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Prospects for a Solid-State Nuclear Clock

Steven M. Girvin, Leo Radzihovsky

TL;DR

The paper surveys the prospects for a solid-state nuclear clock based on the $^{229}$Th transition near $8.4$ eV, arguing that the high transition frequency combined with an intrinsically long $T_1$ offers an avenue for ultra-precise timekeeping, especially if a large number $N$ of doped nuclei in a crystal can be used to boost signal-to-noise. A central challenge is the inhomogeneous broadening arising from local electric-field gradients and lattice strains, which currently dominate over the intrinsic width set by $1/(2T_1)$; understanding and mitigating these solid-state disturbances is essential. The paper reviews key experimental milestones—Zhang et al.’s direct Th-Sr frequency ratio measurement with resolved quadrupole lines and extracted $V_{zz}$, Higgins et al.’s demonstration of a weak temperature dependence enabling $\sim10^{-18}$ fractional stability under microkelvin control, and Ooi et al.’s identification of an operating temperature near $190$ K that minimizes sensitivity and shows long-term reproducibility—along with the imperative for improved material engineering and first-principles modeling to realize a practical solid-state nuclear clock with transformative metrological and fundamental-physics implications.

Abstract

Motivated by recent experimental breakthroughs toward a realization of a solid-state Thorium-229 nuclear clock, we review the technology, basic physics motivation, and limitations of the present generation of atomic clocks. We then discuss prospects for a new generation of clocks based on an anomalous low-energy 8.4 eV nuclear transition in Th-229, with an extremely long lifetime of 641 seconds when doped into CaF crystals. To realize such solid-state nuclear clocks one must confront basic nuclear, AMO, and solid state physics questions. Key challenges are understanding and minimizing the effects of inhomogeneous broadening, associated with strains and electric field gradients due to both the Th dopants and intrinsic crystal defects.

Prospects for a Solid-State Nuclear Clock

TL;DR

The paper surveys the prospects for a solid-state nuclear clock based on the Th transition near eV, arguing that the high transition frequency combined with an intrinsically long offers an avenue for ultra-precise timekeeping, especially if a large number of doped nuclei in a crystal can be used to boost signal-to-noise. A central challenge is the inhomogeneous broadening arising from local electric-field gradients and lattice strains, which currently dominate over the intrinsic width set by ; understanding and mitigating these solid-state disturbances is essential. The paper reviews key experimental milestones—Zhang et al.’s direct Th-Sr frequency ratio measurement with resolved quadrupole lines and extracted , Higgins et al.’s demonstration of a weak temperature dependence enabling fractional stability under microkelvin control, and Ooi et al.’s identification of an operating temperature near K that minimizes sensitivity and shows long-term reproducibility—along with the imperative for improved material engineering and first-principles modeling to realize a practical solid-state nuclear clock with transformative metrological and fundamental-physics implications.

Abstract

Motivated by recent experimental breakthroughs toward a realization of a solid-state Thorium-229 nuclear clock, we review the technology, basic physics motivation, and limitations of the present generation of atomic clocks. We then discuss prospects for a new generation of clocks based on an anomalous low-energy 8.4 eV nuclear transition in Th-229, with an extremely long lifetime of 641 seconds when doped into CaF crystals. To realize such solid-state nuclear clocks one must confront basic nuclear, AMO, and solid state physics questions. Key challenges are understanding and minimizing the effects of inhomogeneous broadening, associated with strains and electric field gradients due to both the Th dopants and intrinsic crystal defects.

Paper Structure

This paper contains 10 sections, 14 equations.

Table of Contents

  1. Introduction and motivation
  2. Brief Background on Atomic Clocks
  3. The nuclear physics of $^{229}$Th
  4. Solid State Effects
  5. Discussion of recent precision measurement results
  6. Frequency ratio of the $^{229}$Th nuclear isomeric transition and the 87Sr atomic clock, Zhang et al. 2024
  7. Temperature Sensitivity of Thorium-${229}$ Solid-State Nuclear Clock, Higgins et al. Phys. Rev. Lett. 134 (11): 113801 (2025)
  8. Frequency reproducibility of solid-state Th-229 nuclear clocks, Ooi et al., arXiv:2507.01180 [Nature (in press)]
  9. Discussion and Open Questions
  10. Appendix: Derivation of the Quadrupolar Coupling