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X-ray free-electron lasers, delivering x-ray pulses of femtosecond duration, are available for experiments for more than a decade and allow for hitherto unachievable x-ray intensities on sample, reaching up to 1021 W/cm2 for hard x-rays. At these intensities, the probability of a single atom or molecule to absorb a photon of an impinging x-ray pulse reaches unity. Moreover, several interactions of photons and matter within the duration of the x-ray pulse – nonlinear x-ray matter interactions – become possible, opening the pathway to nonlinear x-ray optics. For a macroscopic ensemble of atoms, molecules, nanometer-sized clusters or a solid, the interaction with a strongly focused x-ray beam can create macroscopic, highly excited states of matter, far from equilibrium. In particular, saturated absorption with a high-intensity x-ray pulse can result in transient states, present for roughly one femtosecond, with the characteristic feature, that every single atom in the interaction region is in a population inverted state with missing population in the innermost electronic shell. This macroscopic population inversion can lead to collective radiative decay mechanisms, such as amplified spontaneous emission or superfluorescence. In this presentation I will give you an overview over our experimental and theoretical investigations of these single-pass x-ray laser amplifiers in the x-ray spectral domain. I will address applications of this phenomenon in the area of chemical x-ray emission spectroscopy, a new concept of an x-ray laser oscillator, and will highlight recent theoretical developments to describe collective spontaneous emission in the x-ray spectral domain.
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