Topological equivalence in the theory of trapped ions

Abstract

We consider an ion whose motion is confined to a plane perpendicular to a constant magnetic field. A harmonic trapping field is applied within the plane of the ion's motion, together with some unspecified irradiating probe beam. By determining the dynamics of the ion we show that the particle theory is formally equivalent to that of a coupled massive (1 + 2)-dimensional vector Boson field. The field characteristics of current and Proca mass take on the roles of the interaction and harmonic potential respectively of the ion. The topological mass appropriate to the restricted configuration space, which in the case of the vector Boson field is given by the Chern-Simons term, is provided by the constant magnetic field.