Theory of frequency offsets in Th-229 nuclear clockwork

Observations of laser excitation of a uniquely low-energy nuclear isomer transition in Th-229 open the door to a new class of timekeeping devices: nuclear clocks. Solid-state hosts, containing a large number of nuclei, offer the potential for unprecedented clock stability. Given the diverse range of existing and proposed Th-229-containing solid-state hosts, we examine how the nuclear clock frequency depends on the local electronic environment of the nucleus. This dependence arises from the isomer shift (or chemical shift), which results from differences in the nuclear charge distributions between the ground and isomeric states. We develop a method to evaluate this shift in solid-state hosts, compatible with periodic density functional theory (DFT) approaches, while incorporating essential relaxation effects in a relativistic framework. Our results show that clock frequencies can vary by several MHz between different solid-state hosts—many orders of magnitude larger than the current kHz-level resolution of VUV frequency combs.

This work has immediate implications for high-resolution spectroscopy of the nuclear clock transition in both crystals and trapped ions.