Frequency ratio of the ^229mTh nuclear isomeric transition and the ⁸⁷Sr atomic clock

Optical atomic clocks^1,2 use electronic energy levels to precisely keep track of time. A clock based on nuclear energy levels promises a next-generation platform for precision metrology and fundamental physics studies. Thorium-229 nuclei exhibit a uniquely low-energy nuclear transition within reach of state-of-the-art vacuum ultraviolet (VUV) laser light sources and have, therefore, been proposed for construction of a nuclear clock^3,4. However, quantum-state-resolved spectroscopy of the ^229mTh isomer to determine the underlying nuclear structure and establish a direct frequency connection with existing atomic clocks has yet to be performed. Here, we use a VUV frequency comb to directly excite the narrow ²²⁹Th nuclear clock transition in a solid-state CaF₂ host material and determine the absolute transition frequency. We stabilize the fundamental frequency comb to the JILA ⁸⁷Sr clock² and coherently upconvert the fundamental to its seventh harmonic in the VUV range by using a femtosecond enhancement cavity. This VUV comb establishes a frequency link between nuclear and electronic energy levels and allows us to directly measure the frequency ratio of the ²²⁹Th nuclear clock transition and the ⁸⁷Sr atomic clock. We also precisely measure the nuclear quadrupole splittings and extract intrinsic properties of the isomer. These results mark the start of nuclear-based solid-state optical clocks and demonstrate the first comparison, to our knowledge, of nuclear and atomic clocks for fundamental physics studies. This work represents a confluence of precision metrology, ultrafast strong-field physics, nuclear physics and fundamental physics.