Probing Nuclear Interactions Through Isotope Shift Spectroscopy of Mercury

We present precision isotope shift spectroscopy of the $\mathrm{6s^{2}}\, {}^{1}\mathrm{S}_{0}{\rightarrow\,}\mathrm{6s\, 6p}\, {}^{3}\mathrm{P}_{1}$ intercombination line and the $\mathrm{6s\,6p}\, {}^{3}\mathrm{P}_{1}{\rightarrow\,}\mathrm{6s\,6d}\, {}^{3}\mathrm{D}_{J}$ ($J=1,2$) transitions in neutral mercury, performed on the five naturally abundant even isotopes, including the low-abundant isotope ${}^{196}\mathrm{Hg}$. Using laser-cooled atoms in a magneto-optical trap, we achieve uncertainties down to $20\,\mathrm{kHz}$, resolving the isotope shift to a fractional uncertainty of ${\sim}\,2{\,\times\,}10^{-6}$. A King plot analysis comparing our ${}^{1}\mathrm{S}_{0}{\rightarrow}{}^{3}\mathrm{P}_{1}$ data to previous results on the $\mathrm{6s\,6p}\,{}^{3}\mathrm{P}_{2}{\rightarrow\,}\mathrm{6s\,7s}\,{}^{3}\mathrm{S}_{1}$ line reveals a nonlinearity with $4.9\,\sigma$ significance. Our generalized King plot nonlinear decomposition analysis discusses potential contributions from quadratic ($\propto \delta\langle r^{2}\rangle^{2}$) and higher order field shifts ($\propto \delta\langle r^{4}\rangle$) also induced by nuclear deformation. These measurements yield new insights into the structure of the $\mathrm{Hg}$ nucleus and provide benchmarks for nuclear-structure models. They further establish mercury as a potential platform to search for hypothetical Yukawa-type boson-mediated forces coupling electrons to neutrons.