发表机构
JILA, NIST and University of Colorado; Department of Physics, University of Colorado, Boulder; Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder; Institute for Theoretical Physics, TU Wien; Institute for Atomic and Subatomic Physics, TU Wien; Departments of Applied Physics and Physics, Yale University; Yale Quantum Institute, Yale University（JILA、美国国家标准与技术研究院和科罗拉多大学; 科罗拉多大学博尔德分校物理系; 科罗拉多大学博尔德分校物理系与量子物质理论中心; 维也纳工业大学理论物理研究所; 维也纳工业大学原子与亚原子物理研究所; 耶鲁大学应用物理系与物理系; 耶鲁大学耶鲁量子研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过实验与理论结合，揭示固态$^{229}$Th核钟中非均匀线宽源于局部电场梯度变化，随钍浓度线性增加，为设计低展宽核钟材料提供指导。
AI 中文摘要
窄线宽（高Q值）量子鉴别器对于实现固态$^{229}$Th核钟至关重要，然而观测到的跃迁线宽仍处于数十至数百千赫兹水平，远超过由核同质异能素辐射寿命所设定的亚赫兹线宽。在此，我们通过系统测量线宽随温度、钍浓度和四极态的变化，并结合理论分析和第一性原理模拟，研究了$^{229}$Th:CaF$_2$中这种展宽的起源。我们发现线宽与温度无关，随钍浓度线性增加，并强烈依赖于四极态。数据分析确定局部电场梯度（EFG）的变化是非均匀展宽的主要来源，并揭示EFG无序度随钍浓度线性增加。观察到的洛伦兹线形和线宽线性浓度依赖关系可由随机分布的长程掺杂诱导扰动的$1/r^3$标度自然解释。互补的原子级和基于密度泛函理论的从头计算重现了这些特征，并提供了对导致展宽的微观缺陷构型的见解。这些结果确立了固态$^{229}$Th中的主要展宽机制，并为工程化具有降低非均匀展宽的核钟材料提供了指导。
英文摘要
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.
Comments16 pages, 6 figures
