Enhancing and controlling single-atom high-harmonic generation spectra: a time-dependent density-functional scheme

High harmonic generation (HHG) provides a flexible framework for the development of coherent light sources in the extreme-ultraviolet and soft x-ray regimes. However it suffers from low conversion efficiencies as the control of the HHG spectral and temporal characteristics requires manipulating electron trajectories on attosecond time scale. The phase matching mechanism has been employed to selectively enhance specific quantum paths leading to HHG. A few important fundamental questions remain open, among those how much of the enhancement can be achieved by the single-emitter and what is the role of correlations (or the electronic structure) in the selectivity and control of HHG generation. Here we address those questions by examining computationally the possibility of optimizing the HHG spectrum of isolated Hydrogen and Helium atoms by shaping the slowly varying envelope of a 800 nm, 200-cycles long laser pulse. The spectra are computed with a fully quantum mechanical description, by explicitly computing the time-dependent dipole moment of the systems using a time-dependent density-functional approach (or the single-electron Schrödinger equation for the case of H), on top of a one-dimensional model. The sought optimization corresponds to the selective enhancement of single harmonics, which we find to be significant. This selectivity is entirely due to the single atom response, and not to any propagation or phasematching effect. Moreover, we see that the electronic correlation plays a role in the determining the degree of optimization that can be obtained.