Quantum coherence induced second plateau in high-sideband generation

Optically excited electron-hole pairs, driven by a strong terahertz (THz) field, create high-sidebands in the optical spectrum. The sideband spectrum exhibits a 'plateau' up to a cutoff of 3.17Up, where Up is the ponderomotive energy. This cutoff is determined, semi-classically, from the maximum kinetic energy an electron-hole pair can gain from the THz field along a closed trajectory. A full quantum treatment reveals a second, classically forbidden, plateau with a cutoff of 8Up, the maximum kinetic energy an electron-hole pair can gain from the THz field along an open trajectory. The second plateau appears because a spatially separated electron and hole can still recombine if the classical excursion is within the coherence length of the electron-hole wavefunction or, equivalently, the coherence time is longer than the excursion time (half the THz field period). This effect broadens the range of materials and excitation conditions where high-sideband generations can occur, thereby providing a wealth of novel systems for ultrafast electro-optical applications.