Probing Ultralight Dark Matter at the Mega-Planck Scale with the Thorium Nuclear Clock

Abstract

Ultralight dark matter is expected to induce oscillations of nuclear parameters. These oscillations are characterized by extremely weak couplings or high suppression scales, with the Planck scale - the characteristic scale of quantum gravity - serving as a natural benchmark. Probing this phenomenon requires systems with exceptional sensitivity to shifts in nuclear energies. The uniquely low-energy nuclear isomeric transition in ${}^{229}$Th provides such sensitivity: it directly probes the nuclear interaction and, owing to a near cancellation between electromagnetic and nuclear contributions, its response to changes in nuclear structure is greatly amplified. We devise and perform a new type of ultrasensitive search for dark matter which uses the precision nuclear spectroscopy at JILA to set the strongest bounds in the mass range $10^{-21}\,{\rm eV} \lesssim m_{\rm DM} \lesssim 10^{-19}\,{\rm eV}$. Our results probe effective interaction scales exceeding $10^6$ times the Planck scale (the Mega-Planck scale) and establish the ${}^{229}$Th system as the leading probe of dark matter couplings to the nuclear sector.

Figures (9)

• Figure 1: Schematic diagram of the influence of dark matter (DM) on the $^{229}$Th spectroscopy, leading to two search methods relevant for different DM frequency regimes. (A) A cartoon of thorium nuclei embedded in a crystal, in the presence of ULDM waves (dark gray bands). The isomer transition is also shown. (B) A schematic of the time-resolved analysis, which relies on the varying position of the centre frequency of the transition, as relevant for low-mass (frequency) DM. (C) The lineshape analysis, where the DM oscillation frequencies are fast enough such that the shape of the resonance is changed, either through broadening or in the most extreme circumstances, a double peak structure appears.
• Figure 2: Searches for coupling of scalar DM $\phi$ to quark masses (left) and gluons (right). The coloured regions represent constraints from searches for time variations in frequencies, assuming the scalar field constitutes DM. The red region shows the constraint derived in this work under two scenarios for the sensitivity factor $K$ (see text for details on the challenge to calculate $K$). For small masses and correspondingly low frequencies, the bound is inferred from the time-resolved analysis. For larger masses, we apply the lineshape analysis. For the lineshape analysis we further show an agnostic bound relying purely on the recorded width (straight) as well as one where a Lorentzian shape arising from the crystal environment is assumed (dotted). In contrast, the gray regions are excluded by constraints that rely on the scalar being sufficiently massive to support the existence of Milky Way (MW) satellite galaxies DES:2020fxi, as well as from tests of equivalence principle (EP) violations mediated by the scalar field MICROSCOPE:2022doy. The provisional operation of a nuclear clock already bests the bounds coming from atomic clocks reaching the standard quantum limit Hees:2016gopKennedy:2020bacKobayashi:2022vsfSherrill:2023zahFilzinger:2023zrsBanerjee:2023bjc (teal). At masses $m_{\mathrm{DM}}\lesssim 10^{-19}$ the nuclear clock already explores yet unconstrained territory.
• Figure 3: Time-stamped measurements of the central transition frequency used in the analysis. This data set was collected over a total duration of $T_{\rm tot}\approx 10$ months as part of Ref. ooi_frequency_2025, supplemented by an additional scan (last data point). C10 and C13 denote the two lower-doping crystals studied in Ref. ooi_frequency_2025, which exhibited narrower transition linewidths. The extracted line centers are spread around $\nu_0=2,020,407,298,701.18(22)\,{\rm kHz}$ and mutually consistent with no modulation over the full measurement period as a constant fit yields $\chi^2=0.4$ .
• Figure 4: The extracted amplitudes using the Lomb-Scargle periodogram (blue). We display the $95\%$ confidence level bound on the amplitudes (red), as well as a $5\%$ detection threshold determined from MC simulation of the data (black dashed).
• Figure 5: Construction of the agnostic width $\Gamma_{\rm agn}$ used as a basis for the conservative bound of $\delta \nu_{\mathrm{DM}} \leq \frac{1}{2}\Gamma_{\rm agn}$ on the amplitude of the DM-induced frequency modulation. See text for details. The Lorentzian linewidth $\Gamma_L$ agrees with $\Gamma_{\rm agn}$ within less than $1\sigma$.