Attosecond control in solids with high-order wavemixing

Recently, many of the tools from strong-field physics have been adpated to study solids with great success, however, there remains an unexplored potential for using two-color fields to control attosecond processes in condensed matter. Here, we use the gas-phase technique of two-color non-collinear high-harmonic generation (HHG) to isolate the high-order wavemixing pathways in solids. A strong ultrashort pulse and its weak second harmonic are coincident with a small separation angle on an MgO surface. The resulting HHG consists of a series of angularly dispersed beams, where the angle and energy of each harmonic can be used to index the underlying photon mixing pathway. We observe bright extreme-ultraviolet wavemixing peaks with generation efficiencies that can exceed that of the single-color HHG, showing that high-order wavemixing is an excellent control mechanism for solid-state HHG. To gain further insight, we develop a quantum theory within the strong-field approximation that explains how the different pathways are isolated in the far field, demonstrates the origin of their perturbative scaling, and outlines the selection rules governing the diffraction pattern. In this theory, the full HHG dipole arises from the quantum interference of the different pathways, suggesting that two-color HHG can be generally framed as coherent control of high-order wavemixing. Our work shows how high-order wavemixing will be a useful tool to probe and control attosecond processes in condensed matter. For example, we discuss how non-collinear HHG can provide a new window into dephasing or enable all-optical solid-state XUV optics.