$J=0$ metastable state of $\mathrm{Th}^{2+}$ for a hyperfine-free nuclear clock

We present measurements on a metastable state in $\mathrm{Th}^{2+}$ with the electronic configuration $6d^2\,{}^3P_0\,(5090\ \mathrm{cm^{-1}})$. This is motivated by the prospect of using the state in laser excitation of the low-energy $^{229}$Th nuclear resonance independent from the leading hyperfine interactions. The $6d^2\,{}^3P_0$ state has no dipole-allowed radiative decay channel and is connected to the second ground state $6d^2\,{}^3F_2\,(63\ \mathrm{cm^{-1}})$ through an electric quadrupole transition only. We populate the state by laser excitation at 484~nm via a higher excited level and detect its population in laser-induced fluorescence. The isotope shift of the $J=0$ level between $^{232}\mathrm{Th}^{2+}$ and $^{229}\mathrm{Th}^{2+}$ is determined as a measure of the interaction of electronic and nuclear charge distributions. The lifetime of the level in our ion trap with buffer gas is limited by collisional mixing with the nearby state $5f6d\,{}^3G_3\,(5060\ \mathrm{cm^{-1}})$. In ultrahigh vacuum, it could serve as a hyperfine-free nuclear clock that is largely immune to field-induced frequency shifts via the electron shell.