Phase-Locked Multi-THz High-Harmonic Generation by Dynamical Bloch Oscillations in Bulk Semiconductors

Abstract

Bloch oscillations are among the most spectacular quantum manifestations of electrons in crystalline solids. When an electric field accelerates an electron, its wavelength shortens. Once the latter equals twice the lattice constant, the wave should undergo Bragg reflection, causing electrons to oscillate in reciprocal and real space [F. Bloch, Z. Phys. 52, 555–600 (1928); C. Zener, Proc. R. Soc. A 137, 696–702 (1932)]. Ultrafast carrier scattering and dielectric breakdown under constant-field biasing have hampered the experimental observation of this long-standing prediction in bulk crystals [C. Zener, Proc. R. Soc. A 137, 696–702 (1932)]. Recently, high-harmonic generation has been attributed to a dynamical version of Bloch oscillations [S. Ghimire et al., Nature Phys. 7, 138–141 (2010)]. Controlling the precise shape of the optical fields, however, has been out of reach due to the fluctuating carrier-envelope phase (CEP) of the laser pulses. Novel developments in field-resolved multi-terahertz optics provide low-frequency CEP-stable electromagnetic waveforms, which serve as a sub-cycle bias for high-field experiments [A. Sell et al., Opt. Lett. 33, 2767–2769 (2008); F. Junginger et al., Phys. Rev. Lett. 109, 147403 (2012)]. Here, we employ atomically strong and phase-locked multi-THz fields to control all-coherent charge transport in gallium selenide (GaSe) on femtosecond timescales. Off-resonantly driven coherent interband polarization and dynamical Bloch oscillations result in the emission of phase-stable high-order harmonics (HH) covering the frequency range from 0.1 to 675 THz [O. Schubert et al., Nature Photon. 8, 119-123 (2014)].