Ab initiotime-dependent density-functional-theory study of the frequency comb structure, coherence, and dephasing of multielectron systems in the vuv-xuv regimes via high-order harmonic generation

Abstract

We present an ab initio nonperturbative investigation of the frequency comb structure and coherence within each order of the high-order harmonic generation (HHG) of rare-gas atoms by means of the time-dependent density-functional theory (TDDFT) with optimized effective potential (OEP) and self-interaction correction (SIC). The $\text{TDDFT}+\text{OEP}\ensuremath{-}\text{SIC}$ equations are solved accurately and efficiently by means of the time-dependent generalized pseudospectral technique. We found that a nested comb structure appears within each order of the harmonics, ranging from the first harmonic all the way to the cutoff region. We explore in detail the temporal coherence and robustness of the comb structure by varying the laser-pulse separation $\ensuremath{\tau}$, the number of pulses $N$, the phase difference between pulses $\ensuremath{\Delta}\ensuremath{\phi}$, and the laser intensity. The frequency comb structure and coherence are preserved in each harmonic regardless of the values of $\ensuremath{\tau}$ and $N$ used for the case of weak and medium strong incident laser-pulse trains. The time-frequency characteristics of the HHG coherence structure are analyzed in details by means of the wavelet transform of the time-dependent induced dipoles. The interference modulation can be attributed to the constant phase relationship of harmonics among successive pulses. However, under superstrong fields, nonuniform and substantial ionization takes place during each pulse, jeopardizing the temporal coherence of the emitted frequency comb modes. Finally, we found that the dynamical electron correlation, which is included in the present $\text{TDDFT}+\text{OEP}\ensuremath{-}\text{SIC}$ treatment but not in the single-active-electron model, is significant for the quantitative exploration of the frequency comb structure and coherence of higher harmonics.