  Second-order optical nonlinearities can be greatly enhanced by orders of
magnitude in resonantly excited nanostructures, theoretically predicted and
experimentally investigated in a variety of semiconductor systems. These
resonant nonlinearities continually attract attention, particularly in newly
discovered materials, but tend not to be as efficient as currently predicted.
This limits their exploitation in frequency conversion. Here, we present a
clear-cut theoretical and experimental demonstration that the second-order
nonlinear susceptibility can vary by orders of magnitude as a result of giant
cancellation effects in systems with many confined quantum states. Using
terahertz quantum cascade lasers as a model source to investigate interband and
intersubband resonant nonlinearities, we show that these giant cancellations
are a result of interfering second-order nonlinear contributions of light and
heavy hole states. As well as of importance to understand and engineer the
resonant optical properties of materials, this work can be employed as a new,
extremely sensitive tool to elucidate the bandstructure properties of complex
quantum well systems.
