Extracting RABBITT-like phase information from time-dependent transient absorption spectra

We explore how the spectral phase of atto\-second pulse trains influences the optical cross section in transient absorption (TA) spectroscopy. The interaction of extreme ultraviolet (XUV) and time-delayed near-infrared (NIR) fields with an atomic or molecular system governs the dynamics. As already shown in RABBITT experiments, the spectral phase of the XUV pulses can be extracted from the photoionization spectrum as a function of the time delay. Similarly, this XUV phase imprints itself on delay-dependent optical cross-section oscillations. With a perturbative analytical approach and by simulating the quantum dynamics both in a few-level model and via solving the time-dependent Schr\"odinger equation for atomic hydrogen, we reveal the similarity between the spectral phase in RABBITT and TA spectroscopy.