Effects of the Coulomb interaction on intersubband doubling and difference-frequency mixing in asymmetric double quantum wells

We study theoretically the influence of the direct and indirect Coulomb interaction on second-harmonic generation (SHG) and difference-frequency generation (DFG) connected with intersubband transitions in asymmetric double quantum wells. Our approach is based on the time-dependent local density approximation. The exact analytical expressions have been derived for SHG (in a two-subband system) and DFG (in a three-subband system) surface susceptibilities. Unlike in our previous papers, we take into account the nonresonant terms and nonlinear dependence of the exchange-correlation potential upon the electron density. Numerical calculations have been performed for GaAl/AlGaAs asymmetric coupled double-quantum-well structures with small energy separation (about 10 meV) between the ground and excited subband when the effect of the Coulomb interaction is most pronounced and the nonresonant terms become essential. The results obtained show that Coulomb interaction not only shifts the peak positions in SHG and DFG spectra, but also modifies their height. The height modification can be particularly strong (even more than one order of magnitude) in the case of the SHG. The nonlinearity of the exchange-correlation potential is found to lead to a novel feature that cannot be ignored in a correct description of SHG and DFG spectra. The electron-density dependence of the many-body effect is analysed. A critical comparison of the results obtained with those reported in the literature is also given. (author)