A nuclear clock synchronized to ${}^{229}$Th

Abstract

Atomic clocks have made time and frequency the most precisely measured quantities in physics, progressing from microwave standards that realize the SI second to optical clocks with unprecedented precision. A nuclear clock transfers the frequency reference from an electronic to a nuclear transition, and the uniquely low-lying, laser-accessible isomeric transition in ${}^{229}$Th currently offers the most practical route to compact, robust timekeeping and sensitive tests of fundamental physics. Realizing such a clock requires turning spectroscopy of the ${}^{229}$Th nuclear resonance into a stable discriminator for steering a traceable oscillator. Here we demonstrate a ${}^{229}$Th nuclear clock by stabilizing a continuous-wave, narrow-linewidth 148.4-nm vacuum-ultraviolet (VUV) laser to a resolved, weakly temperature-sensitive nuclear transition in ${}^{229}$Th$:$CaF${}_2$ crystals. A $10$-$\mu \mathrm{W}$ VUV source generated by four-wave mixing in cadmium vapour and phototube-based frequency-modulation absorption readout provide a fast, high-signal-to-noise nuclear discriminator. The clock reaches a fractional frequency instability of $5\times 10^{-13}/\sqrt{\tau /\mathrm{s}}$ for averaging time $\tau$. Clock-transition frequencies measured in two independently fabricated crystals agree at the $10^{-13}$ level and are consistent with previous VUV-comb measurements on other ${}^{229}$Th:CaF${}_2$ crystals. These results establish laser-addressed nuclei as operational clock references and provide a reproducible solid-state platform for compact nuclear clocks, nuclear quantum sensors and precision tests of fundamental physics.