Open-system density-matrix approach to image-potential dynamics of electrons at Cu(100): Energy- and time-resolved two-photon photoemission spectra

Dynamical simulations of femtosecond two-photon photoemission spectra of image potential states on a clean Cu(100) surface are presented. A realistic one-electron potential by Chulkov, Silkin, and Echenique [Surf. Sci. 437, 330 (1999)] is employed together with a mapped Fourier grid Hamiltonian method to accurately determine bound continuum, image potential, and free continuum states. The wave functions are used to determine the lifetimes of image potential states, and the dipole matrix elements for the laser pump and probe transitions. A multistate open-system density-matrix approach is adopted to model the pump-probe process including energy and phase relaxation. In contrast to previous work no scaling laws are assumed for any input parameters, a discretized continuum of final states is used to allow for final-state energy resolution, and image states with high quantum numbers n (up to $n=15)$ are considered. Very good agreement between theory and experiment is obtained.