Excluding Hypothetical Light Boson Interpretation of Yb King Plot Nonlinearity with the ${}^1S_0 \leftrightarrow {}^3P_2$ Isotope Shift Measurement

Abstract

We present precision spectroscopy and isotope shift measurement of the ${}^1S_0 \leftrightarrow {}^3P_2$ clock transition in neutral ytterbium ($\mathrm{Yb}$) atoms. By revealing a magic wavelength at $905.4(2)$ nm, we successfully achieve the atomic spectrum narrower than $100$ Hz. The interleaved clock operation between isotopes allows us to determine isotope shifts of four bosonic isotope pairs at Hz-level uncertainties, which is combined with those of other four ultra-narrow transitions in $\mathrm{Yb}$ and $\mathrm{Yb}^+$ to construct the King plot. Importantly, the new isotope shift data reported in this work is a key to exclude the possibility of attributing the observed nonlinearity of the three-dimensional King plot solely to the new physics, while the previous works rely on the other terrestrial bound set by the neutron scattering and $(g-2)_e$ measurements. This work paves the way for the effective use of precision isotope shift data in the King plot analysis and stimulates further measurements in $\mathrm{Yb}$ and other elements.

Figures (3)

• Figure 1: Experimental setup and precision spectroscopy. (a) Energy structure of Yb relevant to our experiments. Note that transitions for laser cooling, imaging, and photo-association are not shown here. (b) Laser configuration around atoms. The small arrows perpendicular to the main ones represent the laser polarization. (c) Magic wavelength search. The AC Stark shift induced by the $y$-axis lattice after normalization by the lattice depth of the $y$-axis is shown as a function of the lattice frequency. The solid line is a linear fit, yielding a magic frequency of $331.13(8)$ THz, corresponding to $905.4(2)$ nm. (d) Atomic spectrum of the $\ket{g} = {}^1S_0 \leftrightarrow \ket{e} = {}^3P_2 \ (m_J = 0)$ transition in $^{174}$Yb. The solid curve is a Rabi line shape fit with a pulse duration of $13.5$ ms, where a maximum excitation fraction is $0.53(2)$.
• Figure 2: Isotope shift measurements. (a) Stability of $\delta \nu_{507}^{170, 174}$ measurements. The solid line is a fitting curve assuming the white frequency noise, yielding $234(9) \ \mathrm{Hz} / \sqrt{\tau \ \mathrm{(s)}}$. (b) The time trace of $\delta \nu_{507}^{170, 174}$ measurements. The left and right axes correspond to two distinct measurements performed on different days. Note that there is no data point during the time interval between the two time durations. The error bar is the $1\sigma$ statistical uncertainty determined from the overlapping Allan deviation. The blue (orange) shaded area represents the statistical (systematic) uncertainty of the entire data set.
• Figure 3: King plot analysis. (a) Product of couplings $y_e y_n$ of a new boson as a function of the mass $m_\phi$. The blue, green, and magenta lines represent the central values of $y_e y_n$ for (411, 431, 578), (411, 467, 578), and (467, 507, 578), respectively, and the corresponding shaded areas display the fitting errors at the 95% confidence level. Note that the shaded regions of the former two transition sets are narrower than the width of the solid lines. The red solid line and shaded area depict the 95% confidence region obtained from the simultaneous fit of the five transitions including $X_i$ uncertainties, which is magnified in the inset. The orange dashed curve is the current best terrestrial bound, determined as the product of the constraint on $y_e$ from a $(g-2)_e$ measurement Fan2023-cz and the constraint on $y_n$ from neutron scattering measurements Leeb1992-viPokotilovski2006-ctNesvizhevsky2008-mf, while the orange shaded area is the corresponding excluded region. The upper bound from the King plot analysis of calcium ions Wilzewski2025-dx is displayed as a gray dashed line. (b) $m_\phi$ dependence of $\chi^2$ in the simultaneous fit. The blue (red) solid line corresponds to the analysis without (with) $X_i$ uncertainties. The black dashed line shows $\chi^2$ of the 3D generalized King plot before including the PS. As a reference, $\chi^2$ values at the 95% confidence level with the dof of 2 is shown as the gray dashed line.