  Electrodynamical processes induced in complex systems like semiconductors by
strong electromagnetic fields, have traditionally/conventionally been described
using semi-classical approaches. Although these approaches, allowed the
investigation of ultrafast dynamics in solids culminating in multi-petahertz
electronics, they do not provide any access in the quantum optical nature of
the interaction as they treat the driving-field classically and unaffected by
the interaction. Here, using a full quantum-optical approach, we demonstrate
that the sub-cycle electronic response in a strongly driven semiconductor
crystal is imprinted in the quantum-state of the driving-field resulting in
non-classical light-states carrying the information of the interaction. This
vital step towards strong-field ultrafast quantum electrodynamics unravels
information inaccessible by conventional approaches and leads to the
development of a new class non-classical light sources.
