Single-Ion Nuclear Clock for Metrology at the 19th Decimal Place

The 7.6(5) eV nuclear magnetic-dipole transition in a single ${}^{229}\mathrm{Th}^{3+}$ ion may provide the foundation for an optical clock of superb accuracy. A virtual clock transition composed of stretched states within the $5F_{5/2}$ electronic ground level of both nuclear ground and isomeric manifolds is proposed. It is shown to offer unprecedented systematic shift suppression, allowing for clock performance with a total fractional inaccuracy approaching $1\times {10}^{-19}$.