Observation of light driven band structure via multi-band high harmonic spectroscopy

Intense light-matter interactions have revolutionized our ability to probe and manipulate quantum systems at sub-femtosecond time scales, opening routes to all-optical control of electronic currents in solids at petahertz rates. Such control typically requires electric field amplitudes $\sim V/\AA$, when the voltage drop across a lattice site becomes comparable to the characteristic band gap energies. In this regime, intense light-matter interaction induces significant modifications of electronic and optical properties, dramatically modifying the crystal band structure. Yet, identifying and characterizing such modifications remains an outstanding problem. As the oscillating electric field changes within the driving field's cycle, does the band-structure follow, and how can it be defined? Here we address this fundamental question, proposing all-optical spectroscopy to probe laser-induced closing of the band-gap between adjacent conduction bands. Our work reveals the link between nonlinear light matter interactions in strongly driven crystals and the sub-cycle modifications in their effective band structure.