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There is a growing interest in high-precision spectroscopy and frequency metrology for fundamental studies using sympathetically cooled highly charged ions (HCIs) embedded in Coulomb crystals of laser-cooled ions. In order to understand how their strong repulsion affects the crystal structure and dynamics, we study the thermal motion and rearrangement of small mixed linear and homogeneous crystals by both measurements and simulations. Co-crystallized HCIs form superlattices and divide the crystal into domains, where different reordering rates, melting points and localized phase transitions are observed due to decoupling of motional modes across boundaries. These results improve our understanding of homogeneous and inhomogeneous ion strings over a wide range of charge-to-mass ratios. This allows us to test our own simulations of the dynamic behavior of ion strings and gives us confidence in their suitability for applications related to quantum simulation as well as computing and the search for new physics., Comment: 19 pages, 15 figures

We propose In-like Pr10+ as a candidate for the development of a high-accuracy optical clock with high sensitivity to a time variation of the fine-structure constant, (\dot alpha}/alpha, as well as favorable experimental systematics. We calculate its low-lying energy levels by combining the configuration interaction and the coupled cluster method, achieving uncertainties as low as 0.1%, and improving previous work. We benchmark these results by comparing our calculations for the (5s^2 5p 2P_1/2) - (5s^2 5p 2P_3/2) transition in Pr10+ with a dedicated measurement and for Pr9+ with a recent experiment, respectively. In addition, we report calculated hyperfine-structure constants for the clock and logic states in Pr10+., Comment: 9 pages, 2 figures