Terahertz optical mixing in biased GaAs single quantum wells

The nonlinear mixing of near-infrared (NIR) and terahertz (THz) laser beams is investigated experimentally in a square $\mathrm{GaAs}$ quantum well structure, where the symmetry of the sample can be controlled by applying an electric field along the growth direction. The mixing produces sidebands, which appear at ${\ensuremath{\omega}}_{\text{sideband}}={\ensuremath{\omega}}_{\mathrm{NIR}}+n{\ensuremath{\omega}}_{\mathrm{THz}}$, where $n=\ifmmode\pm\else\textpm\fi{}1,2,\dots{}$. For a given $\mathrm{THz}$ frequency, the intensity of the $n=\ifmmode\pm\else\textpm\fi{}1$ sidebands displays two main resonances as a function of the NIR frequency. These resonances are separated by the $\mathrm{THz}$ frequency. Their intensity is found to depend strongly on the electric bias and on $\mathrm{THz}$ frequency. The $n=\ifmmode\pm\else\textpm\fi{}1$ sideband intensity is zero when the sample is unbiased and increases significantly with bias. The sideband is strong when the $\mathrm{THz}$ laser frequency is tuned in resonance with an intersubband transition and also at low $\mathrm{THz}$ frequencies. The main features of our results are explained qualitatively, except at very high $\mathrm{THz}$ intensities, by a perturbative model of the nonlinear susceptibility ${\ensuremath{\chi}}^{(\ensuremath{\mid}n\ensuremath{\mid}+1)}$. At high $\mathrm{THz}$ intensities, the resonances are observed to red shift and broaden.