Abstract
Through the use of detailed numerical simulations we predict the existence of a nontrivial region in the Paul trap parameter space (a, q) where stable, singly periodic orbits (crystals) do not exist. As ions are dragged into this region via an adiabatic change in control parameters, a deterministic melting transition is observed. A detailed map of this deterministic melting region is constructed for the 2 and 3 ion cases. As crystals are dragged into this region by an adiabatic change of control parameters, a melting transition will occur. This transition does not depend on external perturbations, such as laser noise or collisions with neutral atoms.
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