Laser cooling and trapping of neutral molecules has made substantial progress in the past few years. On one hand, molecules have more complex energy level structures than atoms, thus bringing great challenges to direct laser cooling and trapping; on the other hand, cold molecules show great advantages in cold molecular collisions and cold chemistry, as well as the applications in many-body interactions and fundamental physics such as searching for fundamental symmetry violations. In recent years, polar diatomic molecules such as SrF, YO, and CaF have been demonstrated experimentally in direct laser cooling techniques and magneto-optic traps (MOTs), all of which require a comprehensive understanding of their molecular internal level structures. Other suitable candidates have also been proposed, such as YbF, MgF, BaF, HgF or even SrOH and YbOH, some of which are already found to play important roles in searching for variations of fundamental constants and the measurement of the electron’s Electric Dipole Moment (<i>e</i>EDM). As early as 2004, the CaH molecule was selected as a good candidate for laser cooling and magneto-optical trapping. In this article, we first theoretically investigate the Franck−Condon factors of CaH in the <inline-formula><tex-math id="M233">\begin{document}${{\rm{A}}}^{2}\Pi _{1/2}\leftarrow {{\rm{X}}}^{2}\Sigma _{1/2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M233.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M233.png"/></alternatives></inline-formula> transition by the Morse potential method, the closed-form approximation method and the Rydberg-Klein-Rees method separately, and prove that Franck−Condon factor matrix between <inline-formula><tex-math id="M234">\begin{document}$ {\mathrm{X}}^{2}\Sigma _{1/2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M234.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M234.png"/></alternatives></inline-formula> state and <inline-formula><tex-math id="M235">\begin{document}$ {\mathrm{A}}^{2}\Pi _{1/2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M235.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M235.png"/></alternatives></inline-formula>state is highly diagonalized, and indicate that sum of <i>f</i>₀₀, <i>f</i>₀₁ and <i>f</i>₀₂ for each molecule is greater than 0.9999 and almost 1 × 10⁴ photons can be scattered to slow the molecules with merely three lasers. The molecular hyperfine structures of <inline-formula><tex-math id="M236">\begin{document}$ {X}^{2}\Sigma _{1/2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M236.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M236.png"/></alternatives></inline-formula>, as well as the transitions and associated hyperfine branching ratios in the <inline-formula><tex-math id="M237">\begin{document}${{\rm{A}}}^{2}\Pi _{1/2}\left(J=1/2, \mathrm{ }+\right)\leftarrow {{\rm{X}}}^{2}\Sigma _{1/2}\left(N=1, \mathrm{ }-\right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M237.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M237.png"/></alternatives></inline-formula> transition of CaH, are examined via the effective Hamiltonian approach. According to these results, in order to fully cover the hyperfine manifold originating from <inline-formula><tex-math id="M238">\begin{document}$ |X, \mathrm{ }N=1, -\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M238.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M238.png"/></alternatives></inline-formula>, we propose the sideband modulation scheme that at least two electro-optic modulators (EOMs) should be required for CaH when detuning within 3<i>Γ</i> of the respective hyperfine transition. In the end, we analyze the Zeeman structures and magnetic <i>g</i> factors with and without <i>J</i> mixing of the <inline-formula><tex-math id="M239">\begin{document}$ |X, \mathrm{ }N=1, -\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M239.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M239.png"/></alternatives></inline-formula> state to undercover more information about the magneto-optical trapping. Our work here not only demonstrates the feasibility of laser cooling and trapping of CaH, but also illuminates the studies related to spectral analysis in astrophysics, ultracold molecular collisions and fundamental physics such as exploring the fundamental symmetry violations.

Metasurface can precisely control degrees of freedom of the phase, polarization, and amplitude of the incident light field. It provides a new way to develop the next generation of the experimental platform of quantum-state manipulation on-chip, which has important application prospects. This paper proposes a new type of metasurface structure, that is, a metalens composed of silicon grating elements with different duty ratios that can form a focusing ring on the focal plane. The intensity distribution of the ring light field in the focal plane and the focusing characteristics of metalens with different numerical apertures are studied. An optical storage ring of magnesium fluoride (MgF) molecule is constructed by using this kind of metalens focusing ring. The optical potential and dipole force of the MgF molecule in the focused light field are calculated, and the dynamic process of MgF molecule motion in the storage ring is simulated by the Monte-Carlo method. The research results show that for the incident light of 1064-nm radially polarized light, the designed metasurface structure has good focusing characteristics, and the light field intensity of the focusing ring is 55.1 times stronger than that of the incident light. The focal length of the annular light field is 22 μm and the full width at half maximum of the light intensity distribution in the focal plane is 0.8 μm, and the numerical aperture of the hyperlens is 0.69. The maximum dipole potential of MgF molecules in the light field is 32 μK, which can realize the loading of MgF molecules and trap them in the surface storage ring.