Laser picoscopy of valence electrons in solids.

Valence electrons contribute a small fraction of the total electron density of materials, but they determine their essential chemical, electronic and optical properties. Strong laser fields can probe electrons in valence orbitals1-3 and their dynamics4-6 in the gas phase. Previous laser studies of solids have associated high-harmonic emission7-12 with the spatial arrangement of atoms in the crystal lattice13,14 and have used terahertz fields to probe interatomic potential forces15. Yet the direct, picometre-scale imaging of valence electrons in solids has remained challenging. Here we show that intense optical fields interacting with crystalline solids could enable the imaging of valence electrons at the picometre scale. An intense laser field with a strength that is comparable to the fields keeping the valence electrons bound in crystals can induce quasi-free electron motion. The harmonics of the laser field emerging from the nonlinear scattering of the valence electrons by the crystal potential contain the critical information that enables picometre-scale, real-space mapping of the valence electron structure. We used high harmonics to reconstruct images of the valence potential and electron density in crystalline magnesium fluoride and calcium fluoride with a spatial resolution of about 26 picometres. Picometre-scale imaging of valence electrons could enable direct probing of the chemical, electronic, optical and topological properties of materials.