Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations

Ultrafast charge transport in strongly biased semiconductors is at the heart of high-speed electronics, electro-optics and fundamental solid-state physics(1-13). Intense light pulses in the terahertz spectral range have opened fascinating vistas(14-21). Because terahertz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias(5,11,17,19). Novel quantum phenomena have been anticipated for terahertz amplitudes, reaching atomic field strengths(8-10). We exploit controlled (multi-)terahertz waveforms with peak fields of 72 MV cm(-1) to drive coherent interband polarization combined with dynamical Bloch oscillations in semiconducting gallium selenide. These dynamics entail the emission of phase-stable high-harmonic transients, covering the entire terahertz-to-visible spectral domain between 0.1 and 675 THz. Quantum interference of different ionization paths of accelerated charge carriers is controlled via the waveform of the driving field and explained by a quantum theory of inter- and intraband dynamics. Our results pave the way towards all-coherent terahertz-rate electronics.