The effective description of some quantum mechanical systems, far from a classical correspondence, can be nonlinear. Strongly driven THz intersubband transitions in AlGaAs/GaAs quantum wells are a good example of such a system and have been shown to exhibit novel nonlinear phenomena. Many-body effects which cause the nonlinearities become much more prominent in wide quantum wells (300 Angstrom) where intersubband spacing is of the order of 10 meV which is approximately that of the electron-electron Coulomb interactions. The main signature of the nonlinearities is the dynamic shielding by the electron gas of the incoming radiation. The screening blue shifts the absorption peak frequency, by an amount proportional to the intersubband population difference and sheet density, to the dressed frequency at which collective oscillations of the entire electron gas occur. This depolarization shift also causes the generation of second-harmonics (super-harmonics) of the drive frequency when it is at half of the dressed frequency.

Multisubband semiconductor Bloch equations are derived to study the effect of many-body interactions on the collective response of confined electrons in doped quantum well (QW) heterostructures to intense far-infrared radiation. For a two-subband system optical bistability is observed and its parameter range is given. For an asymmetrical three-subband QW interference phenomena occur near the resonances. The quantum wells when driven at the difference between the ground and second subband energy undergo first a period-doubling bifurcation, producing a sub-harmonic of the frequency of the drive. At a stronger amplitude of the drive a Hopf bifurcation occurs which generate a strong response at a frequency incommensurate with the drive frequency or any natural frequency of the system.