Progress towards 𝜇 Variation Detection with Hydronium (H₃O⁺)

Polyatomic molecules, with their complex degrees of freedom, offer a promising platform for precision measurements in the search for physics beyond the Standard Model. Inversion transition spectra of hydronium (H3O+), an ammonia-like symmetric top molecule that is abundant in interstellar medium, can be used to probe spatial and temporal variations of the electron-to-proton mass ratio 𝜇. To achieve this goal, we theoretically design the precision spectroscopy scheme to measure the inversion transition frequencies of the hydronium ion using quantum logic spectroscopy (QLS). Here, we present a theoretical investigation of the molecular structure, including the inversion-rotational splitting, Zeeman shift, spin-rotation coupling, and AC Stark shift. In addition, two-photon rabi rates are evaluated to design the state preparation protocols with QLS. To provide a more thorough consideration of symmetry, nuclear spin statistics of the indistinguishable hydrogen atoms are investigated. We expect the protocols developed in this work to be general to precision measurements of polyatomic molecules, for instance, the chiral molecules that have been proposed for parity violation searches.