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 $2^3S - 2^3P$ 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 $2^3S_1 - 2^3P_0$ 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.