Hopping of an impurity defect in ion crystals in linear traps

Ordered arrays of laser-cooled, trapped ions or "ion crystals'' are a novel form of matter with a rich variety of equilibrium structures and dynamics. In this thesis, we investigate the hopping mobility of a $^{172}$Yb$^+$ impurity ion within a crystal of $^{171}$Yb$^+$ ions, confined in a linear Paul trap. The site-to-site hopping of the impurity ion, distinguished by a lack of fluorescence, is studied as a function of the $^{171}$Yb$^+$ laser-cooling parameters and of the anisotropy of the trapping potential. The onset of rapid hopping is found to occur when average thermal energies become comparable to the Coulomb potential energy. Furthermore, the hopping rate is enhanced at trap anisotropies near the critical value for the structural phase transition to a two-dimensional zigzag phase. The impurity ion has the highest hopping mobility near the centre of the crystal, which may be intrinsic to the crystal structure and dynamics near the zigzag transition. Simplified molecular-dynamics simulations reproduce several features of the experimental results.