  In a semiconductor illuminated by a strong terahertz field, optically excited
electron-hole pairs can recombine to emit light in a broad frequency comb
evenly spaced by twice the terahertz frequency. Such high-order terahertz
sideband generation is of interest both as an example of extreme nonlinear
optics and also as a method for ultrafast electro-optical modulation. So far,
this phenomenon has only been observed with large field strengths (~10 kVcm-1),
an obstacle for technological applications. Here we predict that bi-layer
graphene generates high-order sidebands at much weaker terahertz fields. We
find that a terahertz field of strength 1 kVcm-1 can produce a high-sideband
spectrum of about 30 THz, 100 times broader than in GaAs. The sidebands are
generated despite the absence of classical collisions, with the quantum
coherence of the electron-hole pairs enabling recombination. These remarkable
features lower the barrier to desktop electro-optical modulation at terahertz
frequencies, facilitating ultrafast optical communications.
