Extended Data Fig. 1: Spatial intensity distribution in the interaction volume of the experiment, measured with a Hartmann wavefront sensor.

The atomic jet target has a width of ≈ 0.2 mm along the FEL propagation direction, thus the intensity in the direction of propagation can be assumed to be constant. To visualize the intensity distribution in the transverse mode, we generated a histogram of the intensity values measured in the ionization volume (blue). The experimental distribution is compared to an ideal Gaussian TEM₀₀ mode (orange). While the TEM₀₀ mode is characterized by an equal relative occurrence of all intensity values in the ionization volume, the actual intensity occurrences measured in the experiment show a maximum at intensities roughly three orders of magnitude lower than the peak intensity I₀. Hence, in the experiment a much larger fraction of He atoms in the ionization volume were excited by lower intensities than expected theoretically. At these low intensities, the AT splitting is too small to be resolved. This rationalizes the appearance of a pronounced peak in the centre of the measured photoelectron spectra not showing an AT splitting.