Frequency reproducibility of solid-state thorium-229 nuclear clocks

Solid-state thorium-229 (²²⁹Th) nuclear clocks^1,2,3,4,5 are set to provide new opportunities for precision metrology and fundamental physics^6,7,8. Taking advantage of inherent low sensitivity of a nuclear transition to its environment⁹, orders of magnitude more emitters can be hosted in a solid-state crystal compared with current optical lattice atomic clocks¹⁰. Furthermore, solid-state systems needing only simple thermal control¹¹ are key to the development of field-deployable compact clocks. Here we explore and characterize the frequency reproducibility of the ²²⁹Th:CaF₂ nuclear clock transition, a key performance metric for all clocks. We measure the transition linewidth and centre frequency as a function of the doping concentration, temperature and time. We report the concentration-dependent inhomogeneous linewidth of the nuclear transition, limited by the intrinsic host crystal¹² properties. We determine an optimal working temperature for the ²²⁹Th:CaF₂ nuclear clock at 196(5) K, at which the first-order thermal sensitivity vanishes. This would enable in situ temperature co-sensing using different quadrupole-split lines, reducing the temperature-induced systematic shift below the 10⁻¹⁸ fractional frequency uncertainty level. At 195 K, the reproducibility of the nuclear transition frequency is 220 Hz (fractionally 1.1 × 10⁻¹³) for two differently doped ²²⁹Th:CaF₂ crystals over 7 months. These results form the foundation for understanding, controlling and harnessing the coherent nuclear excitation of ²²⁹Th in solid-state hosts and for their applications in constraining temporal variations of fundamental constants.