Driving semiconductor quantum wells with terahertz electric fields strong enough to overcome the Coulomb attraction between bound electron-hole pairs leads to high-order sideband generation (HSG). In HSG, excitons are optically-injected into quantum wells by a weak near-infrared (NIR) laser while simultaneously being illuminated with a terahertz field from the UCSB Free Electron Laser. The phenomenon can be described by the so-called "three step model" developed in high-field atomic physics: (1) the electron and hole tunnel-ionize in the strong field, (2) the now-free particles accelerate in the field, and (3) they recollide, emitting a photon. The two lasers are continuous, so the emitted photons are sidebands on the NIR laser. Because of the large gain of kinetic energy before recollision, an HSG spectrum has a broad bandwidth with many more sidebands above the NIR frequency than below. The largest spectra span over one hundred nanometers, with over 100th order sidebands above and 20th order below.

The electron and hole must remain coherent throughout their trajectories, which can last hundreds of femtoseconds and extend for more than fifty nanometers, if they are to recollide. Sidebands have been observed that result from recollisions with kinetic energies far above the threshold for optical phonon emission. These high orders persist up to room temperature. Not even quenched disorder in the quantum wells strongly attenuates the HSG signal.

Because of this coherence, the electron and hole are very sensitive to the complete band structure of the material. Excitation by linear NIR polarization creates both the electron and hole in a superposition of spin-up and spin-down states with complex coefficients given by the relative orientation of the NIR polarization and the THz polarization. Interference between these the spin-up and spin-down particles, particularly in the valence band and mediated by non-Abelian Berry curvature, has large effects on both the intensity and polarization state of the sidebands. The connection between HSG and complete band structure points to the possibility of directly measuring both the band dispersion relations as well as the non-Abelian Berry curvature of the host material.