Wave-packet manipulation of He Rydberg states by a seeded free-electron laser

We report a two-dimensional pump-control-probe spectroscopic study of the dynamics of singly excited He Rydberg-state wave packets with a seeded extreme ultraviolet (XUV) free-electron laser (FEL) source. A pair of coherent XUV pulses, defined by their coarse time separation and relative phase, created and manipulated the wave packets. The He atoms were postionized by infrared (IR) pulses, and the ion yield was measured as a function of XUV phase and IR arrival time. We tagged and sorted the relative phase of the XUV pulse pair on a single-shot basis by fitting each FEL spectrum with a suitable function that accounts for nonidealities of the XUV pulse pairs, associated with the seeding process; more generally, the fit returns the time-dependent electric field of the FEL spectra. The experimental two-dimensional maps of ion yields, measured as a function of IR (probe) delay and of XUV (pump-control) phase, were compared with the solution of the first-order time-dependent Schr & ouml;dinger equation for this field. Despite the fact that the experimental conditions imply strong excitation, beyond the approximations of first-order perturbation theory, the simulated map satisfactorily reproduces the experimental one for temporally well-separated pulses. We show that by selecting data at appropriate values of pump-control phase, we enhance or suppress the amplitude of chosen wave-packet components consisting of two or more Rydberg states. When the temporal overlap of the pulse pair cannot be neglected, the phase reconstruction is underdetermined, and we provide a simplified comparison between data and simulations.