A single trapped ion in a finite range trap

TL;DR

This paper develops a model for the dynamics of a trapped ion in a finite range potential, revealing that its steady state is a nonlinear coherent state influenced by the trap's finite size.

Contribution

It introduces a solvable potential model for finite range traps and analyzes the resulting nonlinear coherent states of the ion's motion.

Findings

Steady state is a nonlinear coherent state.

Physical properties depend on the trap's finite range.

Model provides a realistic description of ion dynamics in finite traps.

Abstract

This paper presents a method to describe dynamics of an ion confined in a realistic finite range trap. We model this realistic potential with a solvable one and we obtain dynamical variables (raising and lowering operators) of this potential. We consider coherent interaction of this confined ion in a finite range trap and we show that its center-of-mass motion steady state is a special kind of nonlinear coherent states. Physical properties of this state and their dependence on the finite range of potential are studied.