Searches for new physics with precision spectroscopy of highly charged ions

Novel clocks using narrow reference transitions in highly charged ions (HCI) can provide unique leverage to detecting new physics, including variations in fundamental constants \footnote{S. Schiller, \textbf{Phys. Rev. Lett.} 98, 180801 (2007)} \footnote{J. C. Berengut, V. A. Dzuba, V. V. Flambaum, \textbf{Phys. Rev. Lett.} 105, 120801 (2010); J. C. Berengut, V. A. Dzuba, V. V. Flambaum, A. Ong, \textbf{Phys. Rev. Lett.} 106, 210802 (2011)} and violations of Lorentz invariance \footnote{R. Shaniv et al., \textbf{Phys. Rev. Lett.} 120, 103202 (2018)}. Ultra-precise quantum logic spectroscopy of trapped HCIs has now been demonstrated \footnote{P. Micke \textit{et al.}, \textbf{Nature}, doi:10.1038/s41586-020-1959-8 (2020)}, opening the door to optical-clock-level accuracy. The variety of highly charged ions available provides new opportunities for experiment \footnote{M. G. Kozlov, M. S. Safronova, J. R. Crespo L\'opez-Urrutia, P. O. Schmidt, \textbf{Rev. Mod. Phys.} 90, 045005 (2018)}. For example, choosing HCI near orbital crossings allows optical transitions with high sensitivity to new physics, and many opportunities to control systematics. I will present recent results of theory and experiment in this direction, with particular focus recently measured structure of Pr$^{9+}$ \footnote{H. Bekker \textit{et al.}, \textbf{Nat. Comm.} 10, 5651 (2019)}.