We present a theoretical approach for describing collective x-ray emission processes in extended multilevel targets, based on a combination of propagation equations for the quantum correlation functions and the semiclassical Maxwell-Bloch equations. Such a description overcomes the key deficiencies of the two constituent sets of equations, which have until now been independently used to describe these phenomena. The model developed is employed to study the spectral properties of superfluorescence of $K\alpha$ emission in zinc at $\sim 8630\mathrm{eV}$ after inner-shell photoionization with intense attosecond free-electron laser pulses. At high pump intensities, the numerical simulations predict a splitting of the $K{\alpha }_1$ emission line due to a self-induced Autler-Townes effect, which could readily be observed with standard high-resolution x-ray spectrometers. As short duration of the pump pulse is one of the crucial parameters for the manifestation of this phenomenon in the hard-x-ray regime, experimental verification could be possible due to the most recent developments of free-electron laser sources.

• Received 17 March 2020
• Revised 18 May 2020
• Accepted 29 May 2020

DOI:https://doi.org/10.1103/PhysRevA.102.013102