Interferometry of dipole phase in high harmonics from solids

Understanding the temporal profiles of high harmonics is essential for their applications in attosecond science1,2. Microscopically, the dipole phase plays an important role in determining the high-harmonic emission phase2–4. In gas-phase high-harmonic generation, the tunnel-ionized electron spends much of its travel time in the continuum—far from the parent ion, where it accumulates the dipole phase5,6. Therefore, the atomic dipole phase is largely independent of the target atom3. In solid-state high-harmonic generation7–11, since the driven electron experiences a periodic potential during the entire travel time, the dipole phase may depend on the electronic structures of source materials9,12–14. Here, we employ an interferometric method to characterize high harmonics from magnesium oxide and quartz crystals. We measure material-dependent intensity-induced high-harmonic phase delays that we attribute to the intensity-induced changes in the dipole phase originating from the interband polarization10,15,16. The material-dependent dipole phase can provide a robust platform for high-harmonic spectroscopy of solids. An interferometric homodyne method is employed to measure material-dependent intensity-induced phase shifts of extreme-ultraviolet high harmonics emerging from bulk magnesium oxide and quartz crystals, providing a robust platform for high-harmonic spectroscopy of solids.