Frequency ratio of the <SUP>229m</SUP>Th nuclear isomeric transition and the <SUP>87</SUP>Sr 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 Th-229m 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 Th-229 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 Sr-87 clock(2) 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 Th-229 nuclear clock transition and the Sr-87 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.