Computational Progress in Searching for 𝜇 Variation with Hydronium

Polyatomic molecules, with their rich internal structure, are promising platforms for precision measurements that probe physics beyond the Standard Model. Here, we propose using the inversion-transition spectrum of hydronium (H₃O⁺), an ammonia-like symmetric-top molecule abundant in the interstellar medium, to search for spatial and temporal variations of the electron-to-proton mass ratio, 𝜇. To enable such measurements, we design a quantum logic spectroscopy (QLS) scheme for precision determination of H₃O⁺ inversion-transition frequencies. We present a computational study of the relevant molecular structure, including inversion–rotational splittings, Zeeman shifts, spin–rotation couplings, and AC Stark shifts, and we evaluate two-photon Rabi rates to guide QLS-based state-preparation protocols. The protocols developed here are expected to be broadly applicable to precision measurements in other polyatomic systems, including chiral molecules proposed for parity-violation searches.