Precision spectroscopy of the X¹Σg⁺, v=0→ 1 (J=0-2) rovibrational splittings in H₂, HD and D₂

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Accurate experimental values for the vibrational ground tone or fundamental vibrational energy splitting of H₂, HD, and D₂ are presented. Absolute accuracies of 2×10⁻⁴ cm⁻¹ are obtained from Doppler-free laser spectroscopy applied in a collisionless environment. The vibrational splitting frequencies are derived from the combination difference between separate electronic excitations from the X¹Σg⁺, v=0, J and v=1, J vibrational states to a common EF¹Σ⁺g, v=0, J state. The present work on rotational quantum states J=1,2 extends the results reported by Dickenson et al. on J=0 [Phys. Rev. Lett. 110 (2013) 193601]. The experimental procedures leading to this high accuracy are discussed in detail. A comparison is made with full ab initio calculations encompassing Born-Oppenheimer energies, adiabatic and non-adiabatic corrections, as well as relativistic corrections and QED-contributions. The present agreement between the experimental results and the calculations provides a stringent test on the application of quantum electrodynamics in molecules. Furthermore, the combined experimental-theoretical uncertainty can be interpreted to provide bounds to new interactions beyond the Standard Model of Physics or fifth forces between hadrons.