Oscillating nuclear charge radii as sensors for ultralight dark matter

Abstract

We show that coupling of ultralight dark matter (UDM) to quarks and gluons would lead to an oscillation of the nuclear charge radius for both the quantum chromodynamics (QCD) axion and scalar dark matter. Consequently, the resulting oscillation of electronic energy levels could be resolved with optical atomic clocks, and their comparisons can be used to investigate UDM-nuclear couplings, which were previously only accessible with other platforms. We demonstrate this idea using the ${}^2S_{1/2} (F=0)\leftrightarrow {}^2F_{7/2} (F=3)$ electric octupole and ${}^2S_{1/2} (F=0)\leftrightarrow \,{}^2D_{3/2} (F=2)$ electric quadrupole transitions in ${}^{171}Yb^+$. Based on the derived sensitivity coefficients for these two transitions and a long-term comparison of their frequencies using a single trapped ${}^{171}Yb^+$ ion, we find bounds on the scalar UDM-nuclear couplings and the QCD axion decay constant. These results are at a similar level compared to the tightest spectroscopic limits, and future investigations, also with other optical clocks, promise significant improvements.

Figures (2)

• Figure 1: Exclusion plot for the linear scalar DM coupling a) to the gluons $d_g$ and b) to the quark masses $d_{\hat{m}}$ as a function of DM mass $m_\phi$. Using the field shift effect, limits at the 95% confidence level from long-term measurements of the frequency ratio $\nu_{\textrm{E3}}/\nu_{\textrm{E2}}$ in a single-ion optical clock are shown in dark red. Based on the same experiment, the much weaker limit from the mass shift is shown for reference. The dashed line shows a projection assuming amplitude limits at the $1\times10^{-18}$-level. The grey and the blue lines depict the strongest EP bound MICROSCOPE:2022doy and the bound from various fifth force searches Fischbach:1996eq, respectively. Bounds from existing spectroscopy experiments are also shown: Rb/Cs Hees:2016gop (turquoise), Yb/Cs Kobayashi2022 (orange), H/Si Kennedy:2020bac (purple).
• Figure 2: Exclusion plot for the QCD axion coupling $1/f_a$ as a function of the axion mass, $m_a$. The limits based on the long-term measurements of the frequency ratio $\nu_{\textrm{E3}}/\nu_{\textrm{E2}}$ in a single-ion optical clock are shown in dark red. The dashed line is a projection assuming amplitude limits at the $1\times10^{-18}$-level. Existing limits based on oscillating neutron electric dipole moment Abel:2017rtm are shown in brown, and theory limits due to density effects of the Earth Hook:2017psm as a dotted green line. Bounds from existing spectroscopy experiments are also shown: Rb/Cs Hees:2016gop (turquoise), Yb/Cs Kobayashi2022 (orange), H/Si Kennedy:2020bac (purple).