Abstract
We consider the hydrogen atom exposed to an ultrashort laser pulse with a central frequency ranging from several hundreds of eV to 1.5 keV ( a.u.) and a peak intensity of . We study the excitation of the atom by stimulated Raman scattering, a process involving pairs of frequencies (). These frequencies are non-negligible components of the pulse Fourier transform and they satisfy the condition and being the ground-state and the excited-state energy, respectively. The numerical results obtained by integrating the time-dependent Schrödinger equation (TDSE) are compared with calculations in lowest order perturbation theory (LOPT). In LOPT we consider, in the second order of PT, the contribution of the term in the dipole approximation and, in first order of PT, the expression of taken for first-order retardation effects. ( denotes the vector potential of the field and is the momentum operator.) We focus on the Raman excitation of bound states with principal quantum numbers up to . The evaluation in perturbation theory of the contribution to and transition probabilities uses analytic expressions of the corresponding Kramers–Heisenberg matrix elements. At fixed pulse duration a.u. ( fs), we find that the retardation effects play an important role at high frequencies: they progressively diminish as the frequency decreases until the contribution of dominates over the contribution for values of a few a.u. We also study the dependence of the Raman process on the pulse duration for several values of . In the case where dipole and nondipole contributions are of the same order of magnitude, we present the Raman excitation probability as a function of the pulse duration for excited , and states.
- Received 19 October 2016
DOI:https://doi.org/10.1103/PhysRevA.95.023417
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