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We calculate the {\em exact} time-resolved ARPES spectrum of a two-band modelsemiconductor driven out of equilibrium by resonant and nonresonant laserpulses, highlighting the effects of phonon-induced decoherence and relaxation.{\em Resonant} excitations initially yield a replica of the {\em valence} bandshifted upward by the energy of the exciton peak in photoabsorption. This phaseis eventually destroyed by phonon-induced decoherence: the valence-band replicalowers in energy by the Stokes shift, locating at the energy of the excitonpeak in photoluminescence, and its width grows due to phonon dressing. {\emNonresonant} excitations initially yield a map of the conduction band. Thenelectrons transfer their excess energy to the lattice and bind with the holesleft behind to form excitons. In this relaxed regime a replica of the {\emconduction} band appears inside the gap. At fixed momentum the lineshape of theconduction-band replica versus the photoelectron energy is proportional to theexciton wavefunction in "energy space" and it is highly asymmetric. Althoughthe two-band model represents an oversimplified description of real materialsthe highlighted features are qualitative in nature; hence they provide usefulinsights into time-resolved ARPES spectra and their physical interpretation.

From carriers and virtual excitons to exciton populations: Insights into time-resolved ARPES spectra from an exactly solvable model