Origin of the inhomogeneous linewidth in a solid state 229Th:CaF2 nuclear clock
Abstract
Narrow linewidth (high-Q) quantum discriminators are essential for realizing solid-state 229Th 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 229Th:CaF2 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/r3 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 229Th and provide guidance for engineering nuclear-clock materials with reduced inhomogeneous broadening.
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BibTeX
@misc{li2026origin,
title = {{Origin of the inhomogeneous linewidth in a solid state $^229$Th:CaF$_2$ nuclear clock}},
author = {Kai Li and Tian Ooi and Jack F. Doyle and Konstantin Herb and Emil Pellett and Martin Pimon and Thorsten Schumm and Steven M. Girvin and Leo Radzihovsky and Jun Ye},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04205},
eprint = {2610.04205},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04205},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Origin of the inhomogeneous linewidth in a solid state ^229Th:CaF_2 nuclear clock
AU - Kai Li
AU - Tian Ooi
AU - Jack F. Doyle
AU - Konstantin Herb
AU - Emil Pellett
AU - Martin Pimon
AU - Thorsten Schumm
AU - Steven M. Girvin
AU - Leo Radzihovsky
AU - Jun Ye
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04205
UR - https://arxiv.org/abs/2610.04205
AB - Narrow linewidth (high-Q) quantum discriminators are essential for realizing solid-state ^229Th 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 ^229Th: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 ^229Th and provide guidance for engineering nuclear-clock materials with reduced inhomogeneous broadening.
ER -