Using a pump-probe scheme with controllable time-delay in the range of $0–73\mathrm{fs}$, we have solved from first principles the time-dependent Schrödinger equation (TDSE) describing a hyper-fast excitation process that involves both the discrete and the continuous spectrum of the three-electron atomic negative ion, ${\mathrm{He}}^{-}$. Two approaches were implemented, both using state-specific wave functions for two multiply excited discrete states (the initial state, ${\mathrm{He}}^{-}1s2s2p{}^{4}P^o$, and the final state, ${\mathrm{He}}^{-}2p^3{}^{4}S^o$), and one intermediate state which is a shape resonance (${\mathrm{He}}^{-}1s2p^2{}^{4}P$, including the underlying continuum of scattering states. The wavelengths of the two pulses connecting resonantly the states are in the infrared $\left(10080\mathrm{\AA }\right)$ and in the soft x-ray region $\left(323\mathrm{\AA }\right)$. The first approach is analytic and solves the TDSE to first order in perturbation theory. This is acceptable for weak pulses whose duration is of the order of a few tens of femtoseconds. The second approach solves the TDSE nonperturbatively, via the state-specific expansion approach. A series of computations have produced time-dependent probabilities for preparing the triply excited bound state ${\mathrm{He}}^{-}2p^3{}^{4}S^o$ for various combinations of the duration of the two pulses. Apart from providing the first such quantitative data, the results suggest the appearance of effects of short-time nonexponential decay of resonances when it becomes possible to monitor excitation with time-delayed short pulses.

• Received 25 October 2007

DOI:https://doi.org/10.1103/PhysRevA.77.013412