An eikonal approximation model for two-color two-photon attosecond interferometric spectrum

Abstract

The emission time of photoelectrons from atoms, molecules and solids can be accurately measured on an attosecond scale by using two-color two-photon attosecond interferometric spectroscopy, which helps us to understand the ultrafast electronic dynamics in laser-assisted single photoionization. Understanding the photoelectron emission time depends on the physical model, and the relevant theoretical model provides a better physical explanation and numerical prediction for the photoemission time delay. Although the numerical solution of the time-dependent Schrödinger equation can accurately predict the photoelectron emission time, but it cannot provide a physical explanation. Although some other current theoretical models can provide a more reasonable corresponding physical process, the quantitative prediction of the photoemission time delay has a large deviation. Therefore, we improve the exisating eikonal approximation model. Comparing with the existing eikonal approximation model, we use a more accurate final state wave function and calculate the photoelectron trajectory more accurately when calculating the phase accumulated in the photoelectron propagation process, so we can predict the photoemission time delay more accurately. By comparing our numerical simulation results, we find that when the final kinetic energy of photoelectron is low, the calculated results from the existing theoretical model are greatly different from those from the time-dependent Schrödinger equation, reaching tens of attoseconds. The resultsfrom the existing theoretical model are closer to those from the time-dependent Schrödinger equation with the increase of final kinetic energy of photoelectron. However, no matter what the final kinetic energy of the photoelectron is, the difference between the calculation result from the improved eikonal approximation model and that from the time-dependent Schrödinger equation is always very small. Therefore, our improved eikonal approximation model is closer to the results from the time-dependent Schrödinger equation than the existing theoretical model, which greatly deeps our understanding of the ultra-fast process of photoelectron emission.