Numerical simulation of time delays in light-induced ionization

We apply a fundamental definition of time delay, as the difference between the time a particle spends within a finite region of a potential and the time a free particle spends in the same region, to determine results for photoionization of an electron by an extreme ultraviolet laser field using numerical simulations on a grid. Our numerical results are in good agreement with those of the Wigner-Smith time delay, obtained as the derivative of the phase shift of the scattering wave packet with respect to its energy, for the short-range Yukawa potential. In the case of the Coulomb potential we obtain time delays for any finite region, while—as expected—the results do not converge as the size of the region increases towards infinity. The impact of an ultrashort near-infrared probe pulse on the time delay introduced here is analyzed for both the Yukawa and the Coulomb potential and is found to be small for intensities below 1013 W/cm2.