Extended Data Fig. 3: Analysis of the adiabaticity: calculated occupation probability of the upper/lower AT state correlating to the 1s2p bare state during the light-matter interaction.

Left: dominant occupation of either the upper (blue) or the lower (red) AT state at the peak of the FEL pulse (t = 0) as a function of the GDD and the detuning from the resonance. The white dashed lines mark the boundary where the corresponding state is occupied with 90% probability. For resonant driving (horizontal dashed line) the occupation exceeds 90% only for one GDD value from the experiment, that is −1127 fs². Right: occupation probability of the initially occupied AT state as a function of time t (in units of the pulse duration T) for resonant driving. Since for negative and positive GDDs the initially occupied states are the upper and lower AT state, respectively, different colours are used. If the occupation remains ≳ 90% until the peak of the pulse (t = 0), which is the case for ∣GDD∣ ≳ 750fs², the dynamic is adiabatic. As in the left panel, the dashed lines mark occupation of the initial state with 90% probability. In both panels the five experimental GDDs are marked with dotted lines. All calculations are done for a driven two-level system with the energy levels and the dipole coupling of helium for T = 49.3 fs and I = 6 × 10¹⁴ W/cm². The analysis reveals that the population transfer is only adiabatic for a frequency chirp with values of ∣GDD∣ ≳ 750fs². Hence, the majority of the experiment is conducted in the non-adiabatic regime. The analysis also shows that the conditions for rapid adiabatic passage can be generally reached with the experimental approach.