Sub-cycle quantum electrodynamics in strongly laser-driven semiconductors

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.