Precision spectroscopy and nuclear structure information of Li<sup>+</sup> ions
Authors: Guan Hua , Qi Xiao-Qiu , Chen Shao-Long , Shi Ting-Yun , Gao Ke-Lin ,   Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China,   Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China,   Wuhan Institute of Quantum Technology, Wuhan 430206, China
Published: September 2024

Precision spectroscopy of lithium ions offers a unique research platform for exploring bound state quantum electrodynamics and investigating the structure of atomic nuclei. This paper overviews our recent efforts dedicated to the precision theoretical calculations and experimental measurements of the hyperfine splittings of <sup>6,7</sup>Li<sup>+</sup> ions in the <inline-formula><tex-math id="M6">\begin{document}$\,^3{\rm{S}}_1$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M7">\begin{document}$\,^3{\rm{P}}_J$\end{document}</tex-math></inline-formula> states. In our theoretical research, we utilize bound state quantum electrodynamics to calculate the hyperfine splitting of the <inline-formula><tex-math id="M8">\begin{document}$\,^3{\rm{S}}_1$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M9">\begin{document}$\,^3{\rm{P}}_J$\end{document}</tex-math></inline-formula> states with remarkable precision, achieving an accuracy on the order of <inline-formula><tex-math id="M10">\begin{document}$m\alpha^6$\end{document}</tex-math></inline-formula>. Using Hylleraas basis sets, we first solve the non-relativistic Hamiltonian of the three-body system to derive high-precision energy and wave functions. Subsequently, we consider various orders of relativity and quantum electrodynamics corrections by using the perturbation method, with accuracy of the calculated hyperfine splitting reaching tens of kHz. In our experimental efforts, we developed a low-energy metastable lithium-ion source that provides a stable and continuous ion beam in the <inline-formula><tex-math id="M11">\begin{document}$\,^3{\rm{S}}_1$\end{document}</tex-math></inline-formula> state. Using this ion beam, we utilize the saturated fluorescence spectroscopy to enhance the precision of hyperfine structure splittings of <sup>7</sup>Li<sup>+</sup> in the <inline-formula><tex-math id="M12">\begin{document}$\,^3{\rm{S}}_1$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M13">\begin{document}$\,^3{\rm{P}}_J$\end{document}</tex-math></inline-formula> states to about 100 kHz. Furthermore, by utilizing the optical Ramsey method, we obtain the most precise values of the hyperfine splittings of <sup>6</sup>Li<sup>+</sup>, with the smallest uncertainty of about 10 kHz. By combining theoretical calculations and experimental measurements, our team have derived the Zemach radii of the <sup>6,7</sup>Li nuclei, revealing a significant discrepancy between the Zemach radius of <sup>6</sup>Li and the values predicted by the nuclear model. These findings elucidate the distinctive properties of the <sup>6</sup>Li nucleus, promote further investigations of atomic nuclei, and advance the precise spectroscopy of few-electron atoms and molecules.