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.
Dark matter (DM) constitutes most of the matter in the Universe, yet its microscopic nature remains unknown. Ultralight dark matter (ULDM) is arguably the simplest class of DM candidates and is naturally produced via the misalignment mechanism in the early Universe [1][2][3]. Many well-motivated ULDM models predict that the dominant non-gravitational interactions of DM are not with electromagnetism, but with the strong nuclear sector of the Standard Model. More specifically, these interactions are with neutrons and protons (or, more fundamentally, with their quark and gluon constituents). Representative examples for ULDM models with couplings to the strong nuclear sector include the QCD axion [1][2][3], the dilaton [4] (see, however, [5]), relaxion models [6,7], Higgs portals [8], and alternatives to the QCD axion [9]. In these scenarios, the interactions between DM and the Standard Model are suppressed by very large energy scales, rendering them exceptionally weak and challenging to probe experimentally.
More generally, regardless of any specific DM theory, the Planck scale provides an important target, since it is the characteristic scale at which gravity becomes strong and new fundamental physics is expected to emerge. In this work, we break new ground by probing couplings between ULDM and the electromagnetic and nuclear fields that are suppressed by an energy six orders of magnitude above this scale.
ULDM behaves as a classical background field, oscillating at a frequency set by its mass m DM . Such oscillations induce time variations of the fundamental constants via the ULDM couplings (see [10] for a recent review and references therein). In particular, such couplings lead to a modulation of transition frequencies
where the amplitude δν DM depends on the local DM density, the strength of the DM couplings and the sensitivity of the transition in question.
In this work, we use recent and new high-resolution spectroscopic data of the 229 Th isomer transition acquired at JILA, which is recorded via direct frequency comparison with a Sr-based optical atomic clock [11,12]. The 1 S 0 -3 P 0 transition of the Sr clock has one of the lowest sensitivities to changes of fundamental constants and thereby serves as an anchor frequency reference [13,14]. In stark contrast, the uniquely low-energy (∼ 8 eV) nuclear transition in 229 Th , which is accessible to laser spectroscopy [15], exhibits an extraordinary 10 8 -10 10 enhancement in sensitivity to variations of nuclear parameters compared to optical transitions [16,17]. This combination of an exceptionally insensitive reference and an exceptionally sensitive probe enables us to surpass existing searches based on optical atomic clocks and tests of violation of the equivalence principle, even before the nuclear clock has reached atomic clock-level precision.
A key novelty of this work is a unified analysis strategy applied to time-stamped nuclear spectroscopy data recorded over ten months, with individual scans lasting approximately two hours (see Fig. 1). A time-resolved analysis of the transition frequency searches for slow DMinduced oscillations of the transition frequency, with periods ranging from months down to hours. A refined lineshape analysis, building on Ref. [16], probes faster oscillations that occur within a single line scan by detecting DM-induced distortions of the spectral profile. Applied to new and recent spectroscopic data, this combined strategy improves sensitivity by six to seven orders of magnitude compared to Ref. [16].
High-resolution frequency-based precision laser spectroscopy [11,12] was performed in JILA on three 229 Thdoped CaF 2 crystals (C10, C13, X2) produced by TU Wien [18], each with different doping concentrations. The nuclear transition in these crystals is split via the interaction between the nuclear quadrupole moment and the electric field gradient the nuclei experience in the crystal environment, resulting in five main spectral lines. Following the designation given in Ref. [11], the line “b” (m g = ± 5 2 → m e = ± 3 2 ) exhibits the narrowest linewidth and the smallest coefficient of the temperature dependence of its center frequency [12], and is thus used for the model constraint reported in this paper.
The data were taken with a vacuum ultraviolet (VUV) frequency comb [19] referenced to the JILA Sr optical atomic clock [20] ensuring precise and accurate frequency reproducibility. By precisely tuning either the comb carrier-envelope offset frequency or the repetition frequency, we can scan the narrowline comb teeth over any spectral feature of interest within the spectral envelope of the comb.
When a comb tooth is scanned over the nuclear transition, it is held at a fixed frequency to excite nuclei for t e = 400 seconds; nuclear fluorescence is subsequently spectrally filtered and collected with a photomultiplier tube for t d = 200 s, then a new frequency step is taken. About N pts ≈ 13 are taken for a specific re
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