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QED effects in molecules: test on rotational quantum states of H$_2$

Quantum electrodynamic effects have been systematically tested in the progression of rotational quantum states in the $X ^{1}Σ_{g}^{+}, v=0$ vibronic ground state of molecular hydrogen. High-precision Doppler-free spectroscopy of the $EF ^{1}Σ_{g}^{+} - X ^{1}Σ_{g}^{+}$ (0,0) band was performed with 0.005 cm$^{-1}$ accuracy on rotationally-hot H$_2$ (with rotational quantum states J up to 16). QED and relativistic contributions to rotational level energies as high as 0.13 cm$^{-1}$ are extracted, and are in perfect agreement with recent calculations of QED and high-order relativistic effects for the H$_2$ ground state.