Advancing Solid-State Thorium-229 Nuclear Clocks: Frequency Reproducibility in 229Th:CaF2
The development of a nuclear clock based on Thorium-229 has long been recognized as a promising route toward next-generation precision timekeeping. In a recent study by researchers from JILA, NIST, the University of Colorado, and TU Wien, the frequency reproducibility of a solid-state nuclear clock based on 229Th atoms hosted in calcium fluoride was investigated in detail. The work provides an important assessment of the stability and robustness of this emerging clock platform and establishes key performance benchmarks necessary for future applications in precision metrology and fundamental physics.
Optical atomic clocks based on electronic transitions, such as those using 87Sr in optical lattices, have already demonstrated fractional uncertainties below 10−18. Nuclear clocks aim to build on this success by exploiting a transition within the atomic nucleus rather than the electron shell. Because nuclear transitions are buried deep within the atomic structure and shielded from environmental perturbations, they are almost completely immune to the field-induced Stark shifts that pose difficulties for atomic clocks based on electronic excitations. The 229Th isotope is uniquely suited in this regard due to its low-lying isomeric state at approximately 8.4 eV (corresponding to a wavelength near 148 nm), which is accessible with laboratory-based vacuum ultraviolet (VUV) light frequency comb sources.
In the solid-state approach explored in this study, thorium ions are doped into CaF2 crystals, where 229Th4+ substitutes for Ca2+ and forms local defect structures. This configuration allows a very large number of nuclei, far exceeding those in typical atomic clock ensembles, to contribute to the clock signal. At the same time, the crystalline host introduces new considerations, including charge compensation, local electric field gradients and lattice-induced frequency shifts. Understanding and controlling these effects is essential for reliable clock operation.
A central component of the experiment is precision frequency metrology. The nuclear transition was excited using a VUV frequency comb that was phase-coherently linked to a JILA strontium optical clock. Optical frequency comb technology from a Menlo Systems’ FC1500 comb provided the stable and accurate frequency reference required to measure the nuclear transition with kilohertz-level precision. The spectral purity of an ultrastable optical reference at 1542 nm with mHz-level linewidth was transferred over hundreds of thousands of comb lines to the different wavelengths required in the experiment. This frequency calibration infrastructure formed the basis for the reproducibility studies reported in the publication, enabling consistent frequency comparisons over many months.
The researchers examined three separately grown 229Th:CaF2 crystals with different doping concentrations. By recording 73 nuclear resonance scans over a temperature range from 134 K to 294 K, they characterized both the transition linewidth and the center frequency under varying experimental conditions. Each scan involved resonant excitation of the nuclear transition followed by detection of fluorescence photons emitted during nuclear decay. Lorentzian fits to the observed spectra yielded the transition frequency and linewidth with well-defined statistical uncertainties.
One of the first findings concerns the observed linewidth. Although the intrinsic lifetime of the 229Th isomer suggests an extremely narrow natural linewidth, the measured full-width at half-maximum values ranged from tens to hundreds of kilohertz. Importantly, the linewidth showed no measurable dependence on temperature but increased linearly with thorium doping concentration. The narrowest transitions (around 18 kHz) were observed in the lowest-doped crystal.
This concentration-dependent broadening is attributed to inhomogeneous microstrain (small, spatially varying distortions of a crystal lattice on microscopic length scales) within the crystal lattice. Each thorium dopant distorts its local environment, modifying the electric field gradient and electron density at neighboring nuclear sites. As the dopant concentration increases, overlapping strain fields lead to a broader distribution of local transition frequencies. The linear scaling observed in the experiment is consistent with models of defect-induced broadening in crystalline solids. These results represent the first systematic quantification of crystal-limited linewidths in a solid-state nuclear clock system.
Beyond linewidth characterization, the study also examined temperature-dependent shifts of the 229Th nuclear transition in detail. Two sub-transitions, line b and line c, were analyzed: line b exhibits low sensitivity to temperature, while line c responds more strongly to thermal variations. By fitting line-b frequency data to a quadratic temperature dependence, the researchers identified a zero first-order temperature sensitivity point at 196(5) K, where the slope of the frequency-versus-temperature curve vanishes and the transition becomes minimally affected by small thermal fluctuations.
Operating near this zero-shift temperature, two independently grown crystals demonstrated a frequency reproducibility of 220 Hz over a seven-month period, corresponding to a fractional reproducibility of 1.1 × 10−13. Each measurement was referenced to the 87Sr optical clock via the frequency comb, allowing consistent comparison over months. Longer-term measurements at room temperature (293 K) across all three crystals, covering a one-year period, showed frequency agreement at the kHz level, with no systematic drift observed, illustrating both short-term and extended reproducibility of the nuclear transition.
The differing temperature sensitivities of lines b and c also enable precise co-thermometry: by monitoring the strongly temperature-sensitive line c while operating line b at its zero-shift point, the crystal temperature can be stabilized with millikelvin-level precision. This approach suppresses temperature-induced fractional frequency uncertainties to below 10−18, establishing a robust foundation for field-deployable solid-state nuclear clocks.
The study further discusses additional systematic effects relevant to future nuclear clock development, including magnetic field sensitivities, stress-induced shifts, and potential strategies for reducing inhomogeneous broadening. Approaches such as optimizing crystal growth, exploring alternative host materials, or increasing excitation laser power are identified as pathways toward improved stability and narrower effective linewidths.
In summary, the reported work establishes the frequency reproducibility of solid-state 229Th:CaF2 nuclear transitions across different crystals, temperatures, and extended time intervals. The identification of a zero-shift operating temperature, the quantitative analysis of defect-induced linewidth broadening, and the demonstration of sub-kilohertz reproducibility represent significant milestones for the field. Precision frequency metrology, enabled by phase-coherent referencing with optical frequency comb technology from Menlo Systems, provided the stable measurement backbone required for this evaluation. Together, these results strengthen the case for solid-state thorium nuclear clocks as a viable platform for future compact frequency standards and sensitive probes of fundamental physics.
Within this framework, the role of frequency comb technology remains central. Menlo Systems’ frequency comb portfolio is ideally suited to the requirements of Thorium nuclear clocks. Its patented ultra-low-noise (ULN) comb technology preserves exceptional spectral purity across the entire comb spectrum, covering all wavelengths relevant to the experimental setup. In addition, Menlo’s Yb-based product line provides high-power frequency combs at 1040 nm, the exact wavelength required for Thorium nuclear clocks (7th harmonic to reach the 148 nm clock transition). And finally, Menlo has recently launched the ORS-ULN, the best commercial optical reference, delivering unprecedented performance based on an ultra-high-finesse silicon cavity of the type used in this study. Currently, multiple groups worldwide are using Menlo Systems’ frequency combs in the development of thorium-based nuclear clocks.
Author: Emma Caldwell
Original Publication:
[1] Ooi, T., Doyle, J.F., Zhang, C. et al. Frequency reproducibility of solid-state thorium-229 nuclear clocks. Nature 650, 72–78 (2026). https://doi.org/10.1038/s41586-025-09999-5