  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.
