Extracting Classical Trajectories from Atomic Spectra

M. R. Haggerty; Neal Spellmeyer; Daniel Kleppner; J. B. Delos

doi:10.1103/PhysRevLett.81.1592

Access by Xinjiang University

Extracting Classical Trajectories from Atomic Spectra

M. R. Haggerty^1,*, Neal Spellmeyer², Daniel Kleppner², and J. B. Delos¹

¹Physics Department, College of William and Mary, Williamsburg, Virginia 23187
²Research Laboratory of Electronics, George R. Harrison Spectroscopy Laboratory, and Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

^*Current address: Department of Physics, Harvard University, Cambridge, MA 02138.

PDF

Phys. Rev. Lett. 81, 1592 – Published 24 August, 1998

DOI: https://doi.org/10.1103/PhysRevLett.81.1592

Abstract

We describe how to reconstruct individual classical trajectories from spectroscopic data. The ac dipole moment of a trajectory can be found from the effect of an oscillating field on the spectrum. The inverse Fourier transform of such data yields the component of the electron trajectory along the direction of the oscillating field. We demonstrate the method by experimentally extracting $z (t)$ for two electron trajectories that influence the Stark spectrum of Rydberg lithium. Within the experimental resolution, the reconstructed orbits agree well with classical predictions.

References (13)

M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, Berlin,1990).
Inverse scattering methods and the Rydberg-Klein-Rees method use scattering data or eigenvalues to reconstruct a potential energy, from which one can compute classical trajectories. See R. Newton, Scattering Theory (McGraw-Hill, New York,1966), pp. 140 and 610; G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand Reinhold, New York,1950), p. 102.
A. Dvornik, B.Sc. thesis, Massachusetts Institute of Technology, 1998; M. Baranger, A. Dvornik, and D. Provost (to be published).
E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984).
M. L. Du and J. B. Delos, Phys. Rev. A 38, 1896 (1988).
E. B. Bogomol'nyĭ, Zh. Eksp. Teor. Fiz. 96, 487 (1989) [Sov. Phys. JETP 69, 275 (1989)].
A. Holle, J. Main, G. Wiebusch, H. Rottke, and K. H. Welge, Phys. Rev. Lett. 61, 161 (1988).
G. Raithel, M. Fauth, and H. Walther, Phys. Rev. A 47, 419 (1993).
N. Spellmeyer, D. Kleppner, M. R. Haggerty, V. Kondratovich, J. B. Delos, and J. Gao, Phys. Rev. Lett. 79, 1650 (1997).
M. Courtney, N. Spellmeyer, H. Jiao, and D. Kleppner, Phys. Rev. A 51, 3604 (1995).
M. R. Haggerty et al. (to be published).
Because of cylindrical symmetry, Eq. 2 would be modified for the other rf field polarizations.
J. Gao and J. B. Delos, Phys. Rev. A 49, 869 (1994).

[c1] M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, Berlin,1990).

[c2] Inverse scattering methods and the Rydberg-Klein-Rees method use scattering data or eigenvalues to reconstruct a potential energy, from which one can compute classical trajectories. See R. Newton, Scattering Theory (McGraw-Hill, New York,1966), pp. 140 and 610; G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand Reinhold, New York,1950), p. 102.

[c3] A. Dvornik, B.Sc. thesis, Massachusetts Institute of Technology, 1998; M. Baranger, A. Dvornik, and D. Provost (to be published).

[c4] E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984).

[c5] M. L. Du and J. B. Delos, Phys. Rev. A 38, 1896 (1988).

[c6] E. B. Bogomol'nyĭ, Zh. Eksp. Teor. Fiz. 96, 487 (1989) [Sov. Phys. JETP 69, 275 (1989)].

[c7] A. Holle, J. Main, G. Wiebusch, H. Rottke, and K. H. Welge, Phys. Rev. Lett. 61, 161 (1988).

[c8] G. Raithel, M. Fauth, and H. Walther, Phys. Rev. A 47, 419 (1993).

[c9] N. Spellmeyer, D. Kleppner, M. R. Haggerty, V. Kondratovich, J. B. Delos, and J. Gao, Phys. Rev. Lett. 79, 1650 (1997).

[c10] M. Courtney, N. Spellmeyer, H. Jiao, and D. Kleppner, Phys. Rev. A 51, 3604 (1995).

[c11] M. R. Haggerty et al. (to be published).

[c12] Because of cylindrical symmetry, Eq. 2 would be modified for the other rf field polarizations.

[c13] J. Gao and J. B. Delos, Phys. Rev. A 49, 869 (1994).

Physical Review Letters

Export citation

Export citation

Extracting Classical Trajectories from Atomic Spectra

Abstract

References (13)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation