Theoretical Aspects of Developing the Th-229 Nuclear Clock

The low-energy isomer of $^{229}$Th enables a fundamentally new class of quantum sensors: nuclear clocks with exceptional robustness and sensitivities to variation of fundamental constants far beyond existing atomic clocks. The concept was motivated in part by our proposal of a single-ion nuclear clock [1], which demonstrated that the nuclear transition’s narrow linewidth and insensitivity to external fields could support metrology at the $10^{-19}$ level. Realizing this promise in practice requires understanding how the nuclear excitation behaves in realistic environments—especially in emerging solid-state platforms.

I will present our recent theoretical work that establishes the framework for engineering and interpreting solid-state $^{229}$Th clocks. We developed a first-principles theory of internal conversion (IC) in insulating hosts [2,3], identifying the dominant electronic channels for nonradiative decay and providing predictive tools for selecting materials with suppressed quenching. IC can be used as a resource, e.g. opening photo-induced quenching pathways [4] that emerge under off-resonant laser excitation or using electric currents for clock readout [3].

I will also highlight predictions of host-dependent frequency offsets (''clockwork shifts'') [5], essential for connecting solid-state spectroscopy to the free-ion transition envisioned in our 2012 proposal.