Three-Step Model for High-Harmonic Generation in Many-Electron Systems

The three-step model (TSM) of high-harmonic generation (HHG) is generalized to atomic and molecular many-electron systems. Using many-body perturbation theory, corrections to the standard TSM due to exchange and electron-electron correlations are derived. It is shown that canonical Hartree-Fock orbitals represent the most appropriate set of one-electron states for calculating the HHG spectrum. To zeroth order in many-body perturbation theory, a HHG experiment allows direct access, in general, to a combination of occupied Hartree-Fock orbitals rather than to the highest occupied molecular orbital by itself.

Figure 1

HHG spectrum for the Hamiltonian (21) with $V_{\mathrm{HS}}$ corresponding to argon. $E(t)=E_0\sin \omega t$, where $\omega =0.057\mathrm{a}.\mathrm{u}.$ corresponding to a 800 nm laser, and $E_0=0.12\mathrm{a}.\mathrm{u}.$ The spectrum was extracted after one laser cycle. The dotted line and the thin solid line were obtained from a numerical solution of the TDSE with and without projecting out the states below $3p$ at every step. The dashed and the thick lines were obtained using the TSM, with Eqs. (1, 22), respectively.