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We demonstrate the measurement of ultrafast dynamics using ghost spectroscopy and a pump-probe approach with an optical pump and a short-wavelength radiation probe. The ghost spectroscopy approach is used to overcome the challenge of the strong intensity and spectrum fluctuations at free-electron lasers and to provide high -spectral resolution, which enables the measurement of small energy shifts in the absorption spectrum. We exploit the high resolution to explore the dynamics of the charge carrier excitations and relaxations and their impact on the photoinduced structural changes in silicon by measuring the variation of the absorption spectrum of a Si(100) membrane near the silicon L2,3 edge and the accompanying edge shifts in response to the optical illumination.

We demonstrate a simple and robust high-resolution ghost spectroscopy approach for x-ray and extreme ultraviolet absorption spectroscopy at free-electron laser sources. Our approach requires an on-line spectrometer before the sample and a downstream bucket detector. We use this method to measure the absorption spectrum of silicon, silicon carbide and silicon nitride membranes in the vicinity of the silicon L2,3-edge. We show that ghost spectroscopy allows the high-resolution reconstruction of the sample spectral response using a coarse energy scan with self-amplified spontaneous emission radiation. For the conditions of our experiment the energy resolution of the ghost-spectroscopy reconstruction is higher than the energy resolution reached by scanning the energy range by narrow spectral bandwidth radiation produced by the seeded free-electron laser. When we set the photon energy resolution of the ghost spectroscopy to be equal to the resolution of the measurement with the seeded radiation, the measurement time with the ghost spectroscopy method is shorter than scanning the photon energy with seeded radiation. The exact conditions for which ghost spectroscopy can provide higher resolution at shorter times than measurement with narrow band scans depend on the details of the measurements and on the properties of the samples and should be addressed in future studies.