Attosecond high-harmonic interferometry probes orbital- and band-dependent dipole phase in magnesium oxide

Abstract

Control over the spatial coherence, wavefront, and focusability of emitted light relies on understanding the intrinsic phase of the emission process, and vice versa, measuring phase can reveal insights about microscopic generation mechanisms. A thorough understanding of the origin of the dipole phase in solid-state high-harmonic generation is currently missing. Here, by employing attosecond interferometry with phase-locked XUV pulses, we directly assess the intensity- and frequency-dependent dipole phases in magnesium oxide (MgO) in solid-state HHG. We also quantify a nonlinear phase shift of the fundamental and disentangle its contribution from the dipole phase. Theoretical models (analytical, two-band, and full-band numerical simulations) support our results. The analytical approach aids future solid-state HHG experiments and simulations, while the full numerical model details orbital- and band-resolved current contributions to the dipole phase. Our research delivers the first combined quantitative measurement and rigorous theoretical description of the harmonic emission phase in solids.