Hopping of an impurity defect in ion crystals in linear traps

Abstract

Laser-cooled arrays or crystals of $^{171}\mathrm{Yb}$${}^{+}$ ions containing a single impurity, $^{172}\mathrm{Yb}$${}^{+}$ isotope, are confined in a linear radio-frequency Paul trap. Site-to-site hopping of the impurity ion, distinguished by a lack of fluorescence, is studied as a function of the $^{171}\mathrm{Yb}$${}^{+}$ laser-cooling parameters and as a function of the anisotropy of the trapping potential. Imaging of the independently resolved crystal sites permits the extraction of the impurity's hopping trajectory, from which the dwell times at a given site can be obtained as well as the spatial distribution of hopping rate and hopping destination. The onset of rapid hopping is found to occur at average thermal energies approaching a significant fraction of 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. Finally, the hopping mobility of the impurity ion is observed to be highest near the center of the crystal, which may have an intrinsic cause related to the crystal structure and dynamics near the zigzag transition.