Abstract

We predict analytically and confirm numerically the existence of sharply localized quantum states in an ultra-strong circularly polarized electromagnetic field with the probability density that represents non-classical wave packets moving around strongly unstable classical circular orbits.

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References

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  1. J. Mostowski, and J. J. Sanchez-Mondragon, "Interaction of highly excited hydrogen atoms with a resonant oscillating field," Opt. Commun. 29, 293 (1979).
    [CrossRef]
  2. M. Pont and M. Gavrila, "Stabilization of atomic hydrogen in superintence, hight-frequency laser fields of circular polarization," Phys. Rev. Lett. 65, 2362 (1990).
    [CrossRef] [PubMed]
  3. T. Uzer, E. A. Lee, D. Farrelly, and A. F. Brunello, "Synthesis of a classical atom: wavepacket analogs of the Trojan Asteroids," Contemporary Physics 41, 14 (2000).
    [CrossRef]
  4. J. H. Eberly, I. Bialynicki-Birula, and M. Kalinski, "Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons," Phys. Rev. Lett. 73, 1777 (1994).
    [CrossRef] [PubMed]
  5. A. Buchleitner and D. Delande, "Nondispersive electronic wave packets in multiphoton processes," Phys. Rev. Lett. 75, 1487 (1995).
    [CrossRef] [PubMed]
  6. J. Zakrzewski, D. Delande and A. Buchleitner, "Nonspreading electronic wave packets and conductance fluctuations," Phys. Rev. Lett. 75, 4015 (1995).
    [CrossRef] [PubMed]
  7. M. Kalinski, J. H. Eberly, J. A West, and C. R. Stroud, Jr., "The Rutherford atom in quantum theory," Phys. Rev. Lett. (to be published). Physica Scripta 20, 539 (1979).
  8. M. Kalinski and J. H. Eberly, "Guiding electron orbits with chirped light" Opt. Express 1, 216 (1997). http://www.opticsexpress.org/oearchive/source/2328.htm
    [CrossRef]
  9. I. Bialynicki-Birula, and Z. Bialynicka-Birula, "Radiative decay of Trojan wave packets," Phys. Rev. A 56, 3623 (1997).
    [CrossRef]
  10. M. Kalinski and J. H. Eberly, "New states of Hydrogen in circularly polarized electromagnetic field," Phys. Rev. Lett. 77, 2420 (1996).
    [CrossRef] [PubMed]
  11. W. Pauli and M. Fiertz, Nuovo Cimento, 15, 167 (1933).
  12. W. C. Henneberger, "Perturbation method for atoms in intense light beams," Phys. Rev. Lett. 21, 838 (1968).
    [CrossRef]
  13. M. Gavrila and J. Z. Kaminski, "Free-free transitions in intense high-frequency laser fields," Phys. Rev. Lett. 52, 613 (1984).
    [CrossRef]
  14. K. J. LaGattuta, "Laser effect in photoionization: Numerical solution for one-dimensional d potential," Phys. Rev. A 40, 683 (1989)
    [CrossRef] [PubMed]
  15. K. J. LaGattuta, "Laser-assisted scattering from a one-dimensional d -potential: An exact solution," Phys. Rev. A 49, 1745 (1994)
    [CrossRef] [PubMed]
  16. L. I. Schiff, Quantum Mechanics, (McGraw-Hill, Lisbon, 1968).
  17. N. Meyer, L. Benet, C. Lipp, D. Trautmann, C. Jung and T. H. Seliman, "Chaotic scattering off a rotating target," J. Phys. A 28, 2529 (1995).
    [CrossRef]
  18. H. R. Reiss and V. P. Krainov, "Approximation for a Coulomb-Volkov solution in strong fields," Phys. Rev. A 50, R911 (1994).
    [CrossRef]
  19. P. Gross and H. Rabitz, "On the generality of optimal control theory for laser-induced control field design," J. Chem. Phys. 105 (1996).
    [CrossRef]

Other (19)

J. Mostowski, and J. J. Sanchez-Mondragon, "Interaction of highly excited hydrogen atoms with a resonant oscillating field," Opt. Commun. 29, 293 (1979).
[CrossRef]

M. Pont and M. Gavrila, "Stabilization of atomic hydrogen in superintence, hight-frequency laser fields of circular polarization," Phys. Rev. Lett. 65, 2362 (1990).
[CrossRef] [PubMed]

T. Uzer, E. A. Lee, D. Farrelly, and A. F. Brunello, "Synthesis of a classical atom: wavepacket analogs of the Trojan Asteroids," Contemporary Physics 41, 14 (2000).
[CrossRef]

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

A. Buchleitner and D. Delande, "Nondispersive electronic wave packets in multiphoton processes," Phys. Rev. Lett. 75, 1487 (1995).
[CrossRef] [PubMed]

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

M. Kalinski, J. H. Eberly, J. A West, and C. R. Stroud, Jr., "The Rutherford atom in quantum theory," Phys. Rev. Lett. (to be published). Physica Scripta 20, 539 (1979).

M. Kalinski and J. H. Eberly, "Guiding electron orbits with chirped light" Opt. Express 1, 216 (1997). http://www.opticsexpress.org/oearchive/source/2328.htm
[CrossRef]

I. Bialynicki-Birula, and Z. Bialynicka-Birula, "Radiative decay of Trojan wave packets," Phys. Rev. A 56, 3623 (1997).
[CrossRef]

M. Kalinski and J. H. Eberly, "New states of Hydrogen in circularly polarized electromagnetic field," Phys. Rev. Lett. 77, 2420 (1996).
[CrossRef] [PubMed]

W. Pauli and M. Fiertz, Nuovo Cimento, 15, 167 (1933).

W. C. Henneberger, "Perturbation method for atoms in intense light beams," Phys. Rev. Lett. 21, 838 (1968).
[CrossRef]

M. Gavrila and J. Z. Kaminski, "Free-free transitions in intense high-frequency laser fields," Phys. Rev. Lett. 52, 613 (1984).
[CrossRef]

K. J. LaGattuta, "Laser effect in photoionization: Numerical solution for one-dimensional d potential," Phys. Rev. A 40, 683 (1989)
[CrossRef] [PubMed]

K. J. LaGattuta, "Laser-assisted scattering from a one-dimensional d -potential: An exact solution," Phys. Rev. A 49, 1745 (1994)
[CrossRef] [PubMed]

L. I. Schiff, Quantum Mechanics, (McGraw-Hill, Lisbon, 1968).

N. Meyer, L. Benet, C. Lipp, D. Trautmann, C. Jung and T. H. Seliman, "Chaotic scattering off a rotating target," J. Phys. A 28, 2529 (1995).
[CrossRef]

H. R. Reiss and V. P. Krainov, "Approximation for a Coulomb-Volkov solution in strong fields," Phys. Rev. A 50, R911 (1994).
[CrossRef]

P. Gross and H. Rabitz, "On the generality of optimal control theory for laser-induced control field design," J. Chem. Phys. 105 (1996).
[CrossRef]

Supplementary Material (4)

» Media 1: MOV (7608 KB)     
» Media 2: MOV (7563 KB)     
» Media 3: MOV (1348 KB)     
» Media 4: MOV (1142 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Frequencies of small oscillations of the resonant circular orbit as the function of the parameter q=1/r 3 ω 2. The orbit is stable for 8=9≤q≤1. It formally regains stability for q → 0 where the harmonic wavefunction is singular and we find the new states. The weakly unstable orbit supports non-dispersing wavepackets for q<1+3/4ω -1/3.

Fig. 2.
Fig. 2.

Eigenvalues of the equation [-d 2 x/2dx 2+Veff (x)]ϕ= for as functions of the potential radius a. States with the energy EVeff (0) are strongly localized around x=0 (the bold green line). The density of levels exhibists abrupt change across the energy line E=Veff (0)

Fig. 3.
Fig. 3.

First few eigenstates of the equation [-d 2 x=2dx 2+Veff (x)]ϕ= for a=50 a.u. The states for which the energy EVeff (0) are strongly localized around x=0 (the red plot).

Fig. 4.
Fig. 4.

Snapshots of the time evolution of the packet for E=0.27 and ω=0.082. a) t=0, b) t=4, c) t=9 and d) t=19 for the hydrogen in CP field. The radius of packet motion is a=40 a.u. The movie (7.5MB) linked to this figure shows the full 20-cycle evolution.

Fig. 5.
Fig. 5.

Snapshots of the time evolution of the packet for ε=0:27 and ω=0.082. a) t=0, b) t=4, c) t=6 and d) t=9 for the hydrogen in CP field and with removed Coulomb potential. The radius of packet motion is a=40 a.u. The movie (7.5MB) linked to this figure shows the full 20-cycle evolution. [Media 1] [Media 2] [Media 3] [Media 4]

Equations (14)

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H osc = ω + a + a ω b + b ,
H = 2 2 1 r + E ( t ) · r ,
H K H = e i α ( t ) · e id α ( t ) dt · r H e i α ( t ) · e id α ( t ) dt · r ,
H K H Ψ = i d Ψ dt , H K H = 2 2 1 r + α ( t ) , d 2 α ( t ) dt 2 = E ( t ) ,
1 r + α ( t ) = n V n ( r , ω ) e in ω t
V eff ( r ) = V 0 ( r , ω ) = 1 2 π 0 2 π 1 r + α ( τ ) d τ
= 2 π r a E [ 4 ar ( r a ) 2 ] , a = α ( t ) , τ = ω t
( 1 2 2 r 2 1 2 r r 1 2 m 2 r 2 + V eff ( r ) ) ϕ = E ϕ
V eff ( r ) Z δ ( r a ) , Z = 1 2 π a
ϕ k ( r ) = J 0 ( kr ) , J 0 ( k n a ) = 0 , E = k n 2 2 ,
ϕ k ( r ) = m ( 1 ) m e i δ m R m ( r ) e im ϕ ,
R m ( r ) = c m J m ( kr ) r < a ,
R m ( r ) = γ ( k ) ( cos δ m J m ( kr ) sin δ m N m ( kr ) ) r > 0 ,
Ψ k ( r t ) = C e id α ( t ) dt · r J 0 [ k 0 r α ( t ) ] ,

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