Time-dependent method in the laser-atom interactions

We introduce a recent developed time-dependent method used in the study of laser-atom interactions. The key ingredients of the method are that (1) we propagate the wave function in real space in a finite region. The region is split into two parts, an inner-region and an outer-region. Once the electron moved into the outer-region, the wave function is projected into momentum space and propagated analytically to avoid the reflection from the boundary. (2) To increase the numerical accuracy and make the physical processes more transparent, we solve the time-integral Schrödinger equation, instead of time-differential equation. Then we apply the method to study the infrared laser assisted photoionization of helium by a coherent extreme-ultraviolet light. The ionization process can be controlled by tuning the time delay between the two pulses.