Reduced density matrix description of high-harmonic generation in multi-electron atoms: exploring sub-cycle correlation effects

High-harmonic generation (HHG) is one of the fundamental processes at the heart of attosecond physics. Traditionally viewed as an effective single-particle effect, recent advances have focused on contributions beyond this single-particle picture to the harmonic spectrum, as well as on probing electron correlations through HHG in atoms, molecules, and solids. In this paper, we introduce a reduced density matrix description to explore and to quantify correlation effects on a sub-cycle time scale and apply this approach to prototypical multi-electron atoms. By comparing noble gas atoms (He, Ne) with alkaline earth atoms (Be, Mg) exposed to driving fields with similar Keldysh parameters, we show that the sub-cycle variation of correlation parameters differs markedly for noble gases and alkaline earth atoms. We provide an intuitive explanation of these surprising effects based on the dynamics of natural orbitals and discuss the effect of this ultrafast correlation dynamics on the HHG spectrum.