Simulation-based modeling of measuring Attosecond delays in the photoionization process

Abstract Ultrashort attosecond light pulses paved a new way in the research of modern physics. Even a short temporal delay between photon absorption and electron emission reveals rich quantum-level information about an atom or an electron. This paper develops a complete simulation-based modelling framework of the measurement of these attosecond delays and discusses the two most widely utilized pump–probe techniques: RABBITT (Reconstruction of Attosecond Beating by Interference of Two-photon Transitions) and attosecond streaking. In this paper, we have expressed the pump and probe fields as ideal Gaussian envelopes. Our model demonstrates analytical expressions for the temporal overlap cross-correlation, the coherent superposition of the two wave packets, the resulting interference fringes in both the time-domain intensity and the frequency-domain spectrum, and the delay-dependent signal, which reveals clear beat oscillations, and their frequency directly reflects the energy separation between interfering pathways. Then, a linear least-squares phase retrieval method is incorporated to extract the atomic phase shift Δθ from the oscillatory sideband (or streaking trace) intensity. Furthermore, the paper shows the comparison of our framework with real experiments of RABBITT and attosecond streaking on Ar(3p) and Ne(2p). This work bridges between theory and experiment, offering an accessible tool for attosecond science and a foundation for advanced TDSE simulations and machine-learning applications.