THz/Infrared Double Resonance Two-Photon Spectroscopy of HD+ for Determination of Fundamental Constants

A double resonance two-photon spectroscopy scheme is discussed to probe jointly rotational and rovibrational transitions of ensembles of trapped HD+ ions. The two-photon transition rates and lightshifts are calculated with the two-photon tensor operator formalism. The rotational lines may be observed with sub-Doppler linewidth at the hertz level and good signal-to-noise ratio, improving the resolution in HD+ spectroscopy beyond the 10−12 level. The experimental accuracy, estimated at the 10−12 level, is comparable with the accuracy of theoretical calculations of HD+ energy levels. An adjustment of selected rotational and rovibrational HD+ lines may add clues to the proton radius puzzle, may provide an independent determination of the Rydberg constant, and may improve the values of proton-to-electron and deuteron-to-proton mass ratios beyond the 10−11 level