Limitations of the single-active-electron approximation in quantum simulations of solid high-order harmonic generation

Abstract

We investigate the limitations of the single-electron time-dependent Schr\"odinger equation (TDSE) in the studies of solid high-order harmonic generation (HHG). Two main differences are found by comparing the harmonic spectra calculated by TDSE and semiconductor Bloch equations (SBEs) in the same conditions. One is that the spectrum obtained from SBEs only contains clear odd harmonics, but that derived from TDSE consists of even and odd harmonics. The other is that the two approaches derive different linear dependence of cutoff energy on electric strength and wavelengths of laser fields. These discrepancies can be attributed to the single-active-electron approximation used in TDSE. Moreover, we find that the phase mismatching between the dipole interaction and the intrinsic dynamical phase of the system is responsible for the generation of even harmonics in the single-active-electron approximation. Finally, an approach is proposed to expand the applicable range of TDSE further. Our results demonstrate that many-body effects must be taken into account in solid HHG simulations, though the Coulomb interaction between electrons can be neglected in some cases.