  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.
