Double-Resonance Two-Photon Spectroscopy of Hydrogen Molecular Ions for Improved Determination of Fundamental Constants

A spectroscopy scheme is proposed for the detection of the two-photon rotational transition (v, L) = (0, 0) → (0, 2) and the two-photon rovibrational transition (v, L) = (0, 0) → (2, 0) of cold trapped HD+ ions by dissociation. The two-photon line shapes are calculated using a rate equation model. The resolution is at the 10
^-13
level. The lightshift for selected hyperfine components of the two-photon transitions is evaluated using the two-photon operator formalism. The experimental accuracy with two-photon transitions of trapped HD
⁺
ions is estimated at the 10
^-12
level, which corresponds also to the accuracy of the theoretical calculations. The comparison of experimental data and theoretical calculations for HD
⁺
and H
₂
⁺
transitions may lead to an independent determination of the Rydberg constant, the proton-to-electron mass ratio, and the deuteron-to-proton mass ratio. It may provide a measurement of the proton and deuteron radii by the molecular spectroscopy. Depending on possible issues of the proton radius puzzle in atomic spectroscopy, two-photon spectroscopy of hydrogen molecular ions may lead to an improvement of the determination of the proton-to-electron mass ratio and deuteron-to-proton mass ratio at the 10
^-12
level.