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

Rotational and rovibrational transitions of cold trapped HD
⁺
ions may be probed by double resonance two-photon spectroscopy and detected by photodissociation. The two-photon transition rates and the lightshifts are calculated using the two-photon tensor operator formalism. The experimental accuracy is estimated at the 10
^-12
level. An adjustment of selected Doppler-free lines of HD
⁺
and H
₂
⁺
may provide an insight into the proton radius puzzle, may lead to an independent determination of the Rydberg constant, and may improve the values of the proton-to-electron and deuteron-to-proton mass ratios beyond the 10
^-11
level.