Abstract

In Bohr’s original planetary model of the atom the electron moves along orbits of special geometric simplicity. While wave mechanics precludes the idea that a physical path could be ascribed to the electron, a classical or planetary atom can still be envisaged in which the electronic wavepacket neither spreads nor disperses as its center moves along the Kepler orbit, and this orbit is confined to a single plane in space. We show theoretically how an electronic wavepacket may be localized in this fashion in a similar way to ion confinement in a Penning trap. Because external fields are needed to keep the packet confined, a more fitting analogy than a planetary orbit is the motion of a charged dust grain in one of the rings of a giant planet such as Saturn.

© 1997 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  6. H. Dehmelt, “Nobel Prize Lecture”, Rev. Mod. Phys. 62, 525–531 (1992).
    [Crossref]
  7. J. A. Burns and L. Schaffer, “Orbital evolution of circumplanetary dust by resonant charge variations”, Nature 337, 340–343 (1989).
    [Crossref]
  8. L. Schaffer and L. Burns, “Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains”, J. Geophys. Res. 99, 17211–17223 (1994).
    [Crossref]
  9. T. F. Gallagher, Rydberg Atoms, (Cambridge University Press, Cambridge, 1994).
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  11. A. O. Barut and B. W. Xu, “Non-spreading coherent states riding on Kepler orbits”, Helv. Phys. Act. 66, 712–720 (1993).
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  22. M. Kaliński and J. H. Eberly, “Trojan wave packets: Mathieu theory and generation from circular states”, Phys. Rev. A 53, 1715–1724 (1996).
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    [Crossref]
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    [Crossref]
  31. E. Lee, A. F. Brunello, and D. Farrelly, “A single atom Quasi-Penning trap”, Phys. Rev. Lett. 75, 3641–3644 (1995).
    [Crossref] [PubMed]
  32. A. F. Brunello, D. Farrelly, and T. Uzer, “Nonstationary, nondispersive wave packets in a Rydberg atom”, Phys. Rev. Lett. 76, 2874–2877 (1996).
    [Crossref] [PubMed]
  33. E. Lee, A. F. Brunello, and D. Farrelly, “Coherent states in a Rydberg atom: Classical mechanics”, Phys. Rev. A 55, 2203–2221 (1997).
    [Crossref]
  34. C. Cerjan, E. Lee, D. Farrelly, and T. Uzer, “Coherent states in a Rydberg atom: Quantum mechanics”, Phys. Rev. A 55, 2222–2231 (1997).
    [Crossref]
  35. K. Hornberger and A. Buchleitner, “Spontaneous decay of nondispersive wave packets”, (to be published).
  36. Z. Bialynicki-Birula and I. Bialynicki-Birula, “Radiative decay of Trojan wave packets”, (to be published).
  37. G. W. Hill, Am. J. Math. 1, 5–128, (1878).
    [Crossref]
  38. R. Greenberg and D. R. Davis, “Stability at potential maxima: The L4 and L5 points of the Restricted Three-Body Problem”, Am. J. Phys. 46, 1068–1070, (1978).
    [Crossref]
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1997 (2)

E. Lee, A. F. Brunello, and D. Farrelly, “Coherent states in a Rydberg atom: Classical mechanics”, Phys. Rev. A 55, 2203–2221 (1997).
[Crossref]

C. Cerjan, E. Lee, D. Farrelly, and T. Uzer, “Coherent states in a Rydberg atom: Quantum mechanics”, Phys. Rev. A 55, 2222–2231 (1997).
[Crossref]

1996 (2)

A. F. Brunello, D. Farrelly, and T. Uzer, “Nonstationary, nondispersive wave packets in a Rydberg atom”, Phys. Rev. Lett. 76, 2874–2877 (1996).
[Crossref] [PubMed]

M. Kaliński and J. H. Eberly, “Trojan wave packets: Mathieu theory and generation from circular states”, Phys. Rev. A 53, 1715–1724 (1996).
[Crossref]

1995 (10)

M. Kaliński and J. H. Eberly,“New states of hydrogen in a circulary polarized microwave field”, Phys. Rev. Lett. 77, 2420–2423 (1995).
[Crossref]

D. Farrelly, E. Lee, and T. Uzer, Comment on “Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons”, Phys. Rev. Lett. 75, 972 (1995).
[Crossref] [PubMed]

I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly, Reply to Ref. 22, Phys. Rev. Lett. 75, 973 (1995).
[Crossref] [PubMed]

A. Buchleitner and D. Delande, “Nondispersive electronic wave packets in multiphoton processes”, Phys. Rev. Lett. 75, 1487–1490 (1995).
[Crossref] [PubMed]

J. Zakrzewski, D. Delande, and A. Buchleitner,“Nonspreading electronic wave packets and conductance fluctuations”, Phys. Rev. Lett. 75, 4015–4018 (1995).
[Crossref] [PubMed]

D. Delande, J. Zakrzewski, and A. Buchleitner, “A wave packet can be a stationary state”, Europhys. Lett. 32, 107–112 (1995).
[Crossref]

D. Farrelly, E. Lee, and T. Uzer, “Magnetic field stabilization of Rydberg wavepackets in a circulary polarized microwave field”, Phys. Lett. A 204, 359–372 (1995).
[Crossref]

E. Lee, A. F. Brunello, and D. Farrelly, “A single atom Quasi-Penning trap”, Phys. Rev. Lett. 75, 3641–3644 (1995).
[Crossref] [PubMed]

D. Farrelly and T. Uzer, “Ionization mechanism of Rydberg atoms in a circulary polarized microwave field”,Phys. Rev. Lett. 74, 1720–1723 (1995).
[Crossref] [PubMed]

M. Kaliński, J. H. Eberly, and I. Bialynicki-Birula,“Numerical observation of stable field supported Rydberg wave packets”, Phys. Rev. A 52, 2460–2463 (1995).
[Crossref]

1994 (3)

I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly, “Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons”, Phys. Rev. Lett. 73, 1777–1780 (1994).
[Crossref] [PubMed]

C. H. Cheng, C. Y. Lee, and T. F. Gallagher, “Production of circular Rydberg states with circularly polarized microwave fields”, Phys. Rev. Lett. 73, 3078–3081 (1994).
[Crossref] [PubMed]

L. Schaffer and L. Burns, “Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains”, J. Geophys. Res. 99, 17211–17223 (1994).
[Crossref]

1993 (2)

A. O. Barut and B. W. Xu, “Non-spreading coherent states riding on Kepler orbits”, Helv. Phys. Act. 66, 712–720 (1993).

P. Kappertz and M. Nauenberg, “Circularly polarized microwave ionization of hydrogen”, Phys. Rev. A 47, 4749–4755 (1993).
[Crossref] [PubMed]

1992 (1)

H. Dehmelt, “Nobel Prize Lecture”, Rev. Mod. Phys. 62, 525–531 (1992).
[Crossref]

1991 (2)

G. Raithel, M. Fauth, and H. Walther, “Atoms in strong crossed electric and magnetic fields: Evidence for states with large electric-dipole moments”, Phys. Rev. A 47, 419–440 (1991).
[Crossref]

J. A. Yeazell and C. R. Stroud, “Observation of fractional revivals in the evolution of a Rydberg atomic wave packet”, Phys. Rev. A 43, 5153–5156 (1991).
[Crossref] [PubMed]

1990 (3)

P. Fu, T. J. Scholz, J. M. Hettema, and T. F. Gallagher, “Ionization of Rydberg atoms by circularly polarized microwave field”, Phys. Rev. Lett. 64, 511–514 (1990).
[Crossref] [PubMed]

M. Nauenberg, Comment on “Ionization of Rydberg states by a circularly polarized microwave field”, Phys. Rev. Lett. 64, 2731 (1990).
[Crossref] [PubMed]

M. Nauenberg, “Canonical Kepler map”, Europhys. Lett. 13, 611–616 (1990).
[Crossref]

1989 (2)

J. A. Burns and L. Schaffer, “Orbital evolution of circumplanetary dust by resonant charge variations”, Nature 337, 340–343 (1989).
[Crossref]

M. Nauenberg, “Quantum wave packets on Kepler elliptic orbits”, Phys. Rev. A 40, 1133–1136 (1989).
[Crossref] [PubMed]

1978 (1)

R. Greenberg and D. R. Davis, “Stability at potential maxima: The L4 and L5 points of the Restricted Three-Body Problem”, Am. J. Phys. 46, 1068–1070, (1978).
[Crossref]

1913 (1)

N. Bohr, Phil. Mag. 26, 1–25 (1913); ibid., 476–502; ibid., 857–875.
[Crossref]

1911 (1)

E. Rutherford, Phil. Mag. 21, 669 (1911).
[Crossref]

1904 (1)

E. Nagaoka, “Kinetics of a system of particles illustrating the line and the band spectrum and the phenomena of radioactivity”, Phil. Mag. 7, 445–455 (1904).
[Crossref]

1878 (1)

G. W. Hill, Am. J. Math. 1, 5–128, (1878).
[Crossref]

Barut, A. O.

A. O. Barut and B. W. Xu, “Non-spreading coherent states riding on Kepler orbits”, Helv. Phys. Act. 66, 712–720 (1993).

Bialynicki-Birula, I.

M. Kaliński, J. H. Eberly, and I. Bialynicki-Birula,“Numerical observation of stable field supported Rydberg wave packets”, Phys. Rev. A 52, 2460–2463 (1995).
[Crossref]

I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly, Reply to Ref. 22, Phys. Rev. Lett. 75, 973 (1995).
[Crossref] [PubMed]

I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly, “Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons”, Phys. Rev. Lett. 73, 1777–1780 (1994).
[Crossref] [PubMed]

Z. Bialynicki-Birula and I. Bialynicki-Birula, “Radiative decay of Trojan wave packets”, (to be published).

Bialynicki-Birula, Z.

Z. Bialynicki-Birula and I. Bialynicki-Birula, “Radiative decay of Trojan wave packets”, (to be published).

Bohr, N.

N. Bohr, Phil. Mag. 26, 1–25 (1913); ibid., 476–502; ibid., 857–875.
[Crossref]

Born, M.

M. Born, The Mechanics of the Atom, (republished by F. Ungar, New York, 1960) (translated by J.W. Fisher); pp. 130–241.

Brunello, A. F.

E. Lee, A. F. Brunello, and D. Farrelly, “Coherent states in a Rydberg atom: Classical mechanics”, Phys. Rev. A 55, 2203–2221 (1997).
[Crossref]

A. F. Brunello, D. Farrelly, and T. Uzer, “Nonstationary, nondispersive wave packets in a Rydberg atom”, Phys. Rev. Lett. 76, 2874–2877 (1996).
[Crossref] [PubMed]

E. Lee, A. F. Brunello, and D. Farrelly, “A single atom Quasi-Penning trap”, Phys. Rev. Lett. 75, 3641–3644 (1995).
[Crossref] [PubMed]

Buchleitner, A.

J. Zakrzewski, D. Delande, and A. Buchleitner,“Nonspreading electronic wave packets and conductance fluctuations”, Phys. Rev. Lett. 75, 4015–4018 (1995).
[Crossref] [PubMed]

D. Delande, J. Zakrzewski, and A. Buchleitner, “A wave packet can be a stationary state”, Europhys. Lett. 32, 107–112 (1995).
[Crossref]

A. Buchleitner and D. Delande, “Nondispersive electronic wave packets in multiphoton processes”, Phys. Rev. Lett. 75, 1487–1490 (1995).
[Crossref] [PubMed]

A. Buchleitner and Thèse de doctorat, Université Pierre et Marie Currie, Paris, 1993 (unpublished).

K. Hornberger and A. Buchleitner, “Spontaneous decay of nondispersive wave packets”, (to be published).

Burns, J. A.

J. A. Burns and L. Schaffer, “Orbital evolution of circumplanetary dust by resonant charge variations”, Nature 337, 340–343 (1989).
[Crossref]

Burns, L.

L. Schaffer and L. Burns, “Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains”, J. Geophys. Res. 99, 17211–17223 (1994).
[Crossref]

Cerjan, C.

C. Cerjan, E. Lee, D. Farrelly, and T. Uzer, “Coherent states in a Rydberg atom: Quantum mechanics”, Phys. Rev. A 55, 2222–2231 (1997).
[Crossref]

Cheng, C. H.

C. H. Cheng, C. Y. Lee, and T. F. Gallagher, “Production of circular Rydberg states with circularly polarized microwave fields”, Phys. Rev. Lett. 73, 3078–3081 (1994).
[Crossref] [PubMed]

Davis, D. R.

R. Greenberg and D. R. Davis, “Stability at potential maxima: The L4 and L5 points of the Restricted Three-Body Problem”, Am. J. Phys. 46, 1068–1070, (1978).
[Crossref]

de doctorat, Thèse

A. Buchleitner and Thèse de doctorat, Université Pierre et Marie Currie, Paris, 1993 (unpublished).

Dehmelt, H.

H. Dehmelt, “Nobel Prize Lecture”, Rev. Mod. Phys. 62, 525–531 (1992).
[Crossref]

Delande, D.

A. Buchleitner and D. Delande, “Nondispersive electronic wave packets in multiphoton processes”, Phys. Rev. Lett. 75, 1487–1490 (1995).
[Crossref] [PubMed]

J. Zakrzewski, D. Delande, and A. Buchleitner,“Nonspreading electronic wave packets and conductance fluctuations”, Phys. Rev. Lett. 75, 4015–4018 (1995).
[Crossref] [PubMed]

D. Delande, J. Zakrzewski, and A. Buchleitner, “A wave packet can be a stationary state”, Europhys. Lett. 32, 107–112 (1995).
[Crossref]

Eberly, J. H.

M. Kaliński and J. H. Eberly, “Trojan wave packets: Mathieu theory and generation from circular states”, Phys. Rev. A 53, 1715–1724 (1996).
[Crossref]

M. Kaliński and J. H. Eberly,“New states of hydrogen in a circulary polarized microwave field”, Phys. Rev. Lett. 77, 2420–2423 (1995).
[Crossref]

I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly, Reply to Ref. 22, Phys. Rev. Lett. 75, 973 (1995).
[Crossref] [PubMed]

M. Kaliński, J. H. Eberly, and I. Bialynicki-Birula,“Numerical observation of stable field supported Rydberg wave packets”, Phys. Rev. A 52, 2460–2463 (1995).
[Crossref]

I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly, “Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons”, Phys. Rev. Lett. 73, 1777–1780 (1994).
[Crossref] [PubMed]

Farrelly, D.

E. Lee, A. F. Brunello, and D. Farrelly, “Coherent states in a Rydberg atom: Classical mechanics”, Phys. Rev. A 55, 2203–2221 (1997).
[Crossref]

C. Cerjan, E. Lee, D. Farrelly, and T. Uzer, “Coherent states in a Rydberg atom: Quantum mechanics”, Phys. Rev. A 55, 2222–2231 (1997).
[Crossref]

A. F. Brunello, D. Farrelly, and T. Uzer, “Nonstationary, nondispersive wave packets in a Rydberg atom”, Phys. Rev. Lett. 76, 2874–2877 (1996).
[Crossref] [PubMed]

E. Lee, A. F. Brunello, and D. Farrelly, “A single atom Quasi-Penning trap”, Phys. Rev. Lett. 75, 3641–3644 (1995).
[Crossref] [PubMed]

D. Farrelly, E. Lee, and T. Uzer, “Magnetic field stabilization of Rydberg wavepackets in a circulary polarized microwave field”, Phys. Lett. A 204, 359–372 (1995).
[Crossref]

D. Farrelly, E. Lee, and T. Uzer, Comment on “Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons”, Phys. Rev. Lett. 75, 972 (1995).
[Crossref] [PubMed]

D. Farrelly and T. Uzer, “Ionization mechanism of Rydberg atoms in a circulary polarized microwave field”,Phys. Rev. Lett. 74, 1720–1723 (1995).
[Crossref] [PubMed]

Fauth, M.

G. Raithel, M. Fauth, and H. Walther, “Atoms in strong crossed electric and magnetic fields: Evidence for states with large electric-dipole moments”, Phys. Rev. A 47, 419–440 (1991).
[Crossref]

Fu, P.

P. Fu, T. J. Scholz, J. M. Hettema, and T. F. Gallagher, “Ionization of Rydberg atoms by circularly polarized microwave field”, Phys. Rev. Lett. 64, 511–514 (1990).
[Crossref] [PubMed]

Gallagher, T. F.

C. H. Cheng, C. Y. Lee, and T. F. Gallagher, “Production of circular Rydberg states with circularly polarized microwave fields”, Phys. Rev. Lett. 73, 3078–3081 (1994).
[Crossref] [PubMed]

P. Fu, T. J. Scholz, J. M. Hettema, and T. F. Gallagher, “Ionization of Rydberg atoms by circularly polarized microwave field”, Phys. Rev. Lett. 64, 511–514 (1990).
[Crossref] [PubMed]

T. F. Gallagher, Rydberg Atoms, (Cambridge University Press, Cambridge, 1994).
[Crossref]

Greenberg, R.

R. Greenberg and D. R. Davis, “Stability at potential maxima: The L4 and L5 points of the Restricted Three-Body Problem”, Am. J. Phys. 46, 1068–1070, (1978).
[Crossref]

Hettema, J. M.

P. Fu, T. J. Scholz, J. M. Hettema, and T. F. Gallagher, “Ionization of Rydberg atoms by circularly polarized microwave field”, Phys. Rev. Lett. 64, 511–514 (1990).
[Crossref] [PubMed]

Hill, G. W.

G. W. Hill, Am. J. Math. 1, 5–128, (1878).
[Crossref]

Hornberger, K.

K. Hornberger and A. Buchleitner, “Spontaneous decay of nondispersive wave packets”, (to be published).

Kalinski, M.

M. Kaliński and J. H. Eberly, “Trojan wave packets: Mathieu theory and generation from circular states”, Phys. Rev. A 53, 1715–1724 (1996).
[Crossref]

M. Kaliński and J. H. Eberly,“New states of hydrogen in a circulary polarized microwave field”, Phys. Rev. Lett. 77, 2420–2423 (1995).
[Crossref]

I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly, Reply to Ref. 22, Phys. Rev. Lett. 75, 973 (1995).
[Crossref] [PubMed]

M. Kaliński, J. H. Eberly, and I. Bialynicki-Birula,“Numerical observation of stable field supported Rydberg wave packets”, Phys. Rev. A 52, 2460–2463 (1995).
[Crossref]

I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly, “Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons”, Phys. Rev. Lett. 73, 1777–1780 (1994).
[Crossref] [PubMed]

Kappertz, P.

P. Kappertz and M. Nauenberg, “Circularly polarized microwave ionization of hydrogen”, Phys. Rev. A 47, 4749–4755 (1993).
[Crossref] [PubMed]

Lee, C. Y.

C. H. Cheng, C. Y. Lee, and T. F. Gallagher, “Production of circular Rydberg states with circularly polarized microwave fields”, Phys. Rev. Lett. 73, 3078–3081 (1994).
[Crossref] [PubMed]

Lee, E.

E. Lee, A. F. Brunello, and D. Farrelly, “Coherent states in a Rydberg atom: Classical mechanics”, Phys. Rev. A 55, 2203–2221 (1997).
[Crossref]

C. Cerjan, E. Lee, D. Farrelly, and T. Uzer, “Coherent states in a Rydberg atom: Quantum mechanics”, Phys. Rev. A 55, 2222–2231 (1997).
[Crossref]

E. Lee, A. F. Brunello, and D. Farrelly, “A single atom Quasi-Penning trap”, Phys. Rev. Lett. 75, 3641–3644 (1995).
[Crossref] [PubMed]

D. Farrelly, E. Lee, and T. Uzer, “Magnetic field stabilization of Rydberg wavepackets in a circulary polarized microwave field”, Phys. Lett. A 204, 359–372 (1995).
[Crossref]

D. Farrelly, E. Lee, and T. Uzer, Comment on “Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons”, Phys. Rev. Lett. 75, 972 (1995).
[Crossref] [PubMed]

Nagaoka, E.

E. Nagaoka, “Kinetics of a system of particles illustrating the line and the band spectrum and the phenomena of radioactivity”, Phil. Mag. 7, 445–455 (1904).
[Crossref]

Nauenberg, M.

P. Kappertz and M. Nauenberg, “Circularly polarized microwave ionization of hydrogen”, Phys. Rev. A 47, 4749–4755 (1993).
[Crossref] [PubMed]

M. Nauenberg, Comment on “Ionization of Rydberg states by a circularly polarized microwave field”, Phys. Rev. Lett. 64, 2731 (1990).
[Crossref] [PubMed]

M. Nauenberg, “Canonical Kepler map”, Europhys. Lett. 13, 611–616 (1990).
[Crossref]

M. Nauenberg, “Quantum wave packets on Kepler elliptic orbits”, Phys. Rev. A 40, 1133–1136 (1989).
[Crossref] [PubMed]

Raithel, G.

G. Raithel, M. Fauth, and H. Walther, “Atoms in strong crossed electric and magnetic fields: Evidence for states with large electric-dipole moments”, Phys. Rev. A 47, 419–440 (1991).
[Crossref]

Rutherford, E.

E. Rutherford, Phil. Mag. 21, 669 (1911).
[Crossref]

Schaffer, L.

L. Schaffer and L. Burns, “Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains”, J. Geophys. Res. 99, 17211–17223 (1994).
[Crossref]

J. A. Burns and L. Schaffer, “Orbital evolution of circumplanetary dust by resonant charge variations”, Nature 337, 340–343 (1989).
[Crossref]

Scholz, T. J.

P. Fu, T. J. Scholz, J. M. Hettema, and T. F. Gallagher, “Ionization of Rydberg atoms by circularly polarized microwave field”, Phys. Rev. Lett. 64, 511–514 (1990).
[Crossref] [PubMed]

Stroud, C. R.

J. A. Yeazell and C. R. Stroud, “Observation of fractional revivals in the evolution of a Rydberg atomic wave packet”, Phys. Rev. A 43, 5153–5156 (1991).
[Crossref] [PubMed]

Szebehely, V.

V. Szebehely, Theory of orbits: The restricted problem of three bodies, (Academic, New York and London, 1967).

Uzer, T.

C. Cerjan, E. Lee, D. Farrelly, and T. Uzer, “Coherent states in a Rydberg atom: Quantum mechanics”, Phys. Rev. A 55, 2222–2231 (1997).
[Crossref]

A. F. Brunello, D. Farrelly, and T. Uzer, “Nonstationary, nondispersive wave packets in a Rydberg atom”, Phys. Rev. Lett. 76, 2874–2877 (1996).
[Crossref] [PubMed]

D. Farrelly, E. Lee, and T. Uzer, “Magnetic field stabilization of Rydberg wavepackets in a circulary polarized microwave field”, Phys. Lett. A 204, 359–372 (1995).
[Crossref]

D. Farrelly, E. Lee, and T. Uzer, Comment on “Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons”, Phys. Rev. Lett. 75, 972 (1995).
[Crossref] [PubMed]

D. Farrelly and T. Uzer, “Ionization mechanism of Rydberg atoms in a circulary polarized microwave field”,Phys. Rev. Lett. 74, 1720–1723 (1995).
[Crossref] [PubMed]

Walther, H.

G. Raithel, M. Fauth, and H. Walther, “Atoms in strong crossed electric and magnetic fields: Evidence for states with large electric-dipole moments”, Phys. Rev. A 47, 419–440 (1991).
[Crossref]

Xu, B. W.

A. O. Barut and B. W. Xu, “Non-spreading coherent states riding on Kepler orbits”, Helv. Phys. Act. 66, 712–720 (1993).

Yeazell, J. A.

J. A. Yeazell and C. R. Stroud, “Observation of fractional revivals in the evolution of a Rydberg atomic wave packet”, Phys. Rev. A 43, 5153–5156 (1991).
[Crossref] [PubMed]

Zakrzewski, J.

J. Zakrzewski, D. Delande, and A. Buchleitner,“Nonspreading electronic wave packets and conductance fluctuations”, Phys. Rev. Lett. 75, 4015–4018 (1995).
[Crossref] [PubMed]

D. Delande, J. Zakrzewski, and A. Buchleitner, “A wave packet can be a stationary state”, Europhys. Lett. 32, 107–112 (1995).
[Crossref]

Am. J. Math. (1)

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[Crossref]

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R. Greenberg and D. R. Davis, “Stability at potential maxima: The L4 and L5 points of the Restricted Three-Body Problem”, Am. J. Phys. 46, 1068–1070, (1978).
[Crossref]

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[Crossref]

D. Delande, J. Zakrzewski, and A. Buchleitner, “A wave packet can be a stationary state”, Europhys. Lett. 32, 107–112 (1995).
[Crossref]

Helv. Phys. Act. (1)

A. O. Barut and B. W. Xu, “Non-spreading coherent states riding on Kepler orbits”, Helv. Phys. Act. 66, 712–720 (1993).

J. Geophys. Res. (1)

L. Schaffer and L. Burns, “Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains”, J. Geophys. Res. 99, 17211–17223 (1994).
[Crossref]

Nature (1)

J. A. Burns and L. Schaffer, “Orbital evolution of circumplanetary dust by resonant charge variations”, Nature 337, 340–343 (1989).
[Crossref]

Phil. Mag. (3)

E. Rutherford, Phil. Mag. 21, 669 (1911).
[Crossref]

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[Crossref]

N. Bohr, Phil. Mag. 26, 1–25 (1913); ibid., 476–502; ibid., 857–875.
[Crossref]

Phys. Lett. A (1)

D. Farrelly, E. Lee, and T. Uzer, “Magnetic field stabilization of Rydberg wavepackets in a circulary polarized microwave field”, Phys. Lett. A 204, 359–372 (1995).
[Crossref]

Phys. Rev. A (8)

E. Lee, A. F. Brunello, and D. Farrelly, “Coherent states in a Rydberg atom: Classical mechanics”, Phys. Rev. A 55, 2203–2221 (1997).
[Crossref]

C. Cerjan, E. Lee, D. Farrelly, and T. Uzer, “Coherent states in a Rydberg atom: Quantum mechanics”, Phys. Rev. A 55, 2222–2231 (1997).
[Crossref]

M. Kaliński, J. H. Eberly, and I. Bialynicki-Birula,“Numerical observation of stable field supported Rydberg wave packets”, Phys. Rev. A 52, 2460–2463 (1995).
[Crossref]

M. Kaliński and J. H. Eberly, “Trojan wave packets: Mathieu theory and generation from circular states”, Phys. Rev. A 53, 1715–1724 (1996).
[Crossref]

G. Raithel, M. Fauth, and H. Walther, “Atoms in strong crossed electric and magnetic fields: Evidence for states with large electric-dipole moments”, Phys. Rev. A 47, 419–440 (1991).
[Crossref]

M. Nauenberg, “Quantum wave packets on Kepler elliptic orbits”, Phys. Rev. A 40, 1133–1136 (1989).
[Crossref] [PubMed]

P. Kappertz and M. Nauenberg, “Circularly polarized microwave ionization of hydrogen”, Phys. Rev. A 47, 4749–4755 (1993).
[Crossref] [PubMed]

J. A. Yeazell and C. R. Stroud, “Observation of fractional revivals in the evolution of a Rydberg atomic wave packet”, Phys. Rev. A 43, 5153–5156 (1991).
[Crossref] [PubMed]

Phys. Rev. Lett. (12)

P. Fu, T. J. Scholz, J. M. Hettema, and T. F. Gallagher, “Ionization of Rydberg atoms by circularly polarized microwave field”, Phys. Rev. Lett. 64, 511–514 (1990).
[Crossref] [PubMed]

C. H. Cheng, C. Y. Lee, and T. F. Gallagher, “Production of circular Rydberg states with circularly polarized microwave fields”, Phys. Rev. Lett. 73, 3078–3081 (1994).
[Crossref] [PubMed]

M. Nauenberg, Comment on “Ionization of Rydberg states by a circularly polarized microwave field”, Phys. Rev. Lett. 64, 2731 (1990).
[Crossref] [PubMed]

M. Kaliński and J. H. Eberly,“New states of hydrogen in a circulary polarized microwave field”, Phys. Rev. Lett. 77, 2420–2423 (1995).
[Crossref]

D. Farrelly, E. Lee, and T. Uzer, Comment on “Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons”, Phys. Rev. Lett. 75, 972 (1995).
[Crossref] [PubMed]

I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly, Reply to Ref. 22, Phys. Rev. Lett. 75, 973 (1995).
[Crossref] [PubMed]

D. Farrelly and T. Uzer, “Ionization mechanism of Rydberg atoms in a circulary polarized microwave field”,Phys. Rev. Lett. 74, 1720–1723 (1995).
[Crossref] [PubMed]

I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly, “Lagrange equilibrium points in celestial mechanics and nonspreading wave packets for strongly driven Rydberg electrons”, Phys. Rev. Lett. 73, 1777–1780 (1994).
[Crossref] [PubMed]

A. Buchleitner and D. Delande, “Nondispersive electronic wave packets in multiphoton processes”, Phys. Rev. Lett. 75, 1487–1490 (1995).
[Crossref] [PubMed]

J. Zakrzewski, D. Delande, and A. Buchleitner,“Nonspreading electronic wave packets and conductance fluctuations”, Phys. Rev. Lett. 75, 4015–4018 (1995).
[Crossref] [PubMed]

E. Lee, A. F. Brunello, and D. Farrelly, “A single atom Quasi-Penning trap”, Phys. Rev. Lett. 75, 3641–3644 (1995).
[Crossref] [PubMed]

A. F. Brunello, D. Farrelly, and T. Uzer, “Nonstationary, nondispersive wave packets in a Rydberg atom”, Phys. Rev. Lett. 76, 2874–2877 (1996).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

H. Dehmelt, “Nobel Prize Lecture”, Rev. Mod. Phys. 62, 525–531 (1992).
[Crossref]

Other (7)

T. F. Gallagher, Rydberg Atoms, (Cambridge University Press, Cambridge, 1994).
[Crossref]

M. Born, The Mechanics of the Atom, (republished by F. Ungar, New York, 1960) (translated by J.W. Fisher); pp. 130–241.

V. Szebehely, Theory of orbits: The restricted problem of three bodies, (Academic, New York and London, 1967).

K. Hornberger and A. Buchleitner, “Spontaneous decay of nondispersive wave packets”, (to be published).

Z. Bialynicki-Birula and I. Bialynicki-Birula, “Radiative decay of Trojan wave packets”, (to be published).

A. Buchleitner and Thèse de doctorat, Université Pierre et Marie Currie, Paris, 1993 (unpublished).

Deprit, in The Big Bang and George Lemaitre, edt. A. Berger, (Reidel, Dordrecht, 1984), pp. 151–180.

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Figures (4)

Fig. 1.
Fig. 1.

Effective potential (V) with ωc = 3.46T, ωf =50 GHz, and F = 2000V/cm. Energy and distance are in atomic units (a.u.) A section (y = z = 0) through the potential is shown. Also plotted is the harmonic approximation (Vho ) to the potential and the probability density (∣Ψ∣2) of the corresponding vacuum state, which in the laboratory frame constitutes our wave packet. For snapshots of its progress on its orbit, see Fig.3 of Ref. 34.

Fig. 2.
Fig. 2.

Level curves of the potential together with contours (at 0.25, 0.5, 0.75, 0.95) of the vacuum coherent state as obtained by Taylor expansion about the minimum. The parameters are the same as Fig. 1. The outer minimum exists provided F > F c = 3 [ ω f ( ω c ω f ) ] 2 / 3 4 : 3 the well depth, its distance from the nucleus and the width of the barrier all depend sensitively on the fields used, providing considerable flexibility in the selection of appropriate experimental parameters.

Fig. 3:
Fig. 3:

Combined Poincaré surface of sections for 10 classical trajectories obtained by integrating Hamilton’s equations for Eq. (3) with ϵ = 1, Ω = 1/2, (for which value the velocity dependent forces are eliminated) and �� = -2.1.

Fig. 4:
Fig. 4:

Combined Poincaré surface of sections for 75 classical trajectories obtained by integrating Hamilton’s equations for Eq. (3) with ϵ = 0.9, Ω = 0.65, and �� = -1.85. The points generated by each trajectory have been assigned a different color. This allows one to pick out, e.g., groups of islands related by single resonance.

Equations (5)

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

H = p ˜ 2 2 1 r + ω c 2 ( x p y y p x ) + ω c 2 8 ( x 2 + y 2 ) F ( x cos ω f t + y sin ω f t ) .
H = K = p ˜ 2 2 1 r ( ω f ω c 2 ) ( x p y y p x ) + ω c 2 8 ( x 2 + y 2 ) F x
r ' = ω c 2 3 r , p ' = ω c 1 3 p .
H = 𝐾 = 1 2 ( p x 2 + p y 2 ) 1 r ( Ω 1 2 ) ( x p y y p x ) + 1 8 ( x 2 + y 2 ) ϵ x
V = H ( x ˙ 2 + y ˙ 2 ) 2 = 1 r + ω f ( ω c ω f ) 2 ( x 2 + y 2 ) F x

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