Isotopic variation of parity violation in atomic ytterbium: method of measurements and analysis of systematic effects

We present a detailed description of experimental studies of the parity violation effect in an isotopic chain of atomic ytterbium (Yb), whose results were reported in a recent Letter [Antypas et al., Nat. Phys. 15, 120 (2019)]. We discuss the principle of these measurements, made on the Yb 6s$^2$ $^1$S$_0 \rightarrow $5d6s $^3$D$_1$ optical transition at 408 nm, describe the experimental apparatus, and give a detailed account of our studies of systematic effects in the experiment. Our results offer the first direct observation of the isotopic variation in the atomic parity violation effect, a variation which is in agreement with the prediction of the Standard Model. These measurements are used to constrain electron-proton and electron-neutron interactions, mediated by a light $Z'$ boson.