High-precision spectroscopy of the HD⁺ molecule at the 1-p.p.b. level

Recently we reported a high-precision optical frequency measurement of the (v, L): (0, 2) → (8, 3) vibrational overtone transition in trapped deuterated molecular hydrogen (HD+) ions at 10 mK temperature. Achieving a resolution of 0.85 parts-per-billion (p.p.b.), we found the experimental value [Ν ₀ = 383, 407, 177.38 (41) MHz] to be in agreement with the value from molecular theory [Ν_th 383, 407, 177.150 (15) MHz] within 0.6 (1.1) p.p.b. (Biesheuvel et al. in Nat Commun 7:10385, 2016). This enabled an improved test of molecular theory (including QED), new constraints on the size of possible effects due to 'new physics,' and the first determination of the proton-electron mass ratio from a molecule. Here, we provide the details of the experimental procedure, spectral analysis, and the assessment of systematic frequency shifts. Our analysis focuses in particular on deviations of the HD⁺ velocity distribution from thermal (Gaussian) distributions under the influence of collisions with fast ions produced during (laserinduced) chemical reactions, as such deviations turn out to significantly shift the hyperfine-less vibrational frequency as inferred from the saturated and Dopplerbroadened spectrum, which contains partly unresolved hyperfine structure.