\textit{Ab initio} exploration of the frequency comb structure and coherence in high-order harmonics of multi-electron systems driven by a sequence of ultrashort laser pulses

We present an \textit{ab initio }nonpertubative investigation of the frequency comb structure and coherence within each order of the high harmonic generation (HHG) of rare gas atoms by means of the self-interaction-free time dependent density functional theory (TDDFT). The time-dependent exchange-correlation potential is constructed by means of the time dependent optimized effective potential (TDOEP) method. The TDOEP equations are solved accurately and efficiently by means of the time-dependent generalized pseudospectral technique. We explore in detail the temporal coherence and robustness of the comb structure by varying the laser pulse duration $t$, the number of pulses $N$, and the laser intensity. We found that a nested comb structure appears within each order of the harmonics, ranging from the first harmonic all the way to the cut-off harmonic, and this global pattern persists regardless of the values of $t$ and $N$ used, and even in the presence of substantial ionization.