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

TL;DR

This paper reports ultra-precise measurements of HD+ molecular transitions, confirming molecular theory within parts-per-billion, and discusses systematic effects affecting frequency accuracy, advancing tests of fundamental physics and molecular models.

Contribution

It provides detailed experimental procedures, spectral analysis, and systematic shift assessments for high-precision HD+ spectroscopy, including effects of non-thermal velocity distributions.

Findings

Measured vibrational transition frequency with 0.85 p.p.b. resolution

Confirmed agreement with molecular theory within 0.6 p.p.b.

Identified significant shifts due to non-thermal velocity distributions.

Abstract

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 ($\nu_0= 383,407,177.38(41)$ MHz) to be in agreement with the value from molecular theory ($\nu_\text{th}=383,407,177.150(15)$ MHz) within 0.6(1.1) p.p.b. [Biesheuvel et al., 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 (laser-induced) chemical reactions, as such deviations turn out to significantly shift the hyperfine-less vibrational frequency as inferred from the saturated and Doppler-broadened spectrum, which contains partly unresolved hyperfine structure.