Order-Chaos Transition of Two Trapped Ions

Abstract

Phase transitions of trapped particles and ions, observed initially in 1959 by collisional cooling and recently by laser cooling, are explained as order-chaos transitions. Here, two trapped ${\mathrm{Ba}}^{+}$ ions are examined experimentally and by computer solution of the equations of motion. The ordered state, quasiperiodic with two frequencies, becomes chaotic when a bifurcation introduces a third frequency at a critical value of a control parameter. This route evolves from the nonlinear Coulomb coupling of the ion pair's axial and radial motions, displaying frequency locking and hysteresis, which is observed.