Abstract
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.
Highlights
Precision measurements with atoms and molecules improved our understanding of the structure of matter and of its interaction with light
This contribution demonstrates the potential of two-photon rotational and rovibrational transitions probed on trapped HD+ for the determination of fundamental constants
The approach may provide an independent and accurate determination of the Rydberg constant and of the nuclear-to-electron mass ratios and may add new results to the efforts made to measure the size of the proton and of the deuteron
Summary
Precision measurements with atoms and molecules improved our understanding of the structure of matter and of its interaction with light. Doppler-free two-photon spectroscopy of a rovibrational overtone transition of HD+ was proposed to improve the uncertainty beyond the 1 × 10−12 level [20] In this approach, efficient two-photon excitation in. E2 transition for homonuclear diatomic ions, demonstrated with N2 + [21], may be an alternative to increase the accuracy with Doppler-free spectroscopy in the Lamb-Dicke regime This contribution proposes to determine the Rydberg constant, the nuclear-to-electron mass ratios, and the nuclear radii using Doppler-free spectroscopy of hydrogen molecular ions. A THz/infrared double resonance two-photon spectroscopy study on trapped HD+ ions may allow joint measurements of E1-E1 rotational transitions in the vibrational ground state and of E1-E1 rovibrational transitions with different sensitivities on fundamental constants.
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