Proton-electron mass ratio from laser spectroscopy of HD+ at the part-per-trillion level.

Recent mass measurements of light atomic nuclei in Penning traps have indicated possible inconsistencies in closely related physical constants such as the proton-electron and deuteron-proton mass ratios. These quantities also influence the predicted vibrational spectrum of the deuterated molecular hydrogen ion (HD+) in its electronic ground state. We used Doppler-free two-photon laser spectroscopy to measure the frequency of the v = 0→9 overtone transition (v, vibrational quantum number) of this spectrum with an uncertainty of 2.9 parts per trillion. By leveraging high-precision ab initio calculations, we converted our measurement to tight constraints on the proton-electron and deuteron-proton mass ratios, consistent with the most recent Penning trap determinations of these quantities. This results in a precision of 21 parts per trillion for the value of the proton-electron mass ratio.

Fundamental Transitions and Ionization Energies of the Hydrogen Molecular Ions with Few ppt Uncertainty.

We calculate ionization energies and fundamental vibrational transitions for H_{2}^{+}, D_{2}^{+}, and HD^{+} molecular ions. The nonrelativistic quantum electrodynamics expansion for the energy in terms of the fine structure constant α is used. Previous calculations of orders mα^{6} and mα^{7} are improved by including second-order contributions due to the vibrational motion of nuclei. Furthermore, we evaluate the largest corrections at the order mα^{8}. That allows us to reduce the fractional uncertainty to the level of 7.6×10^{-12} for fundamental transitions and to 4.5×10^{-12} for the ionization energies.

Theoretical Hyperfine Structure of the Molecular Hydrogen Ion at the 1 ppm Level.

We revisit the mα^{6}(m/M) order corrections to the hyperfine splitting in the H_{2}^{+} ion and find a hitherto unrecognized second-order relativistic contribution associated with the vibrational motion of the nuclei. Inclusion of this correction term produces theoretical predictions which are in excellent agreement with experimental data [K. B. Jefferts, Phys. Rev. Lett. 23, 1476 (1969)], thereby concluding a nearly 50-year-long theoretical quest to explain the experimental results within their 1-ppm error. The agreement between the theory and experiment corroborates the proton structural properties as derived from the hyperfine structure of atomic hydrogen. Our work furthermore indicates that, for future improvements, a full three-body evaluation of the mα^{6}(m/M) correction term will be mandatory.

Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD(.).

The simplest molecules in nature, molecular hydrogen ions in the form of H2(+) and HD(+), provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD(+) by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but also enables the long predicted determination of the proton-to-electron mass ratio from a molecular system, as well as improved constraints on hypothetical fifth forces and compactified higher dimensions at the molecular scale. With the perspective of comparisons between theory and experiment at the 0.01 part-per-billion level, our work demonstrates the potential of molecular hydrogen ions as a probe of fundamental physical constants and laws.