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 physics1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Intense light pulses in the terahertz spectral range have opened fascinating vistas14, 15, 16, 17, 18, 19, 20, 21. Because terahertz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias5, 11, 17, 19. Novel quantum phenomena have been anticipated for terahertz amplitudes, reaching atomic field strengths8, 9, 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