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arXiv:2606.04997

A thorium-229 optical nuclear clock with feedback loop

L. Toscani De Col, T. Riebner, I. Morawetz, F. Schneider, N. Sempelmann, J. Schlachet-Lépinay, F. Schaden, M. Bartokos, G. A. Kazakov, K. Beeks, B. Gerstenecker, M. Pimon, S. Lahs, A. Hellerschmied, T. Lercher, J. Premper, A. Niessner, M. Matus, H. Denker, M. Cizek, O. Cip, V. Lal, G. Zitzer, V. Petrov, J. Tiedau, M. V. Okhapkin, E. Peik, T. Schumm

physics.atom-phnucl-exquant-phSubmitted Jun 3, 2026• Announced Jun 4, 2026• Revised Jun 5, 2026 (v2)
v1 · Jun 3, 2026v2 · Jun 5, 2026
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Abstract

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 $3\cdot 10^{-12} \sqrt{τ/\text{s}}$ 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.

Comments
12 pages, 6 figures

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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.
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.
A nuclear clock synchronized to 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 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 229^{229}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 229^{229}229Th nuclear resonance into a stable discriminator for steering a traceable oscillator. Here we demonstrate a 229^{229}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 229^{229}229Th:::CaF2_22​ crystals. A 101010-μWμ\mathrm{W}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/s5\times10^{-13}/\sqrt{τ/\mathrm{s}}5×10−13/τ/s​ for averaging time τττ. Clock-transition frequencies measured in two independently fabricated crystals agree at the 10−1310^{-13}10−13 level and are consistent with previous VUV-comb measurements on other 229^{229}229Th:CaF2_22​ 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.
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.
This thesis presents the investigations of Rubidium atoms in magneto-optical traps and triply charged Thorium ions in electrodynamic traps for future advances in long-distance quantum telecommunication, next generation clocks, and fundamental tests of current physical theories. Experimental realizations of two core building blocks of a quantum repeater are described: a multiplexed quantum memory and a telecom interface for long-lived quantum memories. A color change of single-photon level light fields by several hundred nanometers in an optically thick cold gas is demonstrated, while preserving quantum entanglement with a remotely stored matter excitation. These are essential elements for long-distance quantum telecommunication, fundamental tests of quantum mechanics, and applications in secure communication and computation. The first trapping and laser cooling of Thorium-229 ions are described. Thorium-229 nuclear electric quadrupole moment is revealed by hyperfine spectroscopy of triply charged Thorium-229 ions. A system to search for the isomer nuclear transition in Thorium-229 is developed and tested with the excitation of a forbidden electronic transition at 717 nm. Direct excitation of the nuclear transition with laser light would allow for an extremely accurate clock and a sensitive test bed for variations of fundamental physical constants, including the fine structure constant.
Solid-state frequency standards are generally limited by strong decoherence, rendering conventional interrogation schemes inefficient. The 229^{229}229Th nuclear clock provides a unique and timely platform for solid-state optical metrology and nuclear cavity quantum electrodynamics (QED), featuring a coherence time many orders of magnitude shorter than the radiative lifetime in current experiments. Here, we propose and analyze three cavity QED-enhanced clock interrogation schemes that turn this timescale mismatch into an advantage, leveraging collective coupling of thorium nuclei to nanophotonic modes to enable fast interrogation and detection despite the long population lifetime. We reveal the central role of collective cooperativity in determining the clock frequency instability, and derive the optimal conditions (power, working-point detuning, thorium density) for clock operation.
Quantum algorithms such as dynamical decoupling can be used to improve the sensitivity of a quantum sensor to a signal while suppressing sensitivity to noise. Atomic clocks are among the most sensitive quantum sensors, with recent improvements in clock technology allowing for unprecedented precision and accuracy. These clocks are highly sensitive to variations in fundamental constants, making them ideal probes for local ultralight scalar dark matter. Further improvements to the sensitivity are expected in proposed nuclear clocks based on a nuclear transition in the thorium-229 isotope. We investigate the use of various quantum metrology algorithms in the search for dark matter using quantum clocks. We propose a broadband dynamical decoupling algorithm and compare it with quantum metrology protocols that have been previously proposed and demonstrated, namely, differential spectroscopy and narrowband dynamical decoupling. We conduct numerical simulations of scalar dark matter searches with realistic noise sources and accounting for dark matter decoherence. Finally, we propose an alternative thorium nuclear transition excitation method that bypasses the technical challenges associated with vacuum ultraviolet lasers.