Abstract

A simple procedure of dressing the atomic states distorted in the presence of a potential, bound or continuum, by a laser field is discussed, and the validity of the developed dressing procedure is tested by evaluating the harmonic generation and multiphoton ionization processes for a one-dimensional model potential of the form V(x) = −(1 + x2)−1/2. The results are compared with the exact one-dimensional model calculations of Eberly et al. for the same processes [ Phys. Rev. Lett. 62, 881 ( 1989)]. Several other dressed-state wave functions proposed by other authors are also tested.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. B. Bebb and A. Gold, Phys. Rev. 143, 1 (1966).
    [CrossRef]
  2. Y. Gontier and M. Trahin, Phys. Rev. 172, 83 (1968).
    [CrossRef]
  3. L. V. Keldysh, Sov. Phys. JETP,  20, 1307 (1965);H. R. Reiss, Phys. Rev. A 1, 803 (1970);F. Faisal, J. Phys.B 6, L312 (1973).
    [CrossRef]
  4. M. Janjusevic and M. H. Mittleman, J. Phys. B. 21, 2279 (1988).
    [CrossRef]
  5. M. Pont, N. R. Walet, M. Gavrila, and C. W. McCurdy, Phys. Rev. Lett. 61, 939 (1988).
    [CrossRef] [PubMed]
  6. D. M. Volkov, Z. Phys. 94, 250 (1935).
    [CrossRef]
  7. M. Jain and N. Tzoar, Phys. Rev. A 8, 804 (1978).
  8. P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B. 13, 4495 (1980).
    [CrossRef]
  9. H. R. Reiss, Phys. Rev. A 39, 2449 (1989).
    [CrossRef] [PubMed]
  10. M. H. Mittleman, City College, City University of New York, 535 East 80th Street, New York, New York 10021 (personal communication).
  11. C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, and G. Grynberg, Phys. Rev. A 8, 2747 (1973).
    [CrossRef]
  12. M. Janjusevic and Y. Hahn, in Proceedings of the 11th Conference on Atomic Physics, C. Fabre and D. Delande, eds. (Laboratoire de Physique, Ecole Normale Superiéure, Paris, 1988), p. VI-8.
  13. N. F. Mott and H. S. W. Massey, Theory of Atomic Collisions (Clarendon, Oxford, 1949).
  14. H. Bethe and E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Plenum, New York, 1977).
    [CrossRef]
  15. M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
    [CrossRef]
  16. L. Pan, B. Sundaram, and L. Armstrong, J. Opt. Soc. Am. B 4, 754 (1987).
    [CrossRef]
  17. K. Kulander and B. Shore, Phys. Rev. Lett. 62, 524 (1989).
    [CrossRef] [PubMed]
  18. J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
    [CrossRef] [PubMed]

1989 (3)

H. R. Reiss, Phys. Rev. A 39, 2449 (1989).
[CrossRef] [PubMed]

K. Kulander and B. Shore, Phys. Rev. Lett. 62, 524 (1989).
[CrossRef] [PubMed]

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[CrossRef] [PubMed]

1988 (3)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[CrossRef]

M. Janjusevic and M. H. Mittleman, J. Phys. B. 21, 2279 (1988).
[CrossRef]

M. Pont, N. R. Walet, M. Gavrila, and C. W. McCurdy, Phys. Rev. Lett. 61, 939 (1988).
[CrossRef] [PubMed]

1987 (1)

1980 (1)

P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B. 13, 4495 (1980).
[CrossRef]

1978 (1)

M. Jain and N. Tzoar, Phys. Rev. A 8, 804 (1978).

1973 (1)

C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, and G. Grynberg, Phys. Rev. A 8, 2747 (1973).
[CrossRef]

1968 (1)

Y. Gontier and M. Trahin, Phys. Rev. 172, 83 (1968).
[CrossRef]

1966 (1)

H. B. Bebb and A. Gold, Phys. Rev. 143, 1 (1966).
[CrossRef]

1965 (1)

L. V. Keldysh, Sov. Phys. JETP,  20, 1307 (1965);H. R. Reiss, Phys. Rev. A 1, 803 (1970);F. Faisal, J. Phys.B 6, L312 (1973).
[CrossRef]

1935 (1)

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

Armstrong, L.

Bebb, H. B.

H. B. Bebb and A. Gold, Phys. Rev. 143, 1 (1966).
[CrossRef]

Bethe, H.

H. Bethe and E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Plenum, New York, 1977).
[CrossRef]

Cavaliere, P.

P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B. 13, 4495 (1980).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, and G. Grynberg, Phys. Rev. A 8, 2747 (1973).
[CrossRef]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, and G. Grynberg, Phys. Rev. A 8, 2747 (1973).
[CrossRef]

Eberly, J. H.

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[CrossRef] [PubMed]

Fabre, C.

C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, and G. Grynberg, Phys. Rev. A 8, 2747 (1973).
[CrossRef]

Ferrante, G.

P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B. 13, 4495 (1980).
[CrossRef]

Ferray, M.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[CrossRef]

Gavrila, M.

M. Pont, N. R. Walet, M. Gavrila, and C. W. McCurdy, Phys. Rev. Lett. 61, 939 (1988).
[CrossRef] [PubMed]

Gold, A.

H. B. Bebb and A. Gold, Phys. Rev. 143, 1 (1966).
[CrossRef]

Gontier, Y.

Y. Gontier and M. Trahin, Phys. Rev. 172, 83 (1968).
[CrossRef]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, and G. Grynberg, Phys. Rev. A 8, 2747 (1973).
[CrossRef]

Hahn, Y.

M. Janjusevic and Y. Hahn, in Proceedings of the 11th Conference on Atomic Physics, C. Fabre and D. Delande, eds. (Laboratoire de Physique, Ecole Normale Superiéure, Paris, 1988), p. VI-8.

Jain, M.

M. Jain and N. Tzoar, Phys. Rev. A 8, 804 (1978).

Janjusevic, M.

M. Janjusevic and M. H. Mittleman, J. Phys. B. 21, 2279 (1988).
[CrossRef]

M. Janjusevic and Y. Hahn, in Proceedings of the 11th Conference on Atomic Physics, C. Fabre and D. Delande, eds. (Laboratoire de Physique, Ecole Normale Superiéure, Paris, 1988), p. VI-8.

Javanainen, J.

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[CrossRef] [PubMed]

Keldysh, L. V.

L. V. Keldysh, Sov. Phys. JETP,  20, 1307 (1965);H. R. Reiss, Phys. Rev. A 1, 803 (1970);F. Faisal, J. Phys.B 6, L312 (1973).
[CrossRef]

Kulander, K.

K. Kulander and B. Shore, Phys. Rev. Lett. 62, 524 (1989).
[CrossRef] [PubMed]

L’Huillier, A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[CrossRef]

Leone, C.

P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B. 13, 4495 (1980).
[CrossRef]

Li, X. F.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[CrossRef]

Lompré, L. A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[CrossRef]

Mainfray, G.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[CrossRef]

Manus, C.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[CrossRef]

Massey, H. S. W.

N. F. Mott and H. S. W. Massey, Theory of Atomic Collisions (Clarendon, Oxford, 1949).

McCurdy, C. W.

M. Pont, N. R. Walet, M. Gavrila, and C. W. McCurdy, Phys. Rev. Lett. 61, 939 (1988).
[CrossRef] [PubMed]

Mittleman, M. H.

M. Janjusevic and M. H. Mittleman, J. Phys. B. 21, 2279 (1988).
[CrossRef]

M. H. Mittleman, City College, City University of New York, 535 East 80th Street, New York, New York 10021 (personal communication).

Mott, N. F.

N. F. Mott and H. S. W. Massey, Theory of Atomic Collisions (Clarendon, Oxford, 1949).

Pan, L.

Pont, M.

M. Pont, N. R. Walet, M. Gavrila, and C. W. McCurdy, Phys. Rev. Lett. 61, 939 (1988).
[CrossRef] [PubMed]

Reiss, H. R.

H. R. Reiss, Phys. Rev. A 39, 2449 (1989).
[CrossRef] [PubMed]

Salpeter, E.

H. Bethe and E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Plenum, New York, 1977).
[CrossRef]

Shore, B.

K. Kulander and B. Shore, Phys. Rev. Lett. 62, 524 (1989).
[CrossRef] [PubMed]

Su, Q.

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[CrossRef] [PubMed]

Sundaram, B.

Trahin, M.

Y. Gontier and M. Trahin, Phys. Rev. 172, 83 (1968).
[CrossRef]

Tzoar, N.

M. Jain and N. Tzoar, Phys. Rev. A 8, 804 (1978).

Volkov, D. M.

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

Walet, N. R.

M. Pont, N. R. Walet, M. Gavrila, and C. W. McCurdy, Phys. Rev. Lett. 61, 939 (1988).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[CrossRef]

J. Phys. B. (2)

P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B. 13, 4495 (1980).
[CrossRef]

M. Janjusevic and M. H. Mittleman, J. Phys. B. 21, 2279 (1988).
[CrossRef]

Phys. Rev. (2)

H. B. Bebb and A. Gold, Phys. Rev. 143, 1 (1966).
[CrossRef]

Y. Gontier and M. Trahin, Phys. Rev. 172, 83 (1968).
[CrossRef]

Phys. Rev. A (3)

C. Cohen-Tannoudji, J. Dupont-Roc, C. Fabre, and G. Grynberg, Phys. Rev. A 8, 2747 (1973).
[CrossRef]

H. R. Reiss, Phys. Rev. A 39, 2449 (1989).
[CrossRef] [PubMed]

M. Jain and N. Tzoar, Phys. Rev. A 8, 804 (1978).

Phys. Rev. Lett. (3)

K. Kulander and B. Shore, Phys. Rev. Lett. 62, 524 (1989).
[CrossRef] [PubMed]

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[CrossRef] [PubMed]

M. Pont, N. R. Walet, M. Gavrila, and C. W. McCurdy, Phys. Rev. Lett. 61, 939 (1988).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

L. V. Keldysh, Sov. Phys. JETP,  20, 1307 (1965);H. R. Reiss, Phys. Rev. A 1, 803 (1970);F. Faisal, J. Phys.B 6, L312 (1973).
[CrossRef]

Z. Phys. (1)

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

Other (4)

M. Janjusevic and Y. Hahn, in Proceedings of the 11th Conference on Atomic Physics, C. Fabre and D. Delande, eds. (Laboratoire de Physique, Ecole Normale Superiéure, Paris, 1988), p. VI-8.

N. F. Mott and H. S. W. Massey, Theory of Atomic Collisions (Clarendon, Oxford, 1949).

H. Bethe and E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Plenum, New York, 1977).
[CrossRef]

M. H. Mittleman, City College, City University of New York, 535 East 80th Street, New York, New York 10021 (personal communication).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

ATI probabilities as functions of photoelectron energies presented as log PB, where the respective curves follow the references indicated: a, Ref. 18; b, Ref. 7; c, Ref. 12, U2; d, Ref. 10; e, Ref. 9. The frequency of the laser ω = 0.07 a.u., the laser electric field |E| = 0.05 a.u., and the pulse duration T = 16.125 cycles.

Fig. 2
Fig. 2

Harmonic peaks obtained by the various dressed-wave functions for the C test, where PC = |C|2. T = 16.125 cycles, ω = 0.07, and the laser electric field is |E| = 0.05 a.u. Relative intensities are given as functions of harmonic order n′ and are normalized to maximum harmonic for each dressing. The notations for different curves are the same as those in Fig. 1, except that curve c here is for HJ5 and is normalized at n′ = 5.

Tables (4)

Tables Icon

Table 1 Above-Threshold Ionization Probabilities PB = |B|2 as Functions of Photoelectron Energies Eca

Tables Icon

Table 2 |D(ω)|2 Test: Hahn–Janjusevic Dressing UxULU0 Compared with the Result of Eberly et al.a

Tables Icon

Table 3 Comparison between |DT(ω)| and |CT(ω)| Values for the First Harmonic Obtained Using Tzoar’s Dressed-Wave Functiona

Tables Icon

Table 4 Relative Intensity |C|2 as a Function of Harmonic Order Normalized to Maximum Harmonic for Each Dressinga

Equations (32)

Equations on this page are rendered with MathJax. Learn more.

{ i t H } Ψ = 0 , H = [ p ( e / c ) A ] 2 2 m + V ( r ) ,
Ψ ( r , t ) = U ϕ 0 ( r )
H 0 = p 2 2 m + V ( r ) , H = e m c p · A + e 2 2 m c 2 A 2 .
e R + S e R e S e 1 / 2 [ R , S ] ,
R = i H 0 d t and S = i H d t .
[ R , S ] = { α · ( p ̂ V ) ω + α ω t sin ω t p ̂ H ̂ 0 } .
Ψ k L = exp [ i ( E k t k · α s i n ω t ) ] ϕ k ( r ) ,
Ψ T ( r , t ) = U L U 0 ϕ ( r ) ,
Ψ R = exp ( i e r · A ) ψ 0 ( r , t ) .
Ψ M = exp ( i e r · A ) ϕ 0 ( r ) exp [ i ( E 0 t 1 / 2 α s E ( t ) 2 ) ] ,
Ψ H J 1 = U 0 U L ϕ ( r ) , Ψ H J 4 = U L U x U 0 ϕ ( r ) , Ψ H J 5 = U x U L U 0 ϕ ( r ) ,
ϕ ( r ) = 1 ( 2 π ) 3 / 2 ϕ ( p ) exp ( i p · r ) d 3 p .
Ψ L ( r , t ) = d 3 p ϕ ( p ) χ p L ( r , t ) .
exp ( i z sin θ ) = ν = J ν ( z ) exp ( i ν θ ) ,
Ψ L ( r , t ) = ( 2 π ) 3 / 2 ν d 3 p J ν ( α · p ) ϕ ̂ ( p ) × exp ( i p · r ) exp [ i ( E e t + U p t + U p 2 ω sin 2 ω t ) ] ,
e + b + ( e + b + ) + photon ,
= H + r · E R ,
M f i L = Ψ B | ̂ · r exp ( i ω R T ) | Ψ C ,
ϕ B ( p ) = 4 ( 2 π ) 1 / 2 1 ( p 2 + 1 ) 2
ϕ k ( p ) = 1 2 π 2 lim d d { [ p 2 ( k + i ) 2 ] i d [ ( p k ) 2 + 2 ] 1 i d } ,
M f i L = ν ν d r d p d p J ν ( α · p ) J ν ( α · p ) ϕ B * ( p ) ϕ k ( p ) × exp [ i ( p p ) · r ] | ̂ · r | 8 π δ [ E B E k + ( ν ν ) ω ω R ] ,
M f i L ϕ B | U 5 1 D U 5 | ϕ C ,
U 5 D U 5 1 = ̂ ( r α sin ω t ) .
H 0 = ( 2 / 2 m ) 2 / x 2 + V ( x ) ,
ψ 0 ( x , t ) = [ 0.107 exp ( 0.31 x 2 ) + 0.004 x 2 exp ( 0.14 x 2 ) ] × exp ( i E 0 t ) ,
A n m = Ψ n | Ψ m , B k n = ψ k | Ψ n , C k n = ψ k | x | Ψ n , D n m = Ψ n | x | Ψ m .
B k 0 ( t ) = ψ k | Ψ 0 ( t ) ,
( 1 / 2 ) 2 ϕ k / x 2 ϕ k / ( 1 + x 2 ) 1 / 2 = ( k 2 / 2 ) ϕ k ,
D ( ω ) = d t exp ( i ω t ) Ψ 0 ( x , t ) | x | Ψ 0 ( x , t ) x ,
W ( ω , ω p ) = N exp [ Q ( ω ω p ) 2 ] ,
D ¯ ( ω p ) = D ( ω ) W ( ω ω p ) d ω .
D ( ω ) = 2 R e C ( ω ) + D ( ω ) ,

Metrics