Precise test of quantum electrodynamics and determination of fundamental constants with HD⁺ ions

Bound three-body quantum systems are important for fundamental physics^1,2 because they enable tests of quantum electrodynamics theory and provide access to the fundamental constants of atomic physics and to nuclear properties. Molecular hydrogen ions, the simplest molecules, are representative of this class³. The metastability of the vibration-rotation levels in their ground electronic states offers the potential for extremely high spectroscopic resolution. Consequently, these systems provide independent access to the Rydberg constant (R_∞), the ratios of the electron mass to the proton mass (m_e/m_p) and of the electron mass to the deuteron mass (m_e/m_d), the proton and deuteron nuclear radii, and high-level tests of quantum electrodynamics⁴. Conventional spectroscopy techniques for molecular ions^5-14 have long been unable to provide precision competitive with that of ab initio theory, which has greatly improved in recent years¹⁵. Here we improve our rotational spectroscopy technique for a sympathetically cooled cluster of molecular ions stored in a linear radiofrequency trap¹⁶ by nearly two orders in accuracy. We measured a set of hyperfine components of the fundamental rotational transition. An evaluation resulted in the most accurate test of a quantum-three-body prediction so far, at the level of 5 × 10^-11, limited by the current uncertainties of the fundamental constants. We determined the value of the fundamental constants combinations [Formula: see text] and m_p/m_e with a fractional uncertainty of 2 × 10^-11, in agreement with, but more precise than, current Committee on Data for Science and Technology values. These results also provide strong evidence of the correctness of previous key high-precision measurements and a more than 20-fold stronger bound for a hypothetical fifth force between a proton and a deuteron.