Thorium-229 in its Highest Charge States: Single-Ion Nuclear Clocks for Tests of Fundamental Interactions
The prospects and the implementation of single-ion nuclear clocks of $^{229}$Th$^{q+}$ ions in their highest charge states $q=90, \ldots, 87$ are discussed. Highly-ionized-thorium clocks are ideal for tests of fundamental interactions since the ions are elementary quantum systems composed of only a few building blocks. Two cases of $^{229}$Th$^{q+}$ clocks excel: a) one-electron $^{229}$Th$^{89+}$ that combines two nuclear-clock transitions in the VUV with hyperfine IR atomic-clock transitions, and, b) fully ionized $^{229}$Th$^{90+}$ which constitutes the prototype of a nuclear clock, one without any electrons. We evaluate the feasibility of such clocks by means of quantum logic spectroscopy (QLS) in linear Paul traps. Due to its universal nature, the QLS approach allows for systematic clock comparisons using different charge states as well as different spectroscopy transitions on the same experimental platform. A valuable asset towards single-ion $^{229}$Th$^{q+}$ clocks is the process of nuclear hyperfine mixing that enables the tunability of the natural linewidth of the clock transition over more than five orders of magnitude by changing the charge state.