Strong-field quantum control in the extreme ultraviolet domain using pulse shaping

: Tailored light-matter interactions in the strong coupling regime enable the manipulation and control of quantum systems with up to unit efficiency1,2, with applications ranging from quantum information to photochemistry3-7. Although strong light-matter interactions are readily induced at the valence electron level using long-wavelength radiation8, comparable phenomena have been only recently observed with short wavelengths, accessing highly excited multi-electron and inner-shell electron states9,10. However, the quantum control of strong-field processes at short wavelengths has not been possible, so far, because of the lack of pulse-shaping technologies in the extreme ultraviolet (XUV) and X-ray domain. Here, exploiting pulse shaping of the seeded free-electron laser (FEL) FERMI, we demonstrate the strong-field quantum control of ultrafast Rabi dynamics in helium atoms with high fidelity. Our approach reveals a strong dressing of the ionization continuum, otherwise elusive to experimental observables. The latter is exploited to achieve control of the total ionization rate, with prospective applications in many XUV and soft X-ray experiments. Leveraging recent advances in intense few-femtosecond to attosecond XUV to soft X-ray light sources, our results open an avenue to the efficient manipulation and selective control of core electron processes and electron correlation phenomena in real time.