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arXiv:2606.08870

A nuclear clock based on $^{229}$Th

Beichen Huang, Gaowei Yan, Qi Xiao, Wenhao Bu, Zhen Zhang, Chengchun Zhao, Chao Yan, Zhi-Ang Chen, Peixiong Zhang, Gleb Penyazkov, Zhenhai Zhan, Lingfeng Yan, Yuefei Wang, Lin Li, Shanming Li, Xiaobo Qian, Xuegang Liu, Qiange He, Taoxiang Sun, Haochen Tian, Binkun Lu, Ningyuan Ma, Juxian Li, Yanzhang Wu, Qiaorui Gong, Yuxiang Li, Haoyu Shi, Xiangliang Li, Longsheng Ma, Shining Zhu, Yuxiang Mo, Jun Lin, Li You, Yige Lin, Xibo Zhang, Yin Hang, Liangbi Su, Shiqian Ding

physics.atom-phquant-phSubmitted Jun 7, 2026• Announced Jun 9, 2026
v1 · Jun 7, 2026v2 · Oct 7, 2026
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Abstract

Atomic clocks have made time and frequency the most precisely measured quantities in physics, progressing from microwave standards that realize the SI second to optical clocks that now reach unprecedented levels of precision. A nuclear clock would shift the frequency reference from an electronic transition to the uniquely low-lying, laser-accessible isomeric transition in the $^{229}$Th nucleus, offering a route to compact, robust timekeeping and sensitive tests of fundamental physics. However, turning recent advances in spectroscopy of the $^{229}$Th nuclear resonance into clock operation requires the nuclear transition to serve as a stable discriminator for steering a traceable oscillator. Here we demonstrate the operation of a $^{229}$Th nuclear clock by stabilizing a continuous-wave narrow-linewidth 148.4 nm vacuum-ultraviolet (VUV) laser to a resolved nuclear transition in a solid-state host. This clock operation is enabled by fast frequency discrimination based on phototube photocurrent readout of the transmitted VUV power. The 10 $μ$W VUV laser, generated by four-wave mixing in cadmium vapour, provides a high-signal-to-noise absorption signal from a home-grown $^{229}$Th:CaF$_2$ crystal, allowing the laser to be locked to a weakly temperature-sensitive nuclear transition. The clock reaches a fractional frequency instability of $2\times10^{-12}/\sqrt{τ/s} $, where $τ$ is the averaging time. Remarkably, nuclear-clock frequencies measured with two distinct crystals agree at the $10^{-13}$ level, demonstrating the reproducibility of solid-state nuclear frequency references. By making a laser-addressed atomic nucleus an operational clock reference, this work extends quantum metrology from electronic to nuclear transitions, and opens a new platform for compact clocks, solid-state nuclear quantum sensors and precision tests of fundamental physics.

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A nuclear clock based on 229^{229}229Th
Atomic clocks have made time and frequency the most precisely measured quantities in physics, progressing from microwave standards that realize the SI second to optical clocks that now reach unprecedented levels of precision. A nuclear clock would shift the frequency reference from an electronic transition to the uniquely low-lying, laser-accessible isomeric transition in the 229^{229}229Th nucleus, offering a route to compact, robust timekeeping and sensitive tests of fundamental physics. However, turning recent advances in spectroscopy of the 229^{229}229Th nuclear resonance into clock operation requires the nuclear transition to serve as a stable discriminator for steering a traceable oscillator. Here we demonstrate the operation of a 229^{229}229Th nuclear clock by stabilizing a continuous-wave narrow-linewidth 148.4 nm vacuum-ultraviolet (VUV) laser to a resolved nuclear transition in a solid-state host. This clock operation is enabled by fast frequency discrimination based on phototube photocurrent readout of the transmitted VUV power. The 10 μμμW VUV laser, generated by four-wave mixing in cadmium vapour, provides a high-signal-to-noise absorption signal from a home-grown 229^{229}229Th:CaF2_22​ crystal, allowing the laser to be locked to a weakly temperature-sensitive nuclear transition. The clock reaches a fractional frequency instability of 2×10−12/τ/s2\times10^{-12}/\sqrt{τ/s} 2×10−12/τ/s​, where τττ is the averaging time. Remarkably, nuclear-clock frequencies measured with two distinct crystals agree at the 10−1310^{-13}10−13 level, demonstrating the reproducibility of solid-state nuclear frequency references. By making a laser-addressed atomic nucleus an operational clock reference, this work extends quantum metrology from electronic to nuclear transitions, and opens a new platform for compact clocks, solid-state nuclear quantum sensors and precision tests of fundamental physics.
A low-energy nuclear transition in the isotope thorium-229 has been excited in thorium-doped crystals with laser light. This opens the perspective towards a highly stable and robust solid-state optical nuclear clock. The required laser radiation at 148 nm wavelength has so far been produced using pulsed laser systems where only a small fraction of the incident photons has been resonant with the narrow nuclear transition. Here we show that the nuclear resonance can be excited with a continuous-wave narrow-bandwidth laser source with a power of less than 1 nW, and that the resonance signal can be detected in absorption rather than in fluorescence. This eliminates the slow nuclear fluorescence decay from the detection process and offers a considerable advantage for clock operation through fast signal acquisition. The VUV laser source is based on three sequential frequency doublings, starting from a diode laser at 1187 nm that is well suited for linewidth narrowing and for frequency comparisons with optical atomic clocks. We use absorption spectroscopy for the quantitative characterization of two different Th-centers in calcium fluoride crystal and measure the isomeric shift between them. One of the centers shows a very small static electric crystal field gradient 0.1 V/A˚2Å^2A˚2, to be compared to gradients in the range of 100 V/A˚2Å^2A˚2 observed earlier. This indicates a center with high symmetry of the ions surrounding the Th nucleus, promising nuclear resonance lines that are nearly independent of the lattice spacing.
The laser-accessible nuclear transition in the thorium-229 isotope has been identified as a promising candidate for the realization of an optical nuclear clock. Such a nuclear clock might rival or outperform current optical clocks based on electron-shell transitions in atoms or ions, is expected to be more robust against external perturbations, and provides enhanced sensitivity in clock-based tests of fundamental principles of physics. Here, we implement a thorium-229 nuclear clock by stabilizing a continuous-wave laser to the 148 nm nuclear transition with rapid feedback based on continuous absorption spectroscopy. The thorium-229 nuclei are embedded into a millimeter-sized, room temperature calcium fluoride crystal. A subharmonic of the 148 nm radiation is continuously compared to a Yb+ single-ion clock. The nuclear clock shows a simple shot-noise limited scaling of the fractional frequency instability of 3⋅10−12τ/s3\cdot 10^{-12} \sqrt{τ/\text{s}}3⋅10−12τ/s​ where τττ is the averaging time, approaching 10−1510^{-15}10−15 instabilities over 1 day of continuous operation. Improvements of the instability by several orders of magnitude can be projected for future solid-state nuclear clocks. We use the nuclear clock to constrain models of ultralight dark matter by searching for periodic fluctuations and slow drifts in the nuclear transition energy, on time scales between 20 s and 1 day. Drawing benefit from the enhanced sensitivity of the thorium-229 transition, these constraints compete with the best atomic clocks concerning dark matter coupling to photons and go beyond previous measurements regarding coupling to the strong force and quarks.
The Th-229 nuclear isomeric state has the lowest energy of all known nuclear excited states, placing it within the reach of current table-top laser technology. This extraordinary property has made this nuclear isomer an attractive candidate for a nuclear optical clock of incredibly high precision and accuracy, both as isolated trapped Th-229 ions and embedded into solid-state platforms. Activity around Th-229 has surged in recent years, driven by breakthroughs in its direct laser excitation. The underlying nuclear physics that gives rise to this unique isomer will be elucidated, as well as the nearly half-century of efforts that led to its direct excitation. The design and systematics of a Th-229 nuclear clock will be discussed, both in ion traps and in the solid-state. These systematics, such as frequency shifts and quenching channels, can be leveraged both to probe the local chemical environment, and as a control knob during clock operation. Finally, the nuclear clock's high sensitivity to the variations of fundamental constants will be discussed.
Toward nanophotonic platforms for solid-state 229^{229}229Th nuclear clocks
While the 229^{229}229Th nuclear isomer has recently been observed and laser-excited, converting optical nuclear manipulation into a chip-scale solid-state frequency standard remains an open challenge. Here, we present a nanophotonic platform to realize an all-solid-state nuclear clock based on the low-energy isomeric transition of 229^{229}229Th embedded in high-QQQ fluoride photonic resonators. By coupling ensembles of thorium nuclei to confined optical modes, we show that resonant field build-up in the cavity can substantially enhance the nuclear excitation rate, enabling optical interrogation at practical laser intensities. We model the nuclei-photon interaction dynamics and outline a technological roadmap toward addressing this challenge, including resonator fabrication in fluoride crystals, thorium implantation, nuclear excitation with integrated lasers, and on-chip detection of vacuum-ultraviolet photons. As an initial proof of concept, we implant a crystalline fluoride whispering-gallery-mode resonator with 229^{229}229Th and assess the impact of implantation-induced damage on resonator performance. Our platform leverages recent advances in materials integration and nanophotonics to chart a realistic route toward compact and scalable nuclear frequency standards.
We demonstrated a compact 780 nm rubidium optical clock, which includes an optical frequency standard and an optical frequency comb, with an optical volume of 11.6 liters. Unlike the 778 nm rubidium atomic clocks based on two-photon transition, here, the laser frequency is stabilized to the Rb D2 transition, using modulation transfer spectroscopy. This approach effectively eliminates Doppler background and provides a high signal to noise ratio and high sensitivity. A nearly 300 MHz microwave signal, whose phase exactly tracks that of the optical frequency standard, is generated via the optical frequency comb, yielding a frequency instability of 1.91 E-13 @1 s and 5.29 E-14 @1000 s in the electronic domain. To the best of our knowledge, this is the most precise frequency stabilization result for the first-excited-state transition of alkali metal atoms to date and represents the first optical clock based on this transition. These results offer a promising approach for the development of portable optical clocks.
Optical clocks require an ultra-stable laser to probe and precisely measure the frequency of the narrow-linewidth clock transition. We introduce a portable ultraviolet (UV) laser system for use in an aluminum quantum logic clock, demonstrating a fractional frequency instability of approximately mod σy=2×10−16\mathrm{mod}\,σ_\mathrm{y} = 2 \times 10^{-16}modσy​=2×10−16. The system is based on an ultra-stable cavity with crystalline AlGaAs/GaAs mirror coatings, alongside with a frequency quadrupling system employing two single-pass second harmonic generation (SHG) stages. Its acceleration sensitivity, measured in all three axes, does not exceed 4(2)×10−124(2) \times 10^{-12}4(2)×10−12/(ms−2^{-2}−2) and is among the lowest recorded for transportable systems to date. Additionally, partial cancellation between photo-thermal noise and photo-birefringence noise is used to effectively mitigate noise induced by intra-cavity optical power fluctuation at lower Fourier frequencies.