Dressed-State Spectroscopy and Magic Trapping of Microwave-Shielded NaCs Molecules

We report on the optical polarizability of microwave-shielded ultracold NaCs molecules in an optical dipole trap. While dressing a pair of rotational states with a microwave field, we observe a marked dependence of the optical polarizability on the intensity and detuning of the dressing field. To precisely characterize differential energy shifts between dressed rotational states, we establish dressed-state spectroscopy. For strong dressing fields, we find that a magic rotational transition can be engineered and demonstrate its insensitivity to laser intensity fluctuations. The results of this Letter have direct relevance for evaporative cooling and the recent demonstration of molecular Bose-Einstein condensates [Bigagli et al., Nature (London) 631, 289 (2024)NATUAS0028-083610.1038/s41586-024-07492-z] and may open a door to precision microwave spectroscopy in interacting many-body systems of microwave-shielded molecules.