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The physical interpretation of time-resolved photoabsorption experiments isnot as straightforward as for the more conventional photoabsorption experimentsconducted on equilibrium systems. In fact, the relation between the transientphotoabsorption spectrum and the properties of the examined sample can berather intricate since the former is a complicated functional of both thedriving pump and the feeble probe fields. In this work we critically review thederivation of the time-resolved photoabsorption spectrum in terms of thenonequilibrium dipole response function $\chi$ and assess its domain ofvalidity. We then analyze $\chi$ in detail and discuss a few exact propertiesuseful to interpret the transient spectrum {\em during} (overlapping regime)and {\em after} (nonoverlapping regime) the action of the pump. Thenonoverlapping regime is the simplest to address. The absorption energies areindeed independent of the delay between the pump and probe pulses and hence thetransient spectrum can change only by a rearrangement of the spectral weights.We give a close expression of these spectral weights in two limiting cases(ultrashort and everlasting monochromatic probes) and highlight their strongdependence on coherence and probe-envelope. In the overlapping regime we obtaina Lehmann-like representation of $\chi$ in terms of light-dressed states andprovide a unifying framework of various well known effects in pump-drivensystems. We also show the emergence of spectral sub-structures due to thefinite duration of the pump pulse.

Some Exact Properties of the Nonequilibrium Response Function for Transient Photoabsorption