Stimulated Raman scattering in hydrogen by ultrashort laser pulse in the keV regime

This letter addresses the problem of stimulated Raman excitation of a hydrogen atom submitted to an ultrashort and intense laser pulse in the keV regime. The pulse central frequency ω of 55 a.u. (about 1.5 keV) is in the weakly relativistic regime, $\omega \leq c/a_0$ (c is the speed of light in vacuum and a0 the Bohr radius) and the pulse duration is τ ≈ 18.85 a.u. (about 456 attoseconds). We solve the corresponding time-dependent Schrödinger equation (TDSE) using a spectral approach, retardation (or nondipole) effects are included up to $O(1/c)$ , breaking the conservation of the magnetic quantum number m and forcing the resolution of the TDSE in a three-dimensional space. Due to the laser bandwidth, which is of the order of the ionization potential of hydrogen, stimulated Raman scattering populates nlm excited states (n and l are the principal and azimuthal quantum numbers, respectively). The populations of these excited states are calculated and analyzed in terms of l and m quantum numbers, this showing the contributions of the retardation effects and their relative importance