Fig. 2: Experimental excitation of the He⁺ 1S–2S transition and comparison with TDSE calculations.

a Normalized experimental He²⁺ signal as a function of the NIR wavelength for several NIR intensities (in 10¹⁴ W cm⁻²). Gaussian fits are used to estimate the center, height, and width of the resonances. b TDSE simulation of the He²⁺ yield, fitted with Gaussian functions, for several NIR intensities (in 10¹⁴ W cm⁻²). c Fitted center of the resonances from the experiment and the TDSE simulations as a function of the NIR intensity (the vertical error bars are the 1-σ statistical errors based on the fit, the horizontal error bars for the experimental points is the statistical uncertainty of the intensity). The light-blue band represents the uncertainty in the experimental fitted slope due to the uncertainty of the NIR intensity at the position of the helium atoms. d He²⁺ signal (with 1-σ error bars) as a function of the 25th harmonic intensity, at a NIR central wavelength of 793 nm and an intensity of 0.9 × 10¹⁴ W cm⁻². The linear relationship indicates that a single 32 nm photon is involved in the excitation process, as expected from our excitation scheme.