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Extreme ultraviolet and X-ray free-electron lasers (FELs) produce short-wavelength pulses with high intensity, ultrashort duration, well-defined polarization and transverse coherence, and have been utilized for many experiments previously possible only at long wavelengths: multiphoton ionization, pumping an atomic laser and four-wave mixing spectroscopy. However one important optical technique, coherent control, has not yet been demonstrated, because self-amplified spontaneous emission FELs have limited longitudinal coherence. Single-colour pulses from the FERMI seeded FEL are longitudinally coherent, and two-colour emission is predicted to be coherent. Here, we demonstrate the phase correlation of two colours, and manipulate it to control an experiment. Light of wavelengths 63.0 and 31.5nm ionized neon, and we controlled the asymmetry of the photoelectron angular distribution by adjusting the phase, with a temporal resolution of 3as. This opens the door to new short-wavelength coherent control experiments with ultrahigh time resolution and chemical sensitivity

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Electron spin dephasing in a singly charged semiconductor quantum dot can partially be suppressed by periodic laser pulsing. We propose a semi-classical approach describing the decoherence of the electron spin polarization governed by the hyperfine interaction with the nuclear spins as well as the probabilistic nature of the photon absorption. We use the steady-state Floquet condition to analytically derive two subclasses of resonance conditions excellently predicting the peak locations in the part of the Overhauser field distribution which is projected in the direction of the external magnetic field. As a consequence of the periodic pulsing, a non-equilibrium distribution develops as a function of time. The numerical simulation of the coupled dynamics reveals the influence of the hyperfine coupling constant distribution onto the evolution of the electron spin polarisation before the next laser pulse. Experimental indications are provided for both subclasses of resonance conditions.