Temperature sensitivity of a Thorium-229 solid-state nuclear clock

Abstract: Quantum state-resolved spectroscopy of the low energy thorium-229 nuclear transition was recently achieved. The five allowed transitions within the electric quadrupole structure were measured to the kilohertz level in a calcium fluoride host crystal, opening many new areas of research using nuclear clocks. Central to the performance of solid-state clock operation is an understanding of systematic shifts such as the temperature dependence of the clock transitions. In this work, we measure the four strongest transitions of thorium-229 in the same crystal at three temperature values: 150 K, 229 K, and 293 K. We find shifts of the unsplit frequency and the electric quadrupole splittings, corresponding to decreases in the electron density, electric field gradient, and field gradient asymmetry at the nucleus as temperature increases. The $\textit{m}$ = $\pm 5/2 \rightarrow \pm 3/2$ line shifts only 62(6) kHz over the temperature range, i.e., approximately 0.4 kHz/K, representing a promising candidate for a future solid-state optical clock. Achieving 10$^{-18}$ precision requires crystal temperature stability of 5$\mu$K.