The flattening phase transition in systems of trapped ions

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related to the inner-shell configurations of the clusters. The critical exponent for the order parameter of this phase transition (maximum extent in the z direction) was found computationally to have the value β = 1/2. A second critical exponent related to displacements perpendicular to the z axis was found to have the value δ = 1. Using these estimates of the critical exponents, we derive an equation that relates the amplitudes of the displacements of the ions parallel to the x-y plane to the amplitudes along the z axis during the flattening process. Key words: ion trap, flattening, phase transition, critical exponent. Quand on augmente l'anisotropie d'un piege ionique, les ions adoptent tot ou tard une structure aplatie formee de couches concentriques d'ions. Cet aplatissement se comporte comme une transition de phase du deuxieme ordre. Un graphe de l'anisotropie critique contre le nombre d'ions demontre une organisation reliee a la configuration de la couche interne de l'amas. Nos calculs numeriques demontrent que l'exposant critique associe au parametre d'ordre de cette transition de phase (l'etendue maximale le long de l'axe z) a la valeur β = 1/2. Un deuxieme exposant critique associe aux deplacements des ions perpendiculairement a l'axe z a la valeur δ = 1. Ces estimations numeriques des exposants critiques nous permettent d'obtenir une equation qui relie les amplitudes des deplacements des ions paralleles au plan x-y aux deplacements paralleles a l'axe z durant l'aplatissement. Mots-cles : piege ionique, aplatissement, transition de phase, exposant critique.
Introduction The potential energy of a system of N identically charged ions in a harmonic trap, expressed in dimensionless form, is (1,2) [1] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [...]