Precision spectroscopy of the $X\,^{1}\Sigma_{g}^{+}, v=0\rightarrow 1$   ($J=0-2$) rovibrational splittings in H$_{2}$, HD and D$_{2}$
  Accurate experimental values for the vibrational ground tone or fundamental vibrational energy splitting of H$_2$, HD, and D$_2$ are presented. Absolute accuracies of $2\times10^{-4}$ 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 $X^{1}\Sigma_{g}^{+}, v=0, J$ and $v=1, J$ vibrational states to a common $EF^{1}\Sigma^{+}_{g}, v=0, J$ 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 \emph{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. 
Ming Li Niu, Edcel J. Salumbides, Gareth. D. Dickenson, Kjeld S.E.   Eikema, Wim Ubachs
physics.atom-ph