High-harmonic generation (HHG) normally requires a careful adjustment of the driving laser intensity (typically 10 14 − 10 15 W/cm 2 ) and gas medium parameters to enable good phase matching conditions. In contrast with conventional wisdom, we present experimental results indicating phasematched HHG in all rare gases, using a high-density medium and a driver laser intensity of around 10 16 W/cm 2 . The experimental results are corroborated by theoretical simulations, which indicate that ionization-induced self-phase modulation and plasma defocusing self-regulate the driver laser intensity to a level that is appropriate for good phase matching. A ten-fold broadening of the NIR spectrum is observed, which results in the generation of continuous spectra from 18 − 140 eV in spite of using 50-fs-long driving pulses. The presented scheme represents a simple and versatile concept for the generation of XUV and soft X-ray continua, which are ideally suited for transient absorption and reflection spectroscopy.

Multi-electron dynamics in atoms and molecules very often occur on sub-to few-femtosecond timescales. The available intensities of extreme-ultraviolet (XUV) attosecond pulses have previously only allowed the time-resolved investigation of two-photon, two-electron interactions. Here we demonstrate attosecond control over double and triple ionization of argon atoms involving the absorption of up to five XUV photons. In an XUV-pump XUV-probe measurement using a pair of attosecond pulse trains (APTs), the Ar 2+ ion yield exhibits a weak delay dependence, showing that its generation predominantly results from the sequential emission of two electrons by photoabsorption from the two APTs. In contrast, the Ar 3+ ion yield exhibits strong modulations as a function of the delay, which is a clear signature of the simultaneous absorption of at least two XUV photons. The experimental results are well reproduced by numerical calculations that provide detailed insights into the ionization dynamics. Our results open up new opportunities for the investigation and control of multi-electron dynamics and complex electron correlation mechanisms on extremely short timescales.