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.

© 2001 Optical Society of America

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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, “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. Exp. 1, 176 (1997).
    [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 δ potential,” Phys. Rev. A 40, 683 (1989)
    [CrossRef] [PubMed]
  15. K. J. LaGattuta, “Laser-assisted scattering from a one-dimensional δ-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]

2000 (1)

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]

1997 (2)

M. Kalinski and J. H. Eberly, “Guiding electron orbits with chirped light” Opt. Exp. 1, 176 (1997).
[CrossRef]

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

1996 (1)

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

1995 (3)

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]

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]

1994 (3)

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

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

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]

1990 (1)

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]

1989 (1)

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

1984 (1)

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

1979 (2)

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

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

1968 (1)

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

Benet, L.

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]

Bialynicka-Birula, Z.

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

Bialynicki-Birula, I.

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

Brunello, A. F.

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]

Buchleitner, A.

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]

Delande, D.

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

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

Eberly, J. H.

M. Kalinski and J. H. Eberly, “Guiding electron orbits with chirped light” Opt. Exp. 1, 176 (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]

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]

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

Farrelly, D.

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]

Fiertz, M.

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

Gavrila, M.

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]

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

Gross, P.

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

Henneberger, W. C.

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

Jung, C.

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]

Kalinski, M.

M. Kalinski and J. H. Eberly, “Guiding electron orbits with chirped light” Opt. Exp. 1, 176 (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]

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]

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

Kaminski, J. Z.

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

Krainov, V. P.

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

LaGattuta, K. J.

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

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

Lee, E. A.

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]

Lipp, C.

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]

Meyer, N.

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]

Mostowski, J.

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

Pauli, W.

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

Pont, M.

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]

Rabitz, H.

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

Reiss, H. R.

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

Sanchez-Mondragon, J. J.

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

Schiff, L. I.

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

Seliman, T. H.

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]

Stroud, C. R.

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

Trautmann, D.

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]

Uzer, T.

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]

West, J. A

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

Zakrzewski, J.

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

Contemporary Physics (1)

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. Phys. A (1)

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]

Opt. Commun. (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]

Opt. Exp. (1)

M. Kalinski and J. H. Eberly, “Guiding electron orbits with chirped light” Opt. Exp. 1, 176 (1997).
[CrossRef]

Phys. Rev. A (4)

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

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

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

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

Phys. Rev. Lett. (8)

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]

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]

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

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, “The Rutherford atom in quantum theory,” Phys. Rev. Lett. (to be published). Physica Scripta  20, 539 (1979).

Other (3)

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

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

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)

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

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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