Advertisement

Amazing Light pp 333-341 | Cite as

Deterministic Order-Chaos Transition of Two Ions in a Paul Trap

  • John A. Hoffnagle
  • Richard G. Brewer

Abstract

In addition to their many applications in spectroscopy and quantum electronics, ion traps offer unique possibilities to study the nonlinear dynamics of simple systems. This was first realized in a beautiful, early demonstration of electrodynamic confinement of charged aluminum particles [1], which were observed to form regular, “crystalline” arrays. Increasing the trap voltage induced “melting,” i.e., the arrays abruptly disintegrated into shapeless clouds; when the trap voltage was reduced again, the particles recrystallized. Since this first observation of Coulomb crystals in the Paul trap, the use of laser cooling [2] has allowed experiments to be carried out with individual atomic ions and the theory of deterministic chaos has provided a framework in which to understand irregular motion such as the ion cloud. Cold ions were made to crystallize in Paul traps [3] and transitions between regular and chaotic motion were observed upon varying the trap voltage [4,5], in clear analogy withRef. [1].

Keywords

Periodic Orbit Invariant Manifold Chaotic Attractor Chaotic Motion Paul Trap 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. F. Wuerker, H. Shelton, and R. V. Langmuir, J. Appl. Phys. 30, 342 (1959).ADSCrossRefGoogle Scholar
  2. [2]
    W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978).ADSCrossRefGoogle Scholar
  3. [3]
    F. Diedrich, E. Peik, J. M. Chen, W. Quint, and H. Walther, Phys. Rev. Lett. 59,2931 (1987); D. J. Wineland, J. C. Bergquist, W. M. Itano, J. J. Bollinger, and C. H. Manney, Phys. Rev. Lett. 59, 2935 (1987).ADSCrossRefGoogle Scholar
  4. [4]
    J. Hoffnagle, R. G. DeVoe, L. Reyna, and R. G. Brewer, Phys. Rev. Lett. 61, 255 (1988).ADSCrossRefGoogle Scholar
  5. [5]
    R. Blümel et al, Nature (London) 334, 309 (1988).ADSCrossRefGoogle Scholar
  6. [6]
    R. Blümel, C. Kappler, W. Quint, and H. Walther, Phys. Rev. A 40, 808 (1989).ADSCrossRefGoogle Scholar
  7. [7]
    R. G. Brewer, J. Hoffnagle, and R.G. DeVoe, Phys. Rev. Lett. 65, 2619 (1990).ADSCrossRefGoogle Scholar
  8. [8]
    R. G. Brewer, J. Hoffnagle, and R.G. DeVoe, Phys. Rev. Lett. 65, 2619 (1990).ADSCrossRefGoogle Scholar
  9. [9]
    J. Hoffnagle and R. G. Brewer, Phys. Rev. A 50, 4157 (1994).ADSzbMATHCrossRefGoogle Scholar
  10. [10]
    J. Wisdom, Icarus 72, 241 (1987).ADSCrossRefGoogle Scholar
  11. [11]
    J. Hoffnagle and R. G. Brewer, Science 265, 213 (1994).ADSCrossRefGoogle Scholar
  12. [12]
    J. Hoffnagle and R. G. Brewer, Phys. Rev. Lett. 71, 1828 (1993).ADSCrossRefGoogle Scholar
  13. [13]
    E. Fischer, Z. Physik 156, 1 (1959).ADSCrossRefGoogle Scholar
  14. T. Tél, in Directions in Chaos, Vol 3, edited by Hao Bai-Lin ( World Scientific, Singapore, 1990 ).Google Scholar
  15. [15]
    C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982); Physica 7D, 181 (1983); Phys. Rev. Lett. 57, 1284 (1986); C. Grebogi, E. Ott, F. Romeiras, and J. A. Yorkee, Phys. Rev. A 36, 5365 (1987).MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • John A. Hoffnagle
  • Richard G. Brewer

There are no affiliations available

Personalised recommendations