Solution to a Long-Standing Controversy in Paul-Trap Physics

Angus Kan, Wesleyan University

The study of charged particles dynamics in a Paul trap is the foundation of its wide-ranging applications, including analyzing proteins, determining isotope ratios, and constructing a quantum computer. However, in the simplest case of two-particle dynamics, there remains a controversy on whether a two-ion planar crystal undergoes an order-to-chaos transition at a critical, well-defined trap parameter value. Via analytical and numerical investigation of the Mathieu-Coulomb equations, I show that the transition does not exist.