Sensitivity to perturbations for two-ion crystals in a Paul trap: fractal phase space boundary

  • Matthew Mackie
  • R. V. Jensen
  • W. W. Smith
Conference paper


We solve numerically the classical equations of motion [1] for two damped (laser-cooled) ions in a Paul r.f. trap [2]. These equations are very similar to those describing two coupled, driven anharmonic Duffing oscillators and suggest that the two-trapped ion system may be a suitable test system for studies of nonlinear dynamics and chaos on the atomic level. These studies are of interest in part because of the extensive recent experiments with modifications of the original Paul r.f. quadrupole design [3] in order to miniaturize and simplify the trap structure or with the intent of making frequency standards; for frequency standard purposes chaotic motion is something to be studied and avoided. In addition, the possibility has arisen recently of laser cooling trapped ions down to their lowest quantum states with the possibility of generating nonclassical states of motion and even in using stored ions in constructing quantum logic gates [4].


Instability Region Laser Cool Paul Trap Trap Structure Bistable Region 


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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Matthew Mackie
    • 1
  • R. V. Jensen
    • 2
  • W. W. Smith
    • 1
  1. 1.Physics Dept.University of ConnecticutStorrsUSA
  2. 2.Physics Dept.Wesleyan UniversityMiddletownUSA

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