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Communications Physics

Gravitational γ-ray photon echo using Thorium-229 nuclear clock transition in vacuum ultraviolet regime

Wen-Te Liao, Sven Ahrens

Published Jul 15, 2026• 0 citations
Publisher

Abstract

Abstract Gravitational redshift, a striking prediction of Einstein’s theory of general relativity, has been experimentally confirmed on Earth. Yet, exploiting this effect as a controllable resource in coherent quantum systems remains challenging. Here, we theoretically demonstrate gravitationally induced γ -ray photon echoes in solid-state Thorium-229 targets using the 8.4 eV nuclear clock transition, which, owing to its nuclear origin, extends the definition of γ rays down into the vacuum ultraviolet regime. With its ultranarrow linewidth (1 mHz), exceptional quality factor (10 19 ), and long 1740 s isomeric half-life, this transition offers a compact solid-state platform sensitive to millimeter-scale gravitational variations. We further investigate the gravitational photon echo in a spinless crystal with a coherence time on the order of seconds. Controlled target rotations enable the generation, manipulation, and storage of γ -ray echoes, paving the way for a gravitationally driven γ -ray memory, a narrowband γ -ray source, and relativistic geodesy.

DOI
10.1038/s42005-026-02745-x

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Abstract Gravitational redshift, a striking prediction of Einstein’s theory of general relativity, has been experimentally confirmed on Earth. Yet, exploiting this effect as a controllable resource in coherent quantum systems remains challenging. Here, we theoretically demonstrate gravitationally induced γ -ray photon echoes in solid-state Thorium-229 targets using the 8.4 eV nuclear clock transition, which, owing to its nuclear origin, extends the definition of γ rays down into the vacuum ultraviolet regime. With its ultranarrow linewidth (1 mHz), exceptional quality factor (10 19 ), and long 1740 s isomeric half-life, this transition offers a compact solid-state platform sensitive to millimeter-scale gravitational variations. We further investigate the gravitational photon echo in a spinless crystal with a coherence time on the order of seconds. Controlled target rotations enable the generation, manipulation, and storage of γ -ray echoes, paving the way for a gravitationally driven γ -ray memory, a narrowband γ -ray source, and relativistic geodesy.
The generation, controls, and storage of the gravitationally induced photon echo using the 8.4 eV Thorium-229 nuclear clock transition on Earth are theoretically investigated. With its exceptionally narrow linewidth of approximately 1 mHz and high quality factor in the order of 101910^{19}1019, the Thorium-229 clock transition allows for the potential detection of gravitational-redshift effects at millimeter-scale altitude variations. Moreover, the 1740-second half lifetime of the Thorium-229 isomeric state allows for the slow movement of the system within its coherence time. Along this line, we explore the generation, controls, and storage of photon echo arising from a rotation induced inversion of the gravitational frequency shift in a single target or in multiple equally spaced samples. Our approach lays the foundation for the controllable gravitational quantum optics on Earth.
Atomic clocks achieve extraordinary precision through quantum control over large ensembles of atoms, with precision increasing and atom number advancing steadily. Emerging nuclear clock technology encodes clock states in nuclear rather than electronic transitions, offering a new frontier for precision measurement. Here we study whether a large ensemble of such clock nuclei could be used to observe their mutual gravitational interaction. We investigate the gravitational redshift induced by neighboring atoms, including nuclear energy superpositions as sources of gravity, giving rise to a genuinely quantum gravitational interaction between pairs of nuclei. We find that the resulting clock frequency shift due to mutual gravity may become non-negligible for a macroscopic number of nuclei, for instance in a solid-state thorium clock, and we propose approaches to mitigate electromagnetic field effects by exploiting spatial symmetry and high-precision spectroscopy. We further discuss how energy-induced mass superpositions could be directly probed using external gravitational field sensors. By contrast, observing gravity-induced entanglement involving clocks would require substantially greater experimental advances due to decoherence from spontaneous emission. Taken together, our results suggest that nuclear clocks, either alone or in combination with complementary sensors such as optomechanical systems, may offer a future route toward probing gravity at short distances and testing gravitating quantum source masses beyond the Newtonian limit.
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.
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.
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.
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.