Summary

Researchers detected the low-energy nuclear resonance of thorium-229 using a continuous-wave laser and absorption measurements rather than slow fluorescence detection. The technique provides a faster spectroscopy and feedback method for developing a solid-state nuclear clock.

A team of researchers has detected the nuclear resonance of thorium-229 by measuring how a continuous-wave laser is absorbed in a calcium fluoride crystal. The result, published in Nature on 16 September 2026, replaces the slow fluorescence readout used in earlier solid-state experiments with a signal that can be measured during laser excitation.

The technique is an important step towards a solid-state nuclear clock. Thorium-229 has an unusually low-energy nuclear transition of 8.4 electronvolts, corresponding to vacuum-ultraviolet light at about 148 nanometres. A clock can use such a narrow resonance as a frequency reference, but the signal must be measured quickly and precisely enough to stabilise a laser.

Contents

A continuous-wave route to the nuclear resonance

Earlier experiments excited thorium-229 in crystals with pulsed vacuum-ultraviolet sources and detected the resulting nuclear fluorescence. That approach was constrained by the isomer’s long radiative decay time: in calcium fluoride, the excited state takes about 600 seconds to decay. The researchers therefore had to wait for fluorescence and for the excited population to recover before beginning another measurement cycle.

The new experiment used a narrow-bandwidth continuous-wave laser. Infrared light at 1,187 nanometres was frequency-converted through several stages to produce radiation at 148.4 nanometres. The source generated about 1 nanowatt of vacuum-ultraviolet power before losses in the beam path and crystal; the power measured after the thorium-doped crystal was approximately 70 picowatts.

Because the continuous-wave laser concentrates its power into a narrow spectral range, the transmitted light can be compared while the laser is on resonance and when it is detuned. The experiment calculated absorption from the difference between those two transmitted intensities. This directly measures the small depletion of the nuclear ground-state population, rather than waiting for excited nuclei to emit photons.

The absorption signal can be recorded continuously because the ground-state population was not markedly depleted. Frequency-modulation spectroscopy also produced an error signal with a zero crossing at the resonance, the type of signal needed to lock a laser to a clock transition.

What the absorption spectra showed

The researchers studied a thorium-doped calcium fluoride crystal at 294.7(5) kelvin. Absorption measurements revealed six lines associated with two types of thorium site. Five lines came from the D-centre, a thorium dimer configuration with dihedral symmetry. The sixth was assigned to the O-centre, a site with nearly cubic, O(_h) symmetry.

With the narrower laser configuration, the researchers measured a full width at half maximum of 91(2) kilohertz for the D-centre’s 5/2 → 3/2 transition. The result is narrow enough to demonstrate the high-resolution signal required for frequency stabilisation. The experiment also detected the O-centre resonance without resolving a separate quadrupole structure. Its linewidth was about 1.1(1) megahertz.

An electric field gradient describes how the electric field changes around the thorium nucleus. The O-centre showed an upper bound of less than 0.1 volts per square ångström for the relevant static gradient, compared with roughly 100 volts per square ångström for the D-centre. A smaller gradient means the nuclear resonance is less strongly split by the surrounding crystal environment, making the site attractive for further clock studies.

The two sites also differed in their isomeric shift, a frequency change caused by different electron densities at the nucleus. The O-centre line was offset from the D-centre reference by 3.99(2) megahertz. Density-functional-theory calculations gave a corresponding shift of 3.60(29) megahertz, supporting the assignment of the two observed structures.

Why this matters for a nuclear clock

The absorption method changes the timing of the measurement. In the fluorescence experiment described in the paper, the crystal was illuminated for 800 seconds and then observed for another 800 seconds. The absorption measurement instead follows the transmitted laser power during excitation, and the authors report an overall detection-cycle reduction of two orders of magnitude in the high-resolution demonstration.

Using the measured linewidth, photon flux and absorption fraction, the researchers estimate a shot-noise-limited fractional frequency instability of about 2 × 10⁻¹²√τ(s), where τ is the averaging time in seconds. With longer crystals or an optical cavity, more ultraviolet power, and improved crystal materials and linewidths, their projection is an instability of no more than 10⁻¹⁶ at about 10⁴ seconds.

Those figures are performance estimates rather than measurements from a completed clock. The vacuum-ultraviolet laser linewidth was not measured directly; the team inferred that it was 10 kilohertz or less from the spectroscopy signals. The physical sources of the much larger O-centre linewidth also require further study. Even so, the demonstrated absorption signal and its frequency-modulation error signal provide the fast feedback route needed to turn thorium-229 spectroscopy into a solid-state nuclear clock.

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