Deterministic Order-Chaos Transition of Two Ions in a Paul Trap
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 , 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  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  and transitions between regular and chaotic motion were observed upon varying the trap voltage [4,5], in clear analogy withRef. .
KeywordsPeriodic Orbit Invariant Manifold Chaotic Attractor Chaotic Motion Paul Trap
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- T. Tél, in Directions in Chaos, Vol 3, edited by Hao Bai-Lin ( World Scientific, Singapore, 1990 ).Google Scholar