Kramers–Kronig relation in attosecond transient absorption spectroscopy

Kramers-Kronig relation (KKR) has a wide range of applications in extreme ultra-violet (XUV) and X-ray spectroscopy. However, the validity of KKR for many of these applications has not been systematically studied, while it is known to require careful attention in nonlinear and pump-probe experiments in optical domain spectroscopy. Here, we study the validity of KKR in XUV attosecond transient absorption spectroscopy (ATAS) pump-probe experiments both experimentally and theoretically using the argon Fano resonances as a case study. Experiments are enabled by a phase-resolved method dubbed Complex Attosecond Transient-absorption Spectroscopy (CATS). Although the estimations based on the rotating-wave approximation suggest that KKR violation could be expected in the studied case, our results validate KKR and provide a solid basis for its application in a broad range of attosecond spectroscopy experiments.