Topological equivalence in the theory of trapped ions
نویسندگان
چکیده
We consider an ion whose motion is con®ned to a plane perpendicular to a constant magnetic ®eld. A harmonic trapping ®eld is applied within the plane of the ion’s motion, together with some unspeci®ed 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 ®eld. The ®eld characteristics of current and Proca mass take on the r̂oles of the interaction and harmonic potential respectively of the ion. The topological mass appropriate to the restricted con®guration space, which in the case of the vector Boson ®eld is given by the Chern±Simons term, is provided by the constant magnetic ®eld.
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