Abstract

Control of non-circular and non-spreading wave packet states by a resonant radiation field is predicted and numerically confirmed for hydrogen.

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References

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  1. I. Bialynicki-Birula, M. Kalinski and J. H. Eberly, "Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons," Phys. Rev. Lett. 73, 1777 (1994).
    [CrossRef] [PubMed]
  2. D. Farrelly, E. Lee and T. Uzer, "Magnetic field stabilization of Rydberg, Gaussian wave packets in a circularly polarized microwave field," Phys. Lett. A 204, 359-372 (1995).
    [CrossRef]
  3. J. Zakrzewski, D. Delande and A. Buchleitner, "Nonspreading electronic wave packets and con- ductance fluctuations," Phys. Rev. Lett. 75, 4015 (1995).
    [CrossRef] [PubMed]
  4. J. Zakrzewski, D. Delande and A. Buchleitner, "Nondispersing wave packets as solitonic solutions of level dynamics," Z. Phys B 103, 115 (1997).
    [CrossRef]
  5. H. P. Breuer and M. Holthaus, "A semiclassical theory of quasienergies and Floquet wave functions," Ann. Phys. 211, 249 (1991).
    [CrossRef]
  6. J. Henkel and M. Holthaus, "Classical resonances in quantum mechanics," Phys. Rev. A 45, 1978 (1992).
    [CrossRef] [PubMed]
  7. M. Holthaus, "On the classical-quantum correspondence for periodically time dependent systems," Chaos, Solitons and Fractals 5, 1143 (1995).
    [CrossRef]
  8. D. Delande and A. Buchleitner, "Classical and quantum chaos in atomic systems," Adv. At. Mol. Opt. Phys 35, 85 (1994).
    [CrossRef]
  9. M. Kalinski and J. H. Eberly, "Guiding electron orbits with chirped light," Opt. Express 1, 216 (1997); M. Kalinski, J. H. Eberly and E. A. Shapiro, to appear.
    [CrossRef] [PubMed]
  10. M. Kalinski and J. H. Eberly, "Trojan wave packets: Mathieu theory and generation from circular states," Phys. Rev. A 53, 1715 (1996).
    [CrossRef] [PubMed]
  11. B. V. Chirikov, "A universal instability of many-dimensional oscillator systems," Phys. Rep. 52, 263 (1979).
    [CrossRef]
  12. G. P. Berman and A. R. Kolovsky, "Quantum chaos in interactions of multilevel quantum systems with coherent radiation field," Sov. Phys. Usp. 162, 95 (1992).
  13. K. Sacha and J. Zakrzewski, "Resonance overlap criterion for H atom ionization by circularly polarized microwave fields," Phys. Rev. A 55, 568 (1997).
  14. See, e.g., J. E. Howard, "Stochastic ionization of hydrogen atoms in a circularly polarized microwave field," Phys. Rev. A 46, 364 (1992) and references therein.
    [CrossRef]
  15. D. Brouwer and G. Clemence, Methods of celestial mechanics (Academic Press, New York and London, 1961).
  16. See, e.g., S. D. Augustin and H. Rabitz, "Action-angle variables in quantum mechanics," J. Chem. Phys. 71, 4956 (1979).
    [CrossRef]
  17. M. Moshinsky and T. H. Seligman, "Canonical transformations to action and angle variables and their representation in quantum mechanics. II. The Coulomb problem," Ann. Phys. 120, 402 (1979).
    [CrossRef]
  18. R. A. Leacock and M. J. Pladgett, "Quantum action-angle-variable analysis of basic systems," Am. J. Phys. 55, 261 (1986).
    [CrossRef]
  19. B. Mirbach and H. J. Korsch, "Semiclassical quantization of KAM resonances in time-periodic systems," J. Phys. A 27, 6579 (1994).
    [CrossRef]
  20. R. A. Marcus, "Theory of semiclassical transition probabilities (S-matrix) for inelastic and reactive collisions," J. Chem. Phys. 54, 3065 (1971).
    [CrossRef]
  21. T. Uzer, D. W. Noid, and R. A. Marcus, "Uniform semiclassical theory of avoided crossings", J. Chem. Phys. 79, 4412 (1983).
    [CrossRef]
  22. N. W. McLachlan, Theory and Application of Mathieu Functions, Oxford University Press (1947).
  23. X. L. Yang, S. H. Guo and F. T. Chan, "Analytic solution of a two-dimensional hydrogen atom. I. Nonrelativistic theory", Phys. Rev. A 43, 1186-1205 (1991).
    [CrossRef] [PubMed]

Other

I. Bialynicki-Birula, M. Kalinski and J. H. Eberly, "Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons," Phys. Rev. Lett. 73, 1777 (1994).
[CrossRef] [PubMed]

D. Farrelly, E. Lee and T. Uzer, "Magnetic field stabilization of Rydberg, Gaussian wave packets in a circularly polarized microwave field," Phys. Lett. A 204, 359-372 (1995).
[CrossRef]

J. Zakrzewski, D. Delande and A. Buchleitner, "Nonspreading electronic wave packets and con- ductance fluctuations," Phys. Rev. Lett. 75, 4015 (1995).
[CrossRef] [PubMed]

J. Zakrzewski, D. Delande and A. Buchleitner, "Nondispersing wave packets as solitonic solutions of level dynamics," Z. Phys B 103, 115 (1997).
[CrossRef]

H. P. Breuer and M. Holthaus, "A semiclassical theory of quasienergies and Floquet wave functions," Ann. Phys. 211, 249 (1991).
[CrossRef]

J. Henkel and M. Holthaus, "Classical resonances in quantum mechanics," Phys. Rev. A 45, 1978 (1992).
[CrossRef] [PubMed]

M. Holthaus, "On the classical-quantum correspondence for periodically time dependent systems," Chaos, Solitons and Fractals 5, 1143 (1995).
[CrossRef]

D. Delande and A. Buchleitner, "Classical and quantum chaos in atomic systems," Adv. At. Mol. Opt. Phys 35, 85 (1994).
[CrossRef]

M. Kalinski and J. H. Eberly, "Guiding electron orbits with chirped light," Opt. Express 1, 216 (1997); M. Kalinski, J. H. Eberly and E. A. Shapiro, to appear.
[CrossRef] [PubMed]

M. Kalinski and J. H. Eberly, "Trojan wave packets: Mathieu theory and generation from circular states," Phys. Rev. A 53, 1715 (1996).
[CrossRef] [PubMed]

B. V. Chirikov, "A universal instability of many-dimensional oscillator systems," Phys. Rep. 52, 263 (1979).
[CrossRef]

G. P. Berman and A. R. Kolovsky, "Quantum chaos in interactions of multilevel quantum systems with coherent radiation field," Sov. Phys. Usp. 162, 95 (1992).

K. Sacha and J. Zakrzewski, "Resonance overlap criterion for H atom ionization by circularly polarized microwave fields," Phys. Rev. A 55, 568 (1997).

See, e.g., J. E. Howard, "Stochastic ionization of hydrogen atoms in a circularly polarized microwave field," Phys. Rev. A 46, 364 (1992) and references therein.
[CrossRef]

D. Brouwer and G. Clemence, Methods of celestial mechanics (Academic Press, New York and London, 1961).

See, e.g., S. D. Augustin and H. Rabitz, "Action-angle variables in quantum mechanics," J. Chem. Phys. 71, 4956 (1979).
[CrossRef]

M. Moshinsky and T. H. Seligman, "Canonical transformations to action and angle variables and their representation in quantum mechanics. II. The Coulomb problem," Ann. Phys. 120, 402 (1979).
[CrossRef]

R. A. Leacock and M. J. Pladgett, "Quantum action-angle-variable analysis of basic systems," Am. J. Phys. 55, 261 (1986).
[CrossRef]

B. Mirbach and H. J. Korsch, "Semiclassical quantization of KAM resonances in time-periodic systems," J. Phys. A 27, 6579 (1994).
[CrossRef]

R. A. Marcus, "Theory of semiclassical transition probabilities (S-matrix) for inelastic and reactive collisions," J. Chem. Phys. 54, 3065 (1971).
[CrossRef]

T. Uzer, D. W. Noid, and R. A. Marcus, "Uniform semiclassical theory of avoided crossings", J. Chem. Phys. 79, 4412 (1983).
[CrossRef]

N. W. McLachlan, Theory and Application of Mathieu Functions, Oxford University Press (1947).

X. L. Yang, S. H. Guo and F. T. Chan, "Analytic solution of a two-dimensional hydrogen atom. I. Nonrelativistic theory", Phys. Rev. A 43, 1186-1205 (1991).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1.
Fig. 1.

(left) Coefficient η 1 + ζ 1 in equation (9). (right) Energy spectrum in the rotating frame. Color dashed lines are the predictions of the Mathieu theory.

Fig. 2.
Fig. 2.

(a) Probability distribution of the field-free 2D state n = 20, l = 14. (b) Probability distribution of the field-dressed state obtained with the help of matrix elements of 3D aligned states. The gauge in the left lower corner of left plot indicates the distance equal to 100 atomic units.

Fig. 3.
Fig. 3.

Two snapshots of time evolution of the dressed state n = 20, l = 14 obtained by ab initio calculation. The gauge in the left lower corner of left plot indicates the distance equal to 100 atomic units.

Equations (14)

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n ˙ = 0 , i = 0 , θ ˙ = 1 / n 3 , φ ˙ = 0
𝛨 = 𝛨 0 + cos ωt + sin ω t
l ˜ = l n , n ˜ = n φ ˜ = φ , θ ˜ = θ + φ ωt
𝛨 = 1 2 n ˜ 2 ω n ˜ + ε k = [ η k n l + ζ k n l ] cos ( k θ ˜ ( k 1 ) ( φ ˜ ωt ) )
1 2 n ˜ 2 = 1 2 n 0 2 + ( n ˜ n 0 ) n 0 3 3 ( n ˜ n 0 ) 2 2 n 0 4 .
𝛨 = 1 2 n 0 2 ωn 0 3 2 n 0 4 ( n ˜ n 0 ) 2 + ε [ η 1 + ζ 1 ] cos θ ˜
[ 3 2 n 0 4 ( i θ ˜ n 0 + 1 / 2 ) 2 + ( 1 2 n 0 2 ωn 0 E + ε [ η 1 + ζ 1 ] cos θ ˜ ) ψ θ ˜ φ ˜ = 0 . ]
3 2 n 0 4 g ′′ + ( E N 0 E dr + ε [ η 1 + ζ 1 ] cos θ ˜ ) g = 0 ,
ψ NL dr θ ˜ φ ˜ = C * exp [ iN θ ˜ ] exp [ iL φ ˜ ] M ( θ ˜ ) ,
ψ nl dr = const * e ilφ e i ( n 0 1 / 2 ) θ e 0 [ ( θ + φ ωt π ) 2 ]
ψ n 0 l dr const * e A ( ϕ ωt ) 2 e AB 2 sin 2 θ e 2 AB sin θ ( ϕ ω t ) * ψ n 0 l 0
A = [ η 1 + ζ 1 ] ε n 4 2 3 n B = 2 e 1 4 e 3 +
E n 0 l dr E n 0 3 ε [ η 1 + ζ 1 ] 2 n 0 2 + ε [ η 1 + ζ 1 ] .
𝛨 = 𝛨 0 ωl + ε x

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