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arXiv:2610.04205

Origin of the inhomogeneous linewidth in a solid state $^{229}$Th:CaF$_2$ nuclear clock

Kai Li, Tian Ooi, Jack F. Doyle, Konstantin Herb, Emil Pellett, Martin Pimon, Thorsten Schumm, Steven M. Girvin, Leo Radzihovsky, Jun Ye

physics.atom-phcond-mat.mtrl-sciphysics.opticsquant-phSubmitted Oct 3, 2026• Announced Oct 6, 2026
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Abstract

Narrow linewidth (high-Q) quantum discriminators are essential for realizing solid-state $^{229}$Th nuclear clocks, yet the observed transition linewidths remain at the tens-to-hundreds-of-kilohertz level, far exceeding the sub-Hertz linewidth set by the radiative lifetime of the nuclear isomer. Here, we investigate the origin of this broadening in $^{229}$Th:CaF$_2$ through systematic measurements of the linewidth as functions of temperature, thorium concentration, and quadrupole state, accompanied by theoretical analysis and first-principle simulations. We find that the linewidth is independent of temperature, increases linearly with thorium concentration, and depends strongly on the quadrupole state. Data analysis identifies variations of the local electric-field gradient (EFG) as the dominant source of inhomogeneous broadening and reveals that the EFG disorder increases linearly with thorium concentration. The observed Lorentzian line shapes and linewidth linear concentration dependence are explained naturally from the $1/r^3$ scaling of a random distribution of long-range dopant-induced perturbations. Complementary atomistic and \textit{ab initio} density-functional-theory calculations reproduce these characteristic features and provide insights into the microscopic defect configurations responsible for the broadening. These results establish the dominant broadening mechanism in solid-state $^{229}$Th and provide guidance for engineering nuclear-clock materials with reduced inhomogeneous broadening.

Comments
16 pages, 6 figures

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Toward nanophotonic platforms for solid-state 229^{229}229Th nuclear clocks
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