In this talk, I will discuss two recent developments centered on the physics and manipulation of hyperfine interactions in atomic and molecular systems. First, I will introduce an all-optical method for performing qudit gate operations in alkaline-earth and alkaline-earth-like atoms. Our scheme utilizes single-beam Raman transitions within the 1S0 to 3P1 manifold to achieve coherent manipulation of high-dimensional hyperfine levels, compatible with non-destructive readout and two-qudit gates via Rydberg blockade.
Second, I will shift to the molecular domain to explore the coupling between magnetism and atomic or molecular motion. This topic has seen a recent surge of interest due to the study of chiral phonons in solid state systems. Using modern ab initio methods and analytic models, we conduct a theoretically rigorous investigation of vibrational molecular magnetism, re-visiting this long-standing problem to derive relevant coupling parameters for spin-vibration interactions and predict localized, vibrationally induced magnetic fields.