Post-selection shifts the transition frequency of helium in an atomic beam

Abstract

Post-selecting output states in measurements can effectively amplify weak signals and improve precision. However, post-selection effects may also introduce unintended biases in precision measurements. Here, we investigate the influence of post-selection in the precision spectroscopy of the $2^{3}S-2^{3}P$ transition of helium (${}^4$He) using an atomic beam. We directly observe that post-selection based on atomic positions causes a shift in the measured transition frequency, amounting to approximately -55 kHz. After accounting for this post-selection shift, we obtain a corrected frequency of $276,764,094,712.45\pm 0.86$ kHz for the $2^3{S}_1-2^3{P}_0$ transition. Combining this result with existing data for ${}^3$He, we derive a new value for the difference in squared nuclear charge radii, $\delta r^2[r_h^2-r_{\alpha }^2]=1.0733\pm 0.0021$ fm${}^2$. This value shows a $2.8\sigma$ deviation from measurements of muonic helium ions, potentially pointing to new physics that challenges lepton universality in quantum electrodynamics.

14 pages including appendix