Near-infrared sideband generation induced by intense far-infrared radiation in GaAs quantum wells

GaAs quantum wells are simultaneously illuminated with near-infrared (NIR) radiation at frequency ${\omega }_{\mathrm{nir}}$ and intense far-infrared (FIR) radiation from a free-electron laser at ${\omega }_{\mathrm{fir}}.$ Magnetic fields up to 9 T are applied. Strong and narrow sidebands are observed at ${\omega }_{\mathrm{sideband}}{\mathrm{=\omega }}_{\mathrm{nir}}{\text{±2ω}}_{\mathrm{fir}}.$ The intensity of the sidebands is enhanced when either ${\omega }_{\mathrm{sideband}}$ or ${\omega }_{\mathrm{nir}}$ is near the onset of NIR absorption in the quantum well, or when ${\omega }_{\mathrm{fir}}$ is near the free-electron cyclotron frequency. We attribute these sidebands to four-wave mixing of NIR and FIR photons whose energies differ by more than a factor of 100.