Rotational energy levels in the ground vibrational state of methane with kHz-level accuracy from comb-referenced double-resonance and Lamb-dip spectroscopies

Methane is a key spherical-top molecule, yet restrictive selection rules for one-photon transitions have prevented determination of its ground state (GS) energies with state-of-the-art kHz-level accuracy. We report the GS rotational energy level differences with kHz-level accuracy from two frequency-comb-referenced sub-Doppler methods: optical-optical double-resonance spectroscopy in the $\mathrm{\Lambda }$-type configuration, and Lamb-dip spectroscopy of allowed and forbidden transitions. A Hamiltonian fit to the data yields GS term values with rotational numbers up to $J$ = 12 with kHz level accuracy.