Continuous-wave laser absorption spectroscopy of the Thorium-229 nucleus
I. Morawetz, T. Riebner, L. Toscani De Col, F. Schneider, N. Sempelmann, F. Schaden, M. Bartokos, G. A. Kazakov, S. Lahs, K. Beeks, B. Gerstenecker, A. Grüneis, M. Pimon, T. Schumm, V. Lal, G. Zitzer, V. Petrov, J. Tiedau, M. V. Okhapkin, E. Peik
physics.atom-phcond-mat.mtrl-sciquant-phSubmitted Apr 17, 2026• Announced Apr 21, 2026• Revised Jun 16, 2026 (v2)
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/$Å^2$, to be compared to gradients in the range of 100 V/$Å^2$ 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.
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˚2, to be compared to gradients in the range of 100 V/A˚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.
A nuclear clock synchronized to 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 with unprecedented precision. A nuclear clock transfers the frequency reference from an electronic to a nuclear transition, and the uniquely low-lying, laser-accessible isomeric transition in 229Th currently offers the most practical route to compact, robust timekeeping and sensitive tests of fundamental physics. Realizing such a clock requires turning spectroscopy of the 229Th nuclear resonance into a stable discriminator for steering a traceable oscillator. Here we demonstrate a 229Th nuclear clock by stabilizing a continuous-wave, narrow-linewidth 148.4-nm vacuum-ultraviolet (VUV) laser to a resolved, weakly temperature-sensitive nuclear transition in 229Th:CaF2 crystals. A 10-μW VUV source generated by four-wave mixing in cadmium vapour and phototube-based frequency-modulation absorption readout provide a fast, high-signal-to-noise nuclear discriminator. The clock reaches a fractional frequency instability of 5×10−13/τ/s for averaging time τ. Clock-transition frequencies measured in two independently fabricated crystals agree at the 10−13 level and are consistent with previous VUV-comb measurements on other 229Th:CaF2 crystals. These results establish laser-addressed nuclei as operational clock references and provide a reproducible solid-state platform for compact nuclear clocks, nuclear quantum sensors and precision tests of fundamental physics.
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/s where τ is the averaging time, approaching 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.
Toward nanophotonic platforms for solid-state 229Th nuclear clocks
While the 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 229Th embedded in high-Q 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 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.
Hyperfine-resolved laser excitation and detection of nuclear isomer in trapped 229Th3+ ions
We present a comprehensive theoretical investigation of hyperfine-resolved excitation and detection of the low-energy isomeric state of 229Th in trapped 229Th3+ ions. Using a quantum master equation approach, we quantitatively analyze the dependence of the isomeric population on laser linewidth, detuning, and irradiation time, showing that their proper matching is essential for efficient excitation. Going beyond earlier conceptual discussions of electronic-fluorescence-based nuclear-state detection, we propose two concrete nuclear-state detection schemes based on three hyperfine-resolved electronic fluorescence channels at 690, 984, and 1088 nm. Our quantitative analysis shows that, for 50 ions, the 690- and 984-nm scheme yields detectable photon count rates on the order of 103s−1 at 690 nm and 104s−1 at 984 nm, whereas the 1088-nm scheme achieves a detectable photon rate on the order of 103s−1. By quantifying the trade-off between irradiation time and scan-step size, we show that the nuclear transition can be located within one month for a 100-MHz uncertainty using currently available vacuum-ultraviolet laser technology. These results provide practical guidance for trapped-ion 229Th spectroscopy and the development of nuclear clocks.
A possibility of the two-photon excitation of an isomeric state in a nucleus of thorium-229 has been discussed. The fluorescence intensity of the excitation is demonstrated to be identical for the irradiation of nuclei with either monochromatic light or polychromatic radiation consisting of a sequence of short lightpulses of the same intensity. The two-photon excitation of Th3+ ion in an electromagnetic trap with a focused laser beam with a wavelength of about 320 nm and power of 100 mW can lead to the absorption saturation, at which the fluorescence emission with the frequency of the transition in a nucleus is maximal. In crystals doped with Th4+ to a concentration of about 1018 cm-3 and irradiated with a laser radiation 10 W in power, the emission of several photons persecond with a wavelength of about 160 nm becomes possible.
Origin of the inhomogeneous linewidth in a solid state 229Th:CaF2 nuclear clock
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.