Attosecond control of solid-state high harmonic generation using ω-3ω fields

Abstract: High harmonic spectra generated in condensed matter carry the fingerprints of sub-cycle electronic motion and the energy structure of the studied system. Here we show that tailoring the waveform of mid-infrared driving light by using a coherent combination with its third harmonic frequency allows to control the time of electron tunneling to the conduction band within each half-cycle of the fundamental wave with attosecond precision. We introduce an experimental scheme in which we simultaneously monitor the modulation of amplitude and emission delays of high harmonic radiation and the excited electron population generated in crystalline silicon as a function of the relative phase between the $\omega$-3$\omega$ fields. We observe that the mutual $\omega$-3$\omega$ phase required for the maximum yield of high harmonic generation is shifted by approximately $\pi/2$ with respect to the phase leading to maximal generated carrier population. The observed emission delays of high harmonic photons of up to few hundred attoseconds scale with the time delay and with the ratio between the electric field amplitudes of the two-color fields. These results reveal the connection between electron tunneling and high harmonic emission processes in solids.