Theory and Simulation of a Collection of Paul-Trapped Ions

Consider a collection of Paul-trapped particles. Because ions interact via the nonlinear Coulomb force, the equations of motion cannot be solved exactly. As a result, the approximation of single-ion motion in region A (Sec. ) is not valid for strongly correlated multiple-ion simulations. As we shall see, interactions between a collection of particles can lead to interesting ion dynamics, such as chaotic heating and crystallization.

• Equations of Motion for a Collection of Paul-Trapped Particles
• Behaviors Observed for Paul-Trapping in Region A
  • Mathieu Regime
  • Chaotic Regime
  • Quasiperiodic Regime
  • Crystalline Phase
  • The Coulomb Coupling Parameter
  • Orientation of Two-Ion Crystals
  • Equilibrium Spacing for the Two-Ion Crystal
• Investigation of Crystal Stability in Region A
  • Viscous Damping and Crystal Stability in Region A
  • The Mathieu Parameters and Crystal Stability in Region A
    • Response of Crystal to Sudden Changes in Mathieu Parameters
    • Response of Crystal to Continuous Changes in Mathieu Parameters
• Behaviors Simulated for Paul-Trapping in Region B
  • Mathieu Regime
  • Chaotic Regime
  • Ordered Phase
• Investigation of Crystal Stability in Region B