig. 1, except that ω = 8.

Fig. 3
Fig. 3

Transition rates for photoionization from a short-range potential with a binding energy of 0.75 eV by laser fields of frequency ω = 2 a.u. (as in Fig. 1) and ω = 8 a.u. (as in Fig. 2). Note the apparent independence of frequency in the asymptotically large intensity domain.

Equations (41)

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S fi = lim t + ( Φ f , Ψ i ( + ) ) , lim t Ψ i ( + ) = Φ i ,
i t Φ = H 0 Φ
i t Ψ = ( H 0 + H I ) Ψ
S fi δ fi = lim t + ( Φ f , Ψ i ( + ) ) lim t ( Φ f , Ψ i ( + ) ) .
( S 1 ) fi = d t t ( Φ f , Ψ i ( + ) ) ,
( S 1 ) fi = i d t [ ( i t Φ f , Ψ i ( + ) ) + ( Φ f , i t Ψ i ( + ) ) ] .
( S 1 ) fi = i d t ( Φ f , H I Ψ i ( + ) ) .
S fi = lim t ( Ψ f ( ) , Φ i ) , lim t + Ψ f ( ) = Φ f ,
( S 1 ) fi = i d t ( Ψ f ( ) , H I Φ i ) .
lim t + Ψ f ( ) ( t ) = Φ f ( t ) .
z 1 1 or z 1 10 ,
z 1 2 U p / E B
U p = I / 4 ω 2
V ( r ) V ( | r α | ) ,
α ( t ) = t A ( τ ) d τ
U p ω E B .
χ = t d τ A 2 ( τ ) 2 c ,
U ( t ) = exp ( i χ / c ) = exp [ i t d t A 2 ( τ ) 2 c 2 ] .
Φ = U Φ , Ψ = U Ψ
U p = A 2 2 c 2 .
U U = 1
( S 1 ) fi = i d t ( U Φ f , H I U Ψ i ( + ) ) = i d t ( Φ f , H I U Ψ i ( + ) ) .
H = 1 2 ( p A c ) 2 + V ( r ) ,
ϕ ϕ = ϕ 1 c t χ = A 2 2 c 2 .
Ψ = U Ψ ,
i t Ψ = [ p 2 2 A · p c + V ( r ) ] Ψ .
( S 1 ) fi = i d t ( Φ f , H I Ψ i ( + ) ) ,
H I = A · p c
H I = A · p c + A 2 2
d W d Ω = 1 2 3 / 2 π 2 n = n 0 ( n ω z ω ) 2 ( n ω z ω E B ) 1 / 2 × | ϕ ˆ i ( p ) | 2 J n 2 ( z 1 / 2 γ ) ,
n 0 = { z + E B / ω } ,
z U p / ω .
γ ( 2 p ) 1 / 2 sin θ ,
p 2 / 2 = ( n z ) ω E B .
J n ( z 1 / 2 α , z 2 ) ,
α = 4 ( 2 p ) 1 / 2 cos θ ,
d W d Ω = 1 2 3 / 2 π 2 n = n 0 ( n ω ) 2 ( n ω E B ) 1 / 2 × | ϕ ˆ i ( p ) | 2 J n 2 ( z 1 / 2 γ ) ,
n 0 = { E B / ω } ,
J n ( z 1 / 2 α ) ,
lim v 0 J n ( u , v ) = J n ( u ) .
p 2 / 2 = n ω E B .

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