Spectroscopy of $^4$He at 0.25 ppt Uncertainty and Improved Alpha-Helion Charge-Radius Difference Determination
High-precision spectroscopy of simple atomic systems can be used to advance the theory of atomic energy levels but can also serve as a sensitive probe of nuclear charge radii. For this last purpose, we report an improved measurement of the $2\,^3{S}_1 \to 2\,^1{S}_0$ transition frequency in $^4$He with 48 Hz uncertainty (0.25 ppt), using a Bose-Einstein condensed sample confined in a magic-wavelength optical dipole trap. A systematic Doppler shift from condensate motion is suppressed by time-resolved ion detection, and the transition frequency is calibrated via a White Rabbit link to a remote active hydrogen maser clock. Combined with previous $^3$He measurements and improved theory, we obtain the most precise determination to date of the charge-radius difference between the helion and alpha particle ($r_{h}^2 -r_{\alpha}^2$) of $1.0676(10)\text{fm}^2$. This is consistent with other recent determinations and confirms that the current discrepancy between QED theory and experimentally observed ionization energies of excited states in helium is not apparent in the isotope shift.